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Studying mathematics opens up a multitude of possible career pathways as well as encouraging you to think deeply and meta-cognitively about its underlying principles.

Meet the Team:

We have 3 full time staff in our mathematics department:

Ms J Bradbury (curriculum leader) - A Level maths/ further maths

Mr P Brockway - A Level maths / further maths/ core maths

Mr Sam Bates - A level maths

For further information about mathematics at TSFA, please contact the curriculum leader, Ms Bradbury, using

jbradbury@sixth.trinitymat.org

contactus@sixth.trinitymat.org

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Another interesting introduction; this time to Matrices by Paul Chillingworth

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Taster lesson on Further Mathematics: Matrices

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This lesson provides an introduction to the Further Mathematics topic of matrices. There is a short video to watch on the first slide followed by some activities for students.

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Give yourself a head-start with this excellent online lesson!

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Taster lesson on Further Mathematics: Complex numbers

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This activity provides an introduction to the A level Further Mathematics topic of complex numbers. There is a short video to watch on the first slide followed by some activities for students.

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Feel free to email me if you would like to see the solutions!

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Each activity has an uploaded video of me starting an investigation for you to continue...
This one is called Brackets In/Brackets Out.

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Activity 1: - Make a conjecture (Video assistant)

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Activity 1: - Make a conjecture (Video assistant)

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Brackets Out Brackets In (RISPS investigation for GCSE/A Level Maths or Further Maths)

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Activity 2: Simultaneous Magic(?) - Video assistant

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Activity 2: Simultaneous Magic(?) - Video assistant

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Arithmetic Simultaneous Equations (RISPS 8) Investigation GCSE A Level Maths Further Mathematics

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Activity 2:  What is an arithmetic sequence? Here we look at solving simultaneous equations whose coefficients come directly from such a sequence. What do you notice?

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Activity 2:  What is an arithmetic sequence? Here we look at solving simultaneous equations whose coefficients come directly from such a sequence. What do you notice?

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Activity 3: The Gold and Silver Cuboid - Video Assistant

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Activity 3: The Gold and Silver Cuboid - Video Assistant

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Activity 3: The Gold and Silver Cuboid. 

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Activity 3: The Gold and Silver Cuboid. 

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What links a cubic to a cuboid? Explore more here...

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Activity 4: Tangent through the Origin - Video assistant

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Activity 4: Tangent through the Origin - Video assistant

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Some practice at using Desmos and looking for links between a curve and a line. What will you notice? Can you prove it?

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Tangent at the Origin (Risps 5) Investigation for GCSE A Level Maths

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This is not a RISP, but a multiple choice question from a Senior UKMT paper. The film X+Y was about UKMT challenges and features a young Otis from Netflix's S*x Education facing similar problems...  How could we turn this into a richer problem? Maybe if the points weren't midpoints...

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Trachette Jackson works in Mathematical Oncology, that's the study of cancer. Why would oncology need Maths? Find out here.

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Oncology, the study of cancer, is just one of many specialisms which increasingly employs the predictive power of applied mathematics. This issue we chat with Trachette Jackson, professor of mathematics at the University of Michigan, to learn about the surprising effectiveness of mathematics in the treatment of cancer, as well as to hear about her own journey into mathematical oncology.

Modelling in medicine

Trachette starts by bringing us up to date on how mathematics has been used in cancer treatment. "The mathematical approach has been applied to just about every aspect of tumour growth, starting decades ago." One aspect is cancer therapeutics: "We write down equations that describe the mechanism of action of new drugs and how the tumour responds, then make predictions about how best to deliver those drugs." Another aspect is more fundamentally biological, such as how cells are transformed: "You can find mathematical equations about the probabilities of acquiring mutations and under what circumstances a tumour forms, as well as what the composition of that tumour will be and how many cells in that tumour will have these different mutations." This sort of modelling allows us to diagnose or assess the risk of cancer developing, as well as treat it.

Trachette starts by bringing us up to date on how mathematics has been used in cancer treatment. "Mathematical approaches have been applied to just about every aspect of tumour growth, starting decades ago." One aspect is cancer therapeutics: "We write down equations that describe the mechanism of action of new drugs and how the tumour responds, then make predictions about how best to deliver those drugs." Another aspect is more fundamentally biological, such as how cells are transformed: "You can find mathematical equations describing the probabilities of acquiring mutations and under what circumstances a tumour forms, as well as what the composition of that tumour will be and how many cells in that tumour will have these different mutations." This sort of modelling allows us to diagnose or assess the risk of cancer developing, as well as treat it.

Trachette's recently published paper, on the modelling of a drug targeting a chemical needed by cancerous tumours to grow, demonstrates the value of mathematical modelling. "We built a mathematical model that could look at the cross-talk between tumour cells and endothelial cells that secrete the chemical, then used it to predict responses of the tumour to this new treatment, along with traditional chemotherapy." The model predicted something unexpected-administering the two drugs at the same time, as suggested by experimentalists, "would give you the worst results possible. Instead, the model predicted that fortnightly injections of chemotherapy along with continuous weekly administration of low amounts of targeted drugs would lead to synergistic responses."

Could these same achievements have been made without the models? "I think the answer is probably yes. But it would be very expensive, and it would take a lot longer. What does math do? It speeds it up, and it saves the lives of millions of mice these drugs are tested on." We were happy to hear, then, that mathematics is fundamentally better than biology and will soon be replacing it entirely. But Trachette kept us grounded by reminding us that it goes both ways. In fact, it is through her collaboration with experimentalists that she decides where to focus her attention. "They're the ones who know what the big questions in cancer biology are, and which problems they would love answers to; those they think mathematical modelling might help them address."

We couldn't hold in the burning question any longer-what kind of maths are we talking about here? "I mainly use differential equations, both ordinary and partial, and sometimes delay differential equations." In a delay differential equation, the derivative at a certain time is given in terms of the value of the independent variable at previous times. "I also use hybrid models, which are methods that combine continuous differential equations with a discrete approach, to answer questions that look at the interplay between something that diffuses like a chemical, the biochemistry, with the biomechanics, like a cell actually moving on tissue structures."

Instead of having a blanket regime for every type of cancer, we really start looking at what to do for individual patients.

So, it all boils down to solving differential equations. Should be easy enough? "I'm talking about systems of non-linear differential equations, so we're past the point of pen and paper analysis. We have to go to the computer and run simulations." But that doesn't stop Trachette from having fun. "Sometimes, we can do some model reduction to get the system in a form where we can say something about it analytically, but often the systems I work with require solving numerically."

In the future, she expects to see big improvements in how patients' data is used in mathematical modelling, in what is called 'personalised medicine'. "When a patient is diagnosed with cancer, they're put through a battery of tests that gives information about the molecular details of that cancer. We need much more of that data collected, and we need to be able to use all the information clinically available: from a specific person's genetics, to the way that their body processes these drugs. Instead of having a blanket regime for every type of cancer, we really start looking at what to do for individual patients."

A leopard can change its spots

Trachette credits her parents for fostering her love of learning. "They really stressed the importance of education. They let me know that learning is fun, it's OK to be a smart girl, and it's OK to be a girl who is good at math." She moved around a lot as a child, because her father was in the US air force, but she eventually settled in Arizona where she went to high school and became interested in mathematics. She went to a local university to take classes in the summer, and this is where she met her first maths professor. "He didn't look anything like I thought a math professor would look. I was shocked that a normal looking person could be a mathematician. He became a very big role model."

They let me know that learning is fun, it's OK to be a smart girl, and it's OK to be a girl who is good at math.

This professor helped to point her in the right direction when she went on to study for her degree at this same university. Initially, she wasn't studying maths. "Believe it or not, I was an engineering major. I quickly learned I didn't like engineering, so he called me into his office and said you should be a math major." She took the advice, but at first chose pure maths, studying "nothing applied at all".

It took a second role model to show her what applied mathematics can do and to inspire her to go into mathematical biology. James Murray, a pioneer in the field of mathematical biology, came to her university and gave a talk about how leopards get their spots. "I thought, 'This does not belong in the math department! How is math going to have anything to do with leopards and spots?' But I went to the talk, and...my mind was blown."

James Murray later became her PhD advisor. At the time, she didn't understand all the mathematics in his talk, but she took away what turned out to be a much more important message. "I understood that math can play a role in science, in biology, in medical science, and developmental biology, and I had never seen that before. That was when I knew I wanted to be an applied mathematician, because I saw real benefit of math in those areas. I wanted to be like this person I saw giving this talk."

Dreaming of the future

Our conversation turns onto the topic of diversity in academia. Trachette hopes that today's young women can be inspired the way she was to consider mathematics. She says she is a "big fan" of recent initiatives to get more women interested in mathematics and has a lot of praise for the Association of Women in Mathematics in the US and their networking schemes, saying they are "just amazing". She says they have communities where "women can find like-minded women in their own areas and form networks". She is also very impressed by their mentoring programmes, which enable women to "find women at higher career stages, so they can ask those difficult questions through all the critical transitions in your career. Sometimes it feels a little isolating to be a woman in math. And this is a way to get, even at undergraduate level, connected to women."

There needs to be proponents of diversity in each department to try to locally start changing the culture to be more welcoming and inclusive.

Trachette is very passionate about increasing opportunities in mathematics for people of colour. "Being an African-American mathematician at a research institution is very rare, and I want to change that demographic." This is why she "started a programme to help underrepresented minorities progress through the pipeline. I think it's very important to support the movement of diverse people through the PhD and beyond, so that we actually change the face of the professoriate."

Trachette takes lots of opportunities to be a visible role model in her career, for example by appearing in Power in Numbers by Talitha Williams, which tells the stories of over 30 women's journeys through maths. You can find Chalkdust's review here.

She sees two approaches to improving diversity in universities. First, there is the "top-down" approach, involving national level organisations. "I know these big societies have diversity, equity, and inclusion committees, and are aware of the problem. The mathematical community often looks to these societies, so it trickles down." But change can also be from the bottom-up, and it is important that more effort is made to make these kinds of improvements. "There needs to be proponents of diversity in each department to try to locally start changing the culture to be more welcoming and inclusive, and to take seriously the issue of recruiting a diverse graduate student body and faculty. I think the mathematical community really needs a deep dive into where we are and how we got here and what we can do change it."

She seems positive about the future, and her closing message about the next generation of female mathematicians is very inspiring. "I hope they will blossom and find networks of other people to work with and find mentors at all levels. I hope that they find people to give them good advice, and to advocate for them, so they can eventually be agents of change."

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In conversation with Trachette Jackson - Chalkdust

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Oncology, the study of cancer, is just one of many specialisms which increasingly employs the predictive power of applied mathematics. This issue we chat with Trachette Jackson, professor of mathematics at the University of Michigan, to learn about the surprising effectiveness of mathematics in the treatment of cancer, as well as to hear about her own journey into mathematical oncology.

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A brief introduction to partitioning numbers and a chance to practice your recording and notation.

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Activity 7: There are 204 squares on a chess board. Or are there? 

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Activity 7: There are 204 squares on a chess board. Or are there? 

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Prove that there are 204 squares on a chess board.
What patterns do you spot along the way? Can you work out how many squares there will be in a 9x9 board?
How about an 8x9 one?

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A parabola and a straight line.
Change the coefficients using the sliders. What if... a=0? b=0 etc..
What if a<0, b<0 etc...
How are the coefficients linked? What do you notice about the relationship between the line and the curve?

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Here are 2 simple proofs for you to have a go at. They'll test your knowledge of surds, ratio and pythagoras.

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Let's go fly a kite (A4 Origami + Maths) Surds, Ratio and Proof

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What is it showing? Do you recognise the graph? How is it created?
What is the same/different about tan(20) and tan(-20)?
For which angles is inverse tan greater than 1? Why is this?

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This challenge is all about a special triangle.

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Triangle of 1s (Pascal's Triangle challenge)

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Hans Rosling is (was) a superstar. His website, GapMinder, has applications to geography, economics, history, biology... and of course maths.
Here he showing the power of data, something that we are all too aware of watching the pandemic spread.

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Close

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Here is the PDF to accompany this activity's video.

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John Conway died of Coronavirus in April 2020. He's one of the most well know mathematicians of this century.

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He made profound contributions to number theory, coding theory, probability theory, topology, algebra and more - and created games from it all. He died of the coronavirus.

John Horton Conway in his office at Princeton University in 1993. He "was a magical mathematician," a colleague said. Credit... Dith Pran/The New York Times

This obituary is part of a series about people who have died in the coronavirus pandemic. Read about others here.

His wife, Diana Conway, said his death, at a nursing home, was caused by Covid-19.

Dr. Conway's boundless curiosity produced profound contributions to number theory, game theory, coding theory, group theory, knot theory, topology, probability theory, algebra, analysis, combinatorics and more. Foremost, he considered himself a classical geometer.

"His swath was probably broader than anyone who ever lived," said the mathematician Neil Sloane, a collaborator with Dr. Conway and the founder of the On-Line Encyclopedia of Integer Sequences. "I've worked with a lot of people, and he was the fastest at solving a problem and would pursue a topic as far as it would go." (The two were co-authors of 50 papers and published the 706-page book "Sphere Packings, Lattices and Groups.")

His friend Martin Gardner, the longtime mathematical games columnist for Scientific American, called the Game of Life Dr. Conway's "most famous brainchild." He reckoned that at the game's peak of popularity - with users programming it at home and at work - one quarter of the world's computers were playing it.

Hired at Cambridge as an assistant lecturer, Dr. Conway gained a reputation for his high jinks (not to mention his disheveled appearance). Lecturing on symmetry and the Platonic solids, he might bring in a turnip as a prop, carving it one slice at a time into, say, an icosahedron, with its 20 triangular faces, eating the scraps as he went. "He was by far the most charismatic lecturer in the faculty," his Cambridge colleague Peter Swinnerton-Dyer once said.

His first two marriages, to Eileen Howe and Larissa Queen, ended in divorce.

In addition to his wife, he is survived by four daughters from his first marriage, Annie, Ellie and Susie Conway and Rosie Wayman; two sons from his second marriage, Oliver and Alex; a son with Ms. Conway, Gareth; three grandchildren; and six great-grandchildren.

And there were ever more games of Phutball, which Dr. Conway was not very good at. Sometimes, when all seemed lost - when he was almost certainly beaten at his own game, though he might yet magically prevail - he'd delight in borrowing from Mark Twain, admonishing his opponents, "Reports of my death have been greatly exaggerated!"

Siobhan Roberts is the author of "Genius at Play: The Curious Mind of John Horton Conway" (2015).

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John Horton Conway, a 'Magical Genius' in Math, Dies at 82

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He made profound contributions to number theory, coding theory, probability theory, topology, algebra and more - and created games from it all. He died of the coronavirus. This obituary is part of a series about people who have died in the coronavirus pandemic. Read about others here .

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Press play. Watch the bubbles sink, grow, shoot up or shrink. What is going on? Look at the axes. What happens in WW1? WW2? What will happen for 2020? Can you track your favourite country, how does it compare to other countries?

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Animated global statistics that everyone can understand

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Alex Bellos wrote a book called Alex's Adventures in Numberland. It's great! Every week he presents us with 3 problems in the Guardian newspaper for free. Here is this week's. Keep your eye on them in the holidays. The solutions are always posted online too.

The three directors of a bank are deeply suspicious of one another, and agree a system of locks and keys for the bank’s safe, such that:

No single director can open the safe alone.

Any two directors can open the safe by pooling their keys.

What is the smallest number of locks and keys they need to open the safe, and how do they distribute them?

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My puzzle book So You Think You've Got Problems is out in paperback this week. Here are three problems from it. The first is about a vase, the second is about a leg, and third is about a set of keys.
1. With two straight line cuts, divide the vase into three pieces that can be reassembled to form a square.

Note: we're working in 2 dimensions. You need to cut this shape into three pieces that can be reassembled with no overlaps or gaps.
2. Which single word can be placed in each of the eight marked spaces to make eight meaningful sentences? _ I kicked him in the leg yesterday. I _ kicked him in the leg yesterday. I kicked _ him in the leg yesterday. I kicked him _ in the leg yesterday. I kicked him in _ the leg yesterday. I kicked him in the _ leg yesterday. I kicked him in the leg _ yesterday. I kicked him in the leg yesterday _. 3. The three directors of a bank are deeply suspicious of one another, and agree a system of locks and keys for the bank's safe, such that: What is the smallest number of locks and keys they need to open the safe, and how do they distribute them?
I'll be back with the answers at 5pm UK.

Meanwhile, NO SPOILERS!
UPDATE: You can now read the solutions here. I set a puzzle here every two weeks on a Monday. I'm always on the look-out for great puzzles. If you would like to suggest one, email me.

So You Think You've Got Problems is a book of puzzles and word games for all abilities. The paperback is out on Thursday, but you can preorder it here at The Guardian Bookstore.

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My puzzle book So You Think You've Got Problems is out in paperback this week. Here are three problems from it. The first is about a vase, the second is about a leg, and third is about a set of keys. 1.

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What is a parabola? Is there only one way of drawing them?

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Hannah Fry is a celebrity mathematician (if you'll allow such a thing) who is regularly called upon for BBC programmes. She has written books about the Maths of Christmas, monopoly and the future. Here is a lecture aimed at children, but thoroughly engaging. Look out for her books on Amazon, we'll try and get some for the library.

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Christmas Lectures 2019: How to Get Lucky - Hannah Fry

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We celebrate Florence Nightingale's 200th birthday this year. She understood the power of diagrams over tables to show strong connections and trends. This short article tells you a bit about her work in the Crimean War.

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When you're in a medical emergency, you don't typically think of calling a statistician. However, the COVID-19 outbreak has shown just how necessary a clear understanding of data and modelling is to help prevent the spread of disease.

One person understood this a long time ago. Were she alive today, Florence Nightingale would understand the importance of data in dealing with a public health emergency.

Nightingale is renowned for her career in nursing, but less well known for her pioneering work in medical statistics. But it was actually her statistical skills that led to Nightingale saving many more lives.

Read more: Florence Nightingale: a pioneer of hand washing and hygiene for health

An early spark

Nightingale was one of the first female statisticians. She developed an early passion for statistics. As a child she collected shells and supplemented her collection with tables and lists. Nightingale was home-schooled by her father but insisted on learning maths from a mathematician before she trained as a nurse.

Wikimedia Commons

Upon arriving at the British military hospital in Turkey in 1856, Nightingale was horrified at the hospital's conditions and a lack of clear hospital records.

Even the number of deaths was not recorded accurately. She soon discovered three different death registers existed, each giving a completely different account of the deaths among the soldiers. Using her statistical skills, Nightingale set to work to introduce new guidelines on how to record sickness and mortality across military hospitals.

This helped her better understand both the numbers and causes of deaths. Now, worldwide, there are similar standards for recording diseases, such as the International Classification of Diseases.

Outbreak monitoring

The ability to compare datasets from different places is critical to understanding outbreaks. One of the challenges in monitoring the COVID-19 pandemic has been the lack of standardised datasets experts can compare on the number of people infected. This is due to differences in testing rules in different countries.

More than 150 years after Nightingale pointed out the need to standardise datasets before comparing them, we are certain she would have something to say about this.

Read more: From election upsets to climate chaos, rolling the dice helps us appreciate the odds

With her improved data, Nightingale put her statistical skills to use. She discovered deaths due to disease were more than seven times the number of deaths due to combat, because of unsanitary hospital conditions.

However, knowing numbers alone have limited persuasive powers, Nightingale used her skills in statistical communication to convince the British parliament of the need to act. She avoided the dry tables used by most statisticians of the time, and instead devised a novel graph to illustrate the impact of hospital and nursing practice reform on army mortality rates.

Wikimedia/commons

Today, graphs remain one of the most effective ways to understand the effects of health care interventions, including those used to illustrate the effectiveness of physical distancing to curb COVID-19's spread.

Florence Nightingale down under

Nightingale may not have travelled much after her wartime experience in Turkey, but she was engaged in improving public health in many countries, including Australia.

She wrote papers on the benefits of pavilion-style hospital building designs, which were later incorporated into Australian hospitals. This style consists of small wings, or pavilions, leading off a central corridor - this is convenient for nursing staff and encourages good ventilation.

In 1868, Lucy Osburn headed the first team of nurses sent to Australia to establish Nightingale-style nursing. One of the team's first tasks was to nurse Prince Alfred, Queen Victoria's second son, who had been shot in an attempted assassination.

Nightingale never visited Australia herself, but this did not stop her using her usual tactics of requesting data from her wide network of contacts and drawing conclusions from what she found. She was a prolific correspondent - we have more than 12,000 of her letters, and those are only the ones which haven't been burned, lost or otherwise destroyed.

Nightingale would surely have embraced 21st-century communication. We can imagine her sitting at her laptop tweeting under the moniker @ladywiththelamp.

A trailblazer for women

In 1858, Nightingale's achievements in statistics were recognised by the Royal Statistical Society in the UK, when she became the first woman Fellow of the Society.

After Nightingale's fellowship, it would be more than 100 years before a woman was elected President of the Royal Statistical Society, with Stella Cunliffe's election in 1975. It was only in 1995 that the Statistical Society of Australia had a woman as president, with the election of Helen MacGillivray.

As in many STEM (Science, Technology, Engineering and Mathematics) disciplines, female statisticians are still fighting for equal recognition. To date, only two women have received the Statistical Society of Australia's highest honour, the Pitman Medal.

But it's clear female statisticians are still making headway. In 2019, five major statistical associations had women presidents. Today, on her 200th birthday, Nightingale would have been proud.

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The healing power of data: Florence Nightingale's true legacy

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When you're in a medical emergency, you don't typically think of calling a statistician. However, the COVID-19 outbreak has shown just how necessary a clear understanding of data and modelling is to help prevent the spread of disease. One person understood this a long time ago.

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Podcast -Stop working, lie down and put this in your ears.
It's a weekly podcast about numbers in the news, and will encourage you to question any interpretation data you are given by the media.

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More or Less - Vitamin D, explaining R and the 2 meter rule - BBC Sounds

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Catch up on your favourite BBC radio show from your favourite DJ right here, whenever you like. Listen without limits with BBC Sounds.

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Something completely new for me...
Viviani's theorem: From any point within an equilateral triangle, the sum of the perpendicular distances to the three sides is equal to the height of the triangle.

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Rob Eastaway was booked to come into school before C-19 kicked off. He loves a good puzzle - here he looks at a classic and expands it further than you'd think you ever could!

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There aren't many puzzles that became famous as a corporate cliche, but the nine dots problem is certainly one of them.

There are nine dots arranged in a square, and your challenge is to join all the dots using only four straight line strokes of a pen, and with your pen never leaving the paper. No tricks are needed, no folding the paper and no using an ultra-fat pen. You'll have no problem finding a solution with five lines, but in the unlikely event that you've never seen this puzzle before, four lines might prove to be a struggle.

The puzzle first rose to notoriety when Sam Loyd included it in his 1914 cyclopedia of puzzles. He called it the Columbus egg puzzle, after an apocryphal story about Christopher Columbus challenging his colleagues to get a boiled egg to stand on its end - a challenge that seemed impossible until Columbus crushed the base of the egg and rested it on its now flat bottom. Easy when you know how.

The solution to the nine dot puzzle led to the cliche of 'thinking outside the box' (that's a massive clue to the solution, but if you still can't find the answer, you'll find it at the bottom of the article). The solution is a useful metaphor for the challenge of problem solving, when we often become restricted by constraints of our own making. Deliberately challenging your assumptions and allowing yourself to be 'silly', at least for a short period, can be a handy strategy for creative problem solving in all walks of life.

What I find interesting, however, is that the lessons of the nine dots puzzle are often quickly forgotten when the puzzle is modified.

The 16 dots problem

Take the 16 dots problem. It's exactly the same idea, but this time instead of using four straight lines, you are allowed to use six straight lines.

Can you find a solution? And if you want a proper challenge, can you find a solution that nobody else is likely to find? I strongly encourage you at this point to have a go at the 16 dots problem, and allow yourself at least ten minutes on it before returning to this article, because there are spoilers aplenty coming up.

Warning: the rest of the article contains spoilers for this puzzle. Please have a go at the puzzle before reading on...

How did you get on? If you gave the puzzle a serious go, then you probably did find a solution. Take a look at your attempts. Of course, you allowed yourself to go outside the box this time, but what angles did your lines go at? The majority of solvers try lines that go horizontally, vertically, or at a $45^{\circ}$ angle. They do this because (a) that's the pattern they've seen already, and (b) those are the most 'efficient' lines to take out dots. A diagonal line can take out up to four dots, whereas a line at a different angle will take out two dots at most.

If you took the $45^{\circ}$ approach, then most likely your solution looked like one of these two:

Both solutions are just extensions of the 9 dot solution. When it comes to categorising solutions, however, these two are in the same family. If you extend all of the lines off the page, you can see the two solutions use the same set of lines.

Are there other solutions, that don't belong to this family? Yes there are. But to find them, you have to overcome the self-imposed constraint of 90 and 45 degree angles. And to stand out from the crowd, you also have to allow yourself to think further outside the box. Literally.

If you allow one line to go at a more jaunty angle, you'll get some interesting solutions (below, left). But if you really begin to let your hair down, you can find even more zany solutions (below, right):

If we call the distance between two horizontal dots one unit, notice how the right-hand solution has at one point travelled three units outside the box before turning back - that's one whole box width beyond the boundary of the dots. Which might make you wonder, are there any solutions that push even further outside the box? And, happy days, yes there are! For example, this one to the right has gone four units, or 133%, outside the box.

I believe that's the furthest you can get out of the box when solving the $4\times4$ puzzle, but I know that for the $7 \times7$ square
there is at least one solution that is 183% out of the box. For larger $N \times N$ squares there are surely solutions that go more than
200% out of the box - but nobody (yet) knows how big $N$ has to be for this to be possible.

Symmetrical solutions

Some of the solutions to the 16 dot puzzle look a bit messy, but out of mess sometimes comes beauty. It was only by exploring messy solutions that I found these four symmetrical beauties:

To my knowledge, this is the first time the 'Chubby pentagram' solution has ever been published, and possibly the first time that the words chubby and pentagram have been used in the same sentence.

Inside the box

I sometimes wonder if we give too much credit to thinking outside the box, while down-playing the importance of less glamorous inside-the-box thinking. Sometimes in life we have no choice but to think inside the box we've been given. So let's apply this thinking to dot puzzles. We've seen that for the nine dot puzzle there is no solution with four lines that are all inside the box, though a solution with five lines is possible, for example on the left here.

In fact by continuing this spiral outwards, we can see that for the $N \times N$ square there will always be a solution inside the box, as long as you are allowed $2N - 1$ lines. But what if you can only use $2N-2$ lines (so, six lines for the $4\times4$, eight lines for the $5\times5$ etc). No such inside-the-box solution is possible for the $4\times4$ dot puzzle, but if we take our old friend The Archbishop's hat and extend it, it's easy to find an eight line inside-box solution to the $5\times5$ puzzle, which we can then spiral outwards for larger $N \times N$.

So we've shown that for the $N \times N$ puzzle (where $N \geq 2$), not only is there always a solution that uses $2N -2$ lines, but for $N \geq 4$ there is also always at least one solution that is inside the box.

Dot puzzle theorems
For an $N \times N$ square of dots:
There exists at least one solution inside the box using $2N-1$ lines, for all $N$.
There exists at least one solution using $2N-2$ lines for all $N\geq2$.
There exists at least one $2N-2$ solution that is inside the box for all $N\geq4$.

The dot puzzle conjecture

Without bending the rules, or bending the paper, there's no solution to the 9 dot puzzle using three lines. Nor is there any known solution to the 16 dot puzzle using five lines. In fact there is a conjecture, not yet proved as far as I know, that there does not exist any solution to the $N \times N$ puzzle that uses $2N-3$ lines. There may not be a million-dollar prize on offer, but there's still some kudos to whoever comes up with the proof.

And finally...

There is one solution to the 16 dot puzzle that stands above all others. It's the only solution that has two lines of symmetry and the only one with rotational symmetry. It also starts and finishes at the same point, with no dot having more than one line passing through it.

Here it is. For its elegance and the fact that it's two intertwined zigzags, I call this solution DNA.

The solution to the nine dots problem

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Thinking outside outside the box - Chalkdust

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There aren't many puzzles that became famous as a corporate cliche, but the nine dots problem is certainly one of them. There are nine dots arranged in a square, and your challenge is to join all the dots using only four straight line strokes of a pen, and with your pen never leaving the paper.

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A Viral Sudoku video? 3 million views?! People are glued for the whole 25 minutes
Yup! It's lockdown. You'll watch anything.
Now I don't think Sudoku is doing maths- but the amount of reasoning and logic this guy uses shows us otherwise.

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Ying Yang, how two opposite forces can come together for unity. Good and bad, happy and sad, sine and cosine.
Watch ONE LINE. Compare it with another line. What's going on?

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In A-Level, Maths, one of the elements is mechanics- the study of how objects interact with each other and move. Throw a ball, what's the curve? Throw a shuttlecock... what's the curve now?

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Shuttlecocks used for badminton are not like other projectiles found in sports. They are extremely asymmetrical, with a conical skirt about 6cm long and 6cm across that is attached to a cork of higher density at the narrow end of the cone. However, when the shuttlecock is hit it will quickly flip over so that the cork is leading because its pressure centre if different to its centre of mass. This will ensure that it is always approaching your opponent the right way round for her to hit it back.

The effect of hitting the shuttlecock is strange. When you hit a tennis ball or a cricket ball with a racquet or bat it goes further the harder you hit it. But no matter how hard you hit the shuttlecock it won't go much further than about 6 or 7 metres.

The trajectory of a shuttlecock, moving from left to right: it falls steeper than it rises.

The motion of the shuttlecock obeys Newton's laws of motion. Its acceleration is governed by the downward force of gravity and a drag force from the air that is proportional to the square of the shuttlecock's speed through the air. When it is first struck the shuttlecock is moving at its fastest and the drag force is therefore much bigger than gravity. So it moves upwards in a straight line, at an angle determined by the direction of impact from the racquet, gradually being decelerated by gravity. Eventually it is going so slowly that the force of gravity is comparable to the air drag force and the trajectory reaches a maximum height and curves downwards towards the ground. Gravity is now speeding it up and it quickly reaches a speed, termed the terminal speed, where the opposing forces of gravity (downwards) and air drag (upwards) become equal. There is now no net force on the shuttlecock and it moves downwards at this constant terminal speed, without experiencing any acceleration or deceleration. The overall trajectory doesn't look like a parabola: the shuttlecock falls steeper than it rises.

The terminal speed does not depend on the initial launch speed of the shuttlecock. It is determined by the strength of gravity, air density, the size and mass of the shuttlecock, and its smoothness. As a result it is these unchanging properties that fix the distance that the shuttlecock will reach when struck hard. Hitting it even harder can't make it go any further than these properties dictate.

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Shuttlecocks used for badminton are not like other projectiles found in sports. They are extremely asymmetrical, with a conical skirt about 6cm long and 6cm across that is attached to a cork of higher density at the narrow end of the cone.

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Simple pleasure for half term. Donald Duck explores the Maths around us in this sweet 30 minutes cartoon.

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Here's a magical lake- when you place an object in the lake, the object picks up it's own reflection and makes a fractal.
#notagif

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This is called Pascal's Triangle.  Can you see how it if formed? What patterns can you spot?
Extend the triangle yourself to see if you can spot some more.

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"I didn't feel the segregation at NASA, because everybody was doing research, everybody had a mission and you worked on it."

There are plenty of mathematically rich maths films available to watch. One of the most recent is Hidden Figures (2015), about a group of black women working for NASA. Highly recommended. Katherine Johnson is one of the women protrayed in the film, there are many interviews with her, this is one of the best.

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What Matters - Katherine Johnson: NASA Pioneer and "Computer"

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Dr Nira Chamberlain is credited one of the UK's top 100 scientists. Besides his scientific prowess, he is also an advocate for black mathematicians. In this article he has collected his Black Heroes of Maths. Thomas Fuller stands out for me for highlighting the absurdity of the assumed intellectual superiority that white people believed to have over black people in the 1700s.

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As part of Black History Month, Dr Nira Chamberlain has produced a presentation which celebrates black mathematicians from history.

"As Black people we have had more than our share of the academically hereditary disaffection all people seem to experience relative to mathematics...Nowadays our promising youth are even more menacingly threatened by exposure to teachers...who have been convinced that Blacks...are abysmally and irrevocably hopeless as far as mathematics is concerned."

Dr Wade Ellis Sr: 1980 (1909-1989)
10 th African-American to gain a PhD in Mathematics

Francis William: 1702 - 1770, Jamaican Mathematician

Mathematics Degree -Cambridge University

Background

Francis Williams was selected to take part in a social experiment devised by the Duke of Montagu who wished to show that black individuals - with the right education - could match the intellectual achievements of whites.

Challenge

A rival once suggested-"The abstruse problems of mathematical institution turned his brain; and he still remains, I believe, an unfortunate example, to show that every African head is not adapted by nature to such profound contemplations."

Achievements

Degree in Mathematics, Latin and Literature from Cambridge University. He returned to Jamaica to set up a school, teaching Mathematics, Latin, Reading and Writing.

Thomas Fuller 1710 - 1790, Slave and Mathematician

Extraordinary powers of calculation

Background

Thomas Fuller , known as the Virginia Calculator, was kidnapped from his native Africa at the age of fourteen and sold to a planter.

Challenge

He was regularly tested. On being asked, " How many seconds a man has lived who is 70 years, 17 days and 12 hours old?" He answered in a minute and a half 2 210 500 800. One of his examiners who was using pen and paper, advise him his answer
was incorrect! The sum was not so great as he had suggested. Upon which Thomas hastily replied: "Stop, you forget all the
leap years! " On adding the amount of the seconds for the leap years, the total in both their sums agreed exactly.

Achievements

Later in his life was he was discovered by antislavery campaigners, who used him as a role model to demonstrate that blacks were not mentally inferior to whites.

Benjamin Banneker: 1731 - 1806, Astronomer and Civil Rights Leader

The sky was not his limit

Background

Benjamin Banneker was a largely self-educated mathematician, astronomer and first civil rights leader.

Challenge

He would exchanged letters with the soon to be Third U.S. President Thomas Jefferson, whom had stated that negroes are inferior to whites when it comes to high level of mathematical thinking.

Achievements

Banneker was the first scientist to study the relativity of time and space, and his revelations on the topic preceded Einstein's
Theory of Relativity by two centuries. He successfully predicted the solar eclipse that occurred on April 14, 1789, contradicting the forecasts of prominent mathematicians and astronomers of the day. Banneker was the first to disclose in his writings that the Star of Sirius is two stars rather than one. His hypothesis was not confirmed until the event of the Hubble Telescope two and a half centuries later at NASA.

Elbert Cox : 1895 - 1969, 1st Black Mathematics PhD

The Pioneer

Background

After fighting for his country in World War I , Elbert Cox, applied for a PhD program. One of his referees wrote " He would have
certain difficulties, because of the fact, he is of the coloured race."

Challenge

Universities in England and Germany would not recognise his PhD at the time. However, Japan's Imperial University of San
Dei accepted the dissertation.

Achievements

In 1929, became the first Black Mathematician in the world to gain a PhD in Mathematics. From 1929-1961, he taught at
Howard, an Historically Black College and University. Inspiring generations of Black Mathematicians to obtain a PhD

: 1890 - 1980, 1st Black Female Mathematics PhD Euphemia Lofton Haynes

Background

Euphemia Lofton Haynes faced three obstacles in becoming a PhD mathematician. She was female, she was Black and she was in her 50's.

In 1940 the Cambridge Mathematician G.H. Hardy, wrote A Mathematician's Apology , one of the most widely read books about the nature and practice of mathematics. It stated: "No mathematician should ever allow himself to forget that mathematics, more than any other art or science, is a young man's game."

Achievements

Three years after Hardy's book, Euphemia Lofton Haynes completed her PhD in Mathematics. She was living proof that you are never too old and that mathematics is not just for the few, it is for everybody

Further Reading:

Article by Dr Nira Chamberlain

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The Black Heroes of Mathematics - Maths Careers

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As part of Black History Month, Dr Nira Chamberlain has produced a presentation which celebrates black mathematicians from history. "As Black people we have had more than our share of the academically hereditary disaffection all people seem to experience relative to mathematics...Nowadays our promising youth are even more menacingly threatened by exposure to teachers...who have been convinced that Blacks...are abysmally and irrevocably hopeless as far as mathematics is concerned."

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We have returned to schools in small bundles of people- this article looks at the geometrical impossibilities of some of the rules we have to adhere to.

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Here's another article that tries to show some calculations but ends up being distant from the genuine mathematics. And the source data is, in some ways, even funnier.

This blog starts with a filleted version of the article.(The link is provided so you can see the whole thing, but none of the mathematical info has been removed from my version.)

Plans to reopen shops in England 'in chaos' over social distancing rules

High street retailers must give each shopper a minimum of 10 sq metres of space if they are to maintain social distancing rules, a new study has found, prompting businesses to complain that a lack of official guidance has left reopening plans in chaos.

With 10 days to go until most non-essential shops reopen in England, a research paper by Manchester Metropolitan and Cardiff univeristies has concluded that larger shops must allow substantially more than a 2-metre radius for each person so that they can move freely.

The study finds that people need 10 sq metres in smaller shops, 11 sq metres in larger shops, and 12 sq metres in outdoor spaces where they move more rapidly. That is up to three times as much space as the 2-metre radius required when people are stationary.

The report's conclusions are based on the speed and unpredictability of people's movements, which means they are much more likely to get near each other when shopping than when queuing or sitting at a desk - and therefore require a bigger "halo".

Chris Turner, the chief executive of British BIDs - the representative group for Business Improvement Districts - said the report showed that maintaining a 2-metre distance was "hugely problematic".

"There's a real sense that the government is making it up as it goes along," he said.

Each person is in a circle, radius 1 metre. So the area is π m ²

Suggesting 4-sq-metres is therefore a bit strange.

That is, however, the area of a square with each person at its centre.The square would be of side 2m.Maybe they assumed it was a square?Maybe they have rounded up (despite pi being closer to 3 than to 4)?

OK - now let's look at the next diagram:

There's no explanation here as to why each person now needs to be in a circle with a radius of 1.75 metres. This gives, apparently, an area of 11-sq-metres.

Well a circle of radius 1.75m has an area of about 9.6m ², which doesn't round up to give 11, so that theory was wrong.If this were a square for each person then it would have sides of 3.5m, which dives an area of 12.25m ², which isn't 11 either.

Starting with the sensible part:

The research paper points out that when people move around a shop they can't stay exactly 2m away from everyone else.We see this at traffic lights.If you are four or five cars back when the lights turn green, you can't immediately start moving forwards.The first car moves, then the second driver reacts to that movement, then the third car responds a little later, and it is possible that the lights have turned red again before the tenth car has even started moving.In a shop, if one person stops to browse, or moves towards a display, those around are all affected and need to respond.To account for this the authors of the paper suggest a bigger circle is needed.And they go for a circle of radius 1.75m (more on this later).

The paper points out that circles don't tessellate, so they use a 'square tessellation'. When arranged in this square formation, the total area divided by the total number of people gives an area of 4m ² per person.

[Two diagrams (fig 4 and fig 6) from the paper.]

On the same diagrams I have shown the tessellations:

Later in the paper they mention the hexagonal tessellation.Let's try that out with a circle of radius 1.75m

The hexagon goes around the edge of the circle, so the 'height' of the shaded triangle is 1.75m.The base is therefore 2 x 1.75 x tan30.When we work out the area of this triangle and multiply by 6 (to find the area of the hexagon), we get an answer of 10.6088112 m ².Aha - that rounds off to 11 - and is presumably where that figure came from!

What a shame that the article doesn't explain this, and what a shame their diagrams are so unclear.

But, I mentioned there are ridiculous things in the report as well.

Here is a quote from the report:

In square or rectangular tessellations, the density of the circles is 0.7854 (Williams, 1979, p. 49). In other words, 78.5% of the space can be utilised.

Based on a square tessellation, in fixed space each person will require a space of π(r) ²/0.7894m ² (3.9797m ² when r = 1m) for the square or rectangular tessellation.

What is going on here?The diagram shows the scenario, where a circle of radius 1 is inside a square, which clearly has sides of length 2.The area of the circle is π, and the area of the square is 4, so the fraction of the area of the square that is taken up by circle is π ÷ 4 = 0.7853981634...

The book they are quoting uses a rounded version of this value (0.7854) , which is where the figure of 78.5% of the space being filled comes from.

Unfortunately, having written the correct rounded value of 0.7854 in the previous sentence, they then miscopy that in their calculations and divide the area of the circle by 0.78 9 4 instead, which gives 0.979722135, and they have correctly rounded this off to 3.9797.

We set the value of x, the radius of the inner circle giving freedom of movement, as walking speed / stopping time.

It should be speed multiplied by stopping time.

This then gives them different areas required for different sizes of shop, because people walk at different speeds in smaller shops compared to larger ones and therefore the stopping distance is different.

What now with this?

Unfortunately, this is another reason not to trust the maths you see being used in the newspaper.Rather disappointingly, there were basic errors in the news article (which didn't explain the whole square and hexagon thing), and in the university report it was based on, which included multiple ridiculous things.

Perhaps worth using with a class to point out the folly of applying a formula when you don't need to, and the danger of rounding off too early?

Given how much of this is just twaddle, it seems appropriate to end with the last line of the original article:
"There's a real sense that the government is making it up as it goes along," he said.

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Here's another article that tries to show some calculations but ends up being distant from the genuine mathematics. And the source data is, in some ways, even funnier. This blog starts with a filleted version of the article.(The link is provided so you can see the whole thing, but none of the mathematical info has been removed from my version.)

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The art of empty space is highly mathematical

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Matt Parker is a Stand Up Mathematician. He travels around the world visiting schools, train stations with a Platform 0 and wobbly bridges. Watch his Google Talk about repercussions of mathematical mistakes.

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The Greatest Maths Mistakes | Matt Parker | Talks at Google

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Can chickens count? They seem to know when one of their little chicks is missing...What about Bees? What maths do they know?

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Bees are able to grasp basic mathematical ideas, according to a new study, which suggests a small brain may not mean low intelligence.

After training a group of the pollinating insects scientists at the French National Centre for Scientific Research found they were able to perform addition and subtraction.

These abilities require animals to carry out intricate processes in their brains, remembering complex rules while applying them to new situations.

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Sharing the full story, not just the headlines

Maths was therefore long thought an ability unique to humans, but in recent years experiments have shown the skill is found across the animal kingdom.

Chimpanzees, parrots and pigeons are just some of the creatures that have demonstrated the capacity to add and subtract.

In the new study, a team led by Dr Scarlett Howard, first taught their bees to recognise colours as symbols for either addition or subtraction. Specifically, blue meant "more" and yellow meant "less".

Next, their bees were trained to enter Y-shaped mazes in which they had to make a choice between two sets of shapes.

In each case, if they made the correct choice they were rewarded with a sugar water treat, whereas the wrong choice would yield a bitter-tasting quinine liquid.

At the entrance to the maze, the bees were met with between one and five shapes, coloured either blue or yellow.

Next they flew into a chamber where they could fly towards either the original number of shapes, plus or minus one, or the incorrect number of shapes.

No hype, just the advice and analysis you need

If they first encountered blue they had to add, and if yellow they had to subtract.

Over the course of 100 trials, the researchers trained 14 bees to choose the correct option around 75 per cent of the time, the scientists wrote as they published their findings in the journal Science Advances.

Dr Howard compared the experiments to humans first learning to link mathematical symbols with concepts.

"We learn as children that a plus symbol means you need to add two or more quantities, while a minus symbol means you subtract," she said.

Professor Adrian Dyer, who contributed to the study, added: "Our findings suggest that advanced numerical cognition may be found much more widely in nature among non-human animals than previously suspected. If maths doesn't require a massive brain, there might also be new ways for us to incorporate interactions of both long-term rules and working memory into designs to improve rapid AI learning of new problems."

This is not the first time bees have demonstrated a way with numbers.

Previous experiments have shown the insects are capable of counting to four, and even understand the concept of zero.

Work conducted by Dr Howard and her team showed that when bees were incentivised to choose a target with fewer shapes, they recognised that a target with no shapes had fewer than one with two or three.

This was the first time an invertebrate had been shown to understand the abstract idea of zero - a concept even humans find more difficult to appreciate than other numbers.

While the ability to undertake these kind of calculations may not be immediately useful for bees, advanced brain power may help them when foraging for flowers to remember different combinations of colours and shapes.

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Bees are able to understand mathematics, study reveals

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Bees are able to grasp basic mathematical ideas, according to a new study, which suggests a small brain may not mean low intelligence. After training a group of the pollinating insects scientists at the French National Centre for Scientific Research found they were able to perform addition and subtraction.

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What does the GIF below prove? Is it an acceptable proof? Can you find any other ways of proving the same thing?

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Guess Who? Here's a short video on how to win. You'll be doing a statistics module in Further Maths - winning is all to do with stats! Unfortunately so is losing!

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BEST Guess Who Strategy- 96% WIN record using MATH

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This is like something out of a film. . . .  Murderer solves ancient problem in prison!
*We do not consider prison as an alternative education to 6th Form college!

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dw.com 1 day ago Alexander Freund (tj)
A convicted murderer in a US prison has taught himself the basics of higher mathematics, enabling him to solve a complicated arithmetic problem. And he has been passing on his math passion to his fellow inmates.

If Hollywood had made up this story, you would think: "Well, that's pretty far-fetched. Cheesy. All a bit overblown." But, as we know, reality can be stranger than fiction.

For a long time, however, reality was very hard for Christopher Havens from the United States. The 40-year-old has been in prison near Seattle for nine years after being convicted of murder. Havens dropped out of school, went off the rails, couldn't find a job and became a drug addict. He was sentenced to 25 years in prison for the murder and still has 16 to go.
Read more:The math in music: Why numbers don't rule the universe
But in prison, Havens' life changed when he discovered his passion for math. He taught himself the basics of higher mathematics, which was not easy to do because the prison wardens intercepted the books he had ordered by mail. Havens was allowed to have the textbooks only after he had agreed to teach math to other prisoners as well.

After a while, basic higher mathematics was not enough for him. Havens sent a short handwritten letter to a mathematical publisher and asked for some issues of the Annals of Mathematics, a renowned journal in the field.

He wrote that numbers had become his "mission" and that he had decided to use his time in prison for self-improvement. However, he lamented in the letter, he had no one with whom he could discuss complex mathematical topics.
Read more: Women are less visible in STEM: Why?
An editor at Mathematica Science Publisher sent the letter on to his partner, Marta Cerruti, who in her turn forwarded it to her father, the mathematics professor Umberto Cerruti from Turin.

He was initially skeptical, but as a favor to his daughter he wrote an answer to Havens and gave the prisoner in Seattle a problem to solve to test his abilities.

Marta Cerruti, an associate professor for materials engineering at McGill University in Montreal, Canada, has described how Havens' unusual story went on in an article for the website "The Conversation."
Read more: Autistic people are attractive employees
After some time, Umberto Cerruti in Turin received the answer by mail: a 120-centimeter-long (47-inch-long) piece of paper with an incredibly long formula written on it. Cerruti first had to enter the formula in his computer to check what the prisoner had sent him: Havens had solved the tasks correctly. The Turin mathematics professor then invited Havens to help him with an ancient math problem that Cerruti himself had been trying to solve for a long time.

Using only pen and paper, Havens tinkered for a while with the problem from number theory involving so-called continued fractions, over which the ancient Greek mathematician Euclid had already racked his brains.

A continued fraction is - to put it simply - a mixed fraction in which the denominator once more has the form of a mixed fraction, with this structure continuing towards infinity. The fractions are thus linked together. However, continued fractions are not used for simple arithmetic, but to solve the approximation problems with which one approaches a result in complex calculations.

This number theory is used, for example, in modern cryptography, which is of decisive importance today in banking and finance and in military communications. And indeed: Havens cracked the age-old math puzzle and for the first time found some regularities in the approximation of a large class of numbers.

Cerruti helped Havens to formulate the proof in a scientifically correct manner, and a few months later, in January 2020, the two of them published it in the journal Research in Number Theory.

This was already quite an achievement. But the prisoner Havens not only cracked an ancient problem of mathematics: He also managed to inspire a group of fellow prisoners for the world of numbers through his passion. A regular math club has since been formed at the prison.
Read more:US professor first woman to win 'Nobel for math'
Among other things, Havens celebrates March 14 every year with the 14 fellow prisoners in the club as "Pi Day," named after the well-known mathematical constant often approximated as 3.14. Umberto Cerruti from Turin was also able to take part in one of these unusual celebrations under the strictest security measures. The professor was also impressed by a prisoner who recited the first 461 decimal places of pi by heart, as he wrote in an article entitled "Pi Day behind bars - Doing mathematics in prison" in the journal Math Horizons.

During the 16 remaining years of his prison sentence, Havens wants to go on to study other mathematical topics. He feels that doing mathematics is a way for him to pay his "debt to society," according to Marta Cerruti, who has held several conversations with the prisoner. After his time in prison, Havens wants to study the subject officially, she says.

And perhaps his unusual life story will really have been turned into a Hollywood film by then.

Author: Alexander Freund (tj)

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Murderer solves ancient math problem and finds his mission

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dw.com 1 day ago Alexander Freund (tj) A convicted murderer in a US prison has taught himself the basics of higher mathematics, enabling him to solve a complicated arithmetic problem. And he has been passing on his math passion to his fellow inmates. If Hollywood had made up this story, you would think: "Well, that's pretty far-fetched.

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Keeping the quadratic theme... What's going on here? Have you used Algebra tiles before?

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Completing the square and graphs. MathCentre was made in Leeds to help A Level students. The videos are simple, accessible and … dare I say it, relaxing.
Explore the site to find more to help you catch up.

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Advice to a Young Mathematician by Michael Atiya, a Lebanese mathematician.
You're all young mathematicians. Read it. Take his advice.

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Mathematical Things to Do!
An amazing list of things you could do to top up your maths learning.

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Image by congerdesign from Pixabay

If you find yourself at a loose end this month, want a break from focusing on work, or have younger mathematicians to entertain, here are some suggestions for online activities you can do/watch/attend. If you have any suggestions of your own, add them in the comments!

Here on the Aperiodical

Elsewhere online

Events this month

Tags: events, interactive, maths, online, podcasts, things to do, videos

About the author

Publicly engaging mathematician, Sheffield Hallam Uni part-timer, Manchester MathsJam organiser, hairdo.

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If you find yourself at a loose end this month, want a break from focusing on work, or have younger mathematicians to entertain, here are some suggestions for online activities you can do/watch/attend. If you have any suggestions of your own, add them in the comments!

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One of the most important skills in math's is learning how to be systematic and record your results. What is this GIF recording?

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Grant Sanderson is a math's YouTuber, he's made 10 videos during lockdown for you to get a new understanding of topics and improve your problems solving, here's the first one.

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The simpler quadratic formula | Lockdown math ep. 1

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Ofsted, 2021

Leaders and governors foster a culture of exceptionally high expectations for students' academic success

Ofsted, 2021

Students enjoy their lessons, which are taught by skilled, enthusiastic and knowledgeable teachers

You're treated as an individual... Everything is geared towards getting you ready for life and the staff really help prepare you for your exams

Ofsted, 2021

Leaders and staff create an exceptionally safe and welcoming culture

Ofsted, 2021

Students participate in an extensive range of activities and projects that develop their confidence and broaden their interests

Ofsted, 2021

There exists an ambitious curriculum that equips students exceptionally well with the knowledge and skills that they need to progress

Ofsted, 2021

Students thrive in the academy's calm and harmonious environment

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Trinity Sixth Form Academy - Outstanding Sixth Form in Halifax

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Ofsted, 2021 Leaders and governors foster a culture of exceptionally high expectations for students' academic success Ofsted, 2021 Students enjoy their lessons, which are taught by skilled, enthusiastic and knowledgeable teachers You're treated as an individual...