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Continue the pattern you see here and fill the gaps.
Challenge students to find the Fibonacci sequence in the triangle (the answer is SECRET #5, found HERE).

COMMENT BELOW ABOUT YOUR EXPERIENCE WITH PASCAL'S TRIANGLE IN ONE WORD.

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A fib poem is a six-line poem in which the syllables in each line of the poem reflect the sequence. The first two lines have 1 syllable, the next 2 syllables, then 3, 5, and 8 syllables. Students can be encouraged to experiment with longer poems or poems in which the words replace syllables in the composition. Here’s an example of a longer poem, and you can find many examples on the web, including these.

A PERFECT BLEND OF MATH & ENGLISH.
POST YOUR POEMS BELOW - PICTURES OR TEXT.

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Maths
Can
Be hard
But also
Fun if you're en garde
So toil away and don't say no

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line of best fit by fibonacci

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Side note- is there an 𝑒 day as well in maths. What would its date be (2.71828). Perhaps 27th January or 18th July? Or the 71st day of the year?

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When the students are already familiar with the sequence, then think:
Why November 23rd was chosen to be Fibonacci Day. What other dates could have been chosen? (January 12th, for one) How many dates can be made from the sequence (day and month only)? I count nine in all, but New Year’s Day is already taken!

What if we included month, day, and year (2 digits)? Was anyone born on a Fib Day (e.g. May 8, 2013)?

WRITE YOUR ALTERNATIVE DATES WITH JUSTIFICATIONS BELOW IN COMMENTS.

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Other sequences can be made that are similar to Fibonacci’s but start off with two different numbers.
One example is the Lucas Series. Students might enjoy creating their own sequences, but below is a puzzle to present that invites students to guess the mystery sequence based on clues. Once they’ve solved this one, challenge students to create their own by writing clues to their sequences.

Leonard writes down a sequence of numbers. After the first two numbers, each number is the sum of the previous two numbers in the sequence. The fourth number is 6 and the sixth number is 15. What is the seventh number in the sequence?

THE FIRST TO ANSWER IN COMMENTS IS A MATH WIZARD!!
OTHERS... DO COMMENT YOUR ANSWERS. WHO KNOWS WHO'S RIGHT?

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Jonathan Ross created 987, which is similar to 2048 puzzle but involves merging Fibonacci numbers.

POST SCREENSHOTS BELOW IN COMMENTS. LET'S FIND THE OVERALL SCHOOL WINNER.

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Join the Fibonacci numbers and get to the 987 tile!

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You may have seen this sequence before:

1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 ,...

It is called the Fibonacci Sequence, and each term is calculated by adding together the previous two terms in the sequence.

Try adding together any three consecutive Fibonacci numbers. What do you notice? Can you explain it?

Choose any four consecutive Fibonacci numbers. Add the first and last, and divide by two. What do you notice?

Can you explain it?

Add together any six consecutive Fibonacci numbers and divide by four. What do you notice?

Can you explain it?

Can you discover any Fibonacci Surprises of your own?

SHARE YOUR WORK AND SURPRISES BELOW IN COMMENTS.

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Jadyn Rodrigues - Fibonacci Function on Desmos

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Jadyn Rodrigues - Fibonacci Function on Desmos

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Arthur Benjamin: The magic of Fibonacci numbers

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Math is logical, functional and just ... awesome. Mathemagician Arthur Benjamin explores hidden properties of that weird and wonderful set of numbers, the Fibonacci series. (And reminds you that mathematics can be inspiring, too!)

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POST YOUR PICTURES WITH THE FLOWERS IN COMMENTS

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If you’d like to create a display about the Fibonacci sequence, HERE are directions for creating the spiral centers of sunflowers with origami paper.

THIS IS FOR THE RISK TAKERS.. COME ON!!
POST YOUR ORIGAMI PICTURES BELOW. EVEN SOME PART PROCESS IS WELCOME.

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Post your pattern pictures here.. teachers and students!!

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In computer science a Heap is a special Binary Tree-based data structure, used to show the relationship between parents and children.

A Fibonacci heap is a specific implementation of the heap data structure that makes use of Fibonacci numbers. Fibonacci heaps are used to implement the priority queues, giving the algorithm a very efficient running time.

Fibonacci heaps have a faster amortized running time than other heap types. (Amortized analysis is a method of analyzing the costs associated with a data structure that averages the worst operations out over time.)

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"Math in the World Around Us: Fibonacci Sequence" by Adventure Academy

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I

With

My mom

Went to eat

Some cheesy pizza

On the busy streets of New York city

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Oh
What
A Time
Christmas Time
It's the time for wine
And holiday cheer so divine

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Bang!
Blank!
Gun shooting!
Crowd keeps on snoring..
Bank not adoring

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Jane
Would
Always
Cry out loud
Whenever her dad
Would scream at her for missing school

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Dhiyansh trying a hand at origami with Fibonacci sequence

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Dhiyansh trying a hand at origami with Fibonacci sequence

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The
World
Is filled
With garbage and plastic
But we can help and make it fantastic

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Yashvi trying to draw a pattern drawing 

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Yashvi trying to draw a pattern drawing 

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Fibonacci quasiparticle' could form basis of future quantum computers

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Fibonacci quasiparticle' could form basis of future quantum computers

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https://phys.org/news/2014-12-fibonacci-quasiparticle-basis-future-quantum.html

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Illustration of "braids," i.e., the trajectories of anyon quasiparticles through time as they move around each other. Braiding patterns can form the logic gates in a quantum computer, and have the advantage of being more stable than trapped particles. Credit: Abolhassan Vaezi

(Phys.org)-Topological quantum computing (TQC) is a newer type of quantum computing that uses "braids" of particle tracks, rather than actual particles such as ions and electrons, as the qubits to implement computations. Using braids has one important advantage: it makes TQCs practically immune to the small perturbations in the environment that cause decoherence in particle-based qubits and often lead to high error rates.

Ever since TQC was first proposed in 1997, experimentally realizing the appropriate braids has been extremely difficult. For one thing, the braids are formed not by the trajectories of ordinary particles, but by the trajectories of exotic quasiparticles (particle-like excitations) called anyons. Also, movements of the anyons must be non-Abelian, a property similar to the non-commutative property in which changing the order of the anyons' movements changes their final tracks. In most proposals of TQC so far, the non-Abelian statistics of the anyons has not been powerful enough, even in theory, for universal TQC.

Now in a new study published in Physical Review Letters, physicists Abolhassan Vaezi at Cornell University and Maissam Barkeshli at Microsoft's research lab Station Q have theoretically shown that anyons tunneling in a double-layer system can transition to an exotic non-Abelian state that contains "Fibonacci" anyons that are powerful enough for universal TQC.

"Our work suggests that some existing experimental setups are rich enough to yield a phase capable of performing 'universal' TQC, i.e., all of the required logical gates for the performance of a quantum computer can be made through the braiding of anyons only," Vaezi told Phys.org. "Since braiding is a topological operation and does not perturb the low-energy physics, the resulting quantum computer is fault-tolerant."

The physicists' work builds on previous research that has shown that anyons can arise due to the fractional quantum Hall effect. To realize this effect, a 2-D electron gas is sandwiched between two flat semiconductor plates. When cooled to temperatures near absolute zero and exposed to strong magnetic fields, excitations form in the 2-D electron gas and give rise to anyons. So far, only Abelian anyons have been detected in fractional quantum Hall systems, but studies suggest that non-Abelian anyons might also be realized.

In the new study, the scientists considered a double-layer fractional quantum Hall system in which anyons can tunnel between the two layers. When modeling this system on a torus, the scientists showed that sufficiently large tunneling drives the evolution of six ground states that correspond to six topologically distinct types of quasiparticles, one of which is the Fibonacci anyon.

Vaezi explains that the Fibonacci anyon is related to the famous Fibonacci sequence (where a number in the sequence is the sum of the previous two numbers) as well as the golden ratio, 1.617... (which is approximately the ratio of any number in the Fibonacci sequence to the previous number). These mathematical patterns arise in the Fibonacci anyon because of its quantum properties, particularly those related to the so-called fusion rules that govern particle spins.

"The Fibonacci anyon is a non-Abelian anyon whose quantum dimension is the golden ratio (1.617...), and is the simplest anyon capable of performing universal quantum computation," Vaezi explained. "Using the fusion rule of Fibonacci anyons, it can be shown that the degeneracy of the ground state in the presence of n well-separated Fibonacci anyons on a sphere is the n th number in the Fibonacci sequence."

So what makes the Fibonacci anyon so attractive for TQC? The answer lies in its braiding statistics, or the way that these quasiparticles move around each other, creating braids and knots of tracks. Three or four Fibonacci anyons may correspond to a single qubit, and their braiding statistics corresponds to single-qubit gates. Building multiple-qubit gates requires braiding multiple qubits, often in intricate ways.

Here the physicists explain that another way to view this process is by looking at quasiparticles as domain walls that separate different ground state patterns of electrons. Different quasiparticles have different electric charges, so they separate different electron patterns. From this perspective, the Fibonacci anyon is appealing due to the particular ground state patterns it separates.

The physicists show that their finding that interlayer tunneling can result in Fibonacci anyons is well-supported by a variety of distinct methods. Further, the researchers raise the possibility that these Fibonacci anyons may have already been realized in past experiments on double-layer quantum Hall systems, although these experiments were not specifically looking for them. This is one area that they hope to investigate in the future.

"To test our prediction, we are numerically studying bilayer quantum Hall states with a number of interlayer interactions and searching for non-Abelian phases and, in particular, Fibonacci anyons in the case of the 2/3 state," Vaezi said. "We are also working on various experimental aspects of our proposal and potential signatures of the Fibonacci anyons."

More information: Abolhassan Vaezi and Maissam Barkeshli. "Fibonacci Anyons From Abelian Bilayer Quantum Hall States." Physical Review Letters. DOI: 10.1103/PhysRevLett.113.236804
arXiv:1403.3383 [cond-mat.str-el]

Corrected: 3:30pm EST, 12/15/2014: Thanks to El_Nose.

© 2014 Phys.org

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'Fibonacci quasiparticle' could form basis of future quantum computers

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(Phys.org)-Topological quantum computing (TQC) is a newer type of quantum computing that uses "braids" of particle tracks, rather than actual particles such as ions and electrons, as the qubits to implement computations. Using braids has one important advantage: it makes TQCs practically immune to the small perturbations in the environment that cause decoherence in particle-based qubits and often lead to high error rates.

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New Sequence by Eshaan and Zayaan - 7 Ekam

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New Sequence by Eshaan and Zayaan - 7 Ekam

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Consecutive sums by Aryan Salvi and Nyra 

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Consecutive sums by Aryan Salvi and Nyra 

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A few examples of the Fibonacci sequence. 

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A few examples of the Fibonacci sequence. 

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https://www.youtube.com/watch?v=nt2OlMAJj6o

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Adhishree,Ayaan,Aarika,Danica,Krishay,Yuvraj,Ahana

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Adhishree,Ayaan,Aarika,Danica,Krishay,Yuvraj,Ahana

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Language follows the golden (divine) ratio — The Language Matrix

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Most language learning resources focus on the process of what YOU can do to learn a language. But what I’m interested in is how a language is an organic, living, naturally occurring phenomenon, like rivers, trees, and humans, and what that has to do with efficient language learning, as well as wh

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This art project is processed based. You will not be encouraging your children to make something, but to explore shapes based on a specific proportion.

Check out the whole process here:

https://www.whatdowedoallday.com/fibonacci-art-project/

SO MUCH FUN.. MATH & ART ADD TO EACH OTHERS VALUE. POST YOUR FUN CIRCLE DESIGN PICTURES BELOW IN COMMENTS.

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A fun, processed based Fibonacci art project for kids. Great for S.T.E.A.M. learning at home or at school.

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Krutika Tyagi, Rene Walia, Khwaish Kamathia

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Krutika Tyagi, Rene Walia, Khwaish Kamathia

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Game Time !!

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By Chitrangada, Sharanya, Kiara, and Tanishkaa

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By Serah Danny, Sanaa K , Tiana Mehta, Sargon Goel

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The knock off Mona Lisa by Sharanya, Kiara, Chitrangda, and Tanishkaa

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By Kiara, Sharanya, Chitrangda, and Tanishkaa

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By Sargon, Tiana, Sarah and Sanaa -6 uno

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By Sargon, Tiana, Sarah and Sanaa -6 uno

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- 0
Cry - 1
Cry - 1
My eyes - 2
Burn with pain - 3
The weight on my brain - 5
Oh sweet sweet night with nightmares bright - 8
The blood-red moonlight crescents in my palm burn just right - 13
Shadows lurk eerie chirps and eyes stare back at me all while the howls go off sheets ripped off - 21

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Origami spiral shell - Sanaa k, Sarah d, Sargun G, Tiana M

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Origami spiral shell - Sanaa k, Sarah d, Sargun G, Tiana M

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Ayera Lulla- Pascals Triangle connection

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Ayera Lulla- Pascals Triangle connection

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Eyes
Bright
like the
starry night sky
vincent van Gogh would smile
if he saw the spark of interest inside

(I tried)

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A really fun concept as well as super cool. It is a really illuminating concept once you solve it.

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See
Patterns
Around you.
Comprehend, feel, sense...
Circle of life takes many shapes!

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come at me

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Every
Time
That I
try to have
a little bit of fun
Narayan sir says “ why are you so dumb”

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Superb game. Much like 2048.

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me
we
us all
are here now
on this occasion
gathered for mathematics day
i hope that our grade will win this fibonacci day.
When we win, we will be sure to rub it in all of your pathetic losing faces.

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Aryan n rhishaan

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A
Thought
That stays
Brings to light
The breaking of dawn
In more ways than one imagines
For the beauty of thought is not customary
But, a privilege that is undermined and quite often underappreciated.

Damn, this got more philosophical than I had ever hoped it could amount to. By the way, Happy JBCN Fibonacci Day.