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Real life examples include:
The "dice race"
Taxi cab matrix
The price is right

Binomial coefficients

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Place value
Speed up calculations
lead to production of negative numbers
Use of different bases - link to binary system and hence computer computations.
Rabbit puzzle using Fibonacci sequence.
0! = 1 why?
a^0 = 1 why?
a + 0 v a.0

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Group 4: BEHOLD!

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Group 5: Euler in Action

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Math Applications vs Math Analysis - An obnoxious infographic

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Amazingly Simple Graphic Design Software - Canva

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Create beautiful designs with your team. Use Canva's drag-and-drop feature and layouts to design, share and print business cards, logos, presentations and more.

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Cambodia

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Did ancient Cambodians invent the zero?

A little way outside Siem Reap, a few sheds and a makeshift office house thousands of ancient relics rarely seen by the millions who pass through the city to see the temples each year. On the ground at the Conservation d'Angkor Centre lie broken Buddha statues and severed stone heads - a Jayavarman VII here, a dusty linga there. Last year, on the January morning that Amir Aczel arrived, the place was empty.

The sixty-something American, a mathematician and author, had come to search for the evidence he had chased for the previous five years: an ancient stone slab on which was inscribed what he believed to be the first numeric zero ever recorded.

Between his fingers Aczel gripped the pencil rubbings and documents he believes prove that Cambodians were among the first people on earth - before the Europeans and Arabs - to use 0 to signify nothingness. Not even the Romans had invented such an advanced system as the one, illustrated by a stone marked "K-127", that was somewhere in that room.

Finally, after hours of stalking the backs of stones to find one he recognised, Aczel landed on a familiar-looking reddish block. "I recognised the writing and thought: 'Wow, this is it,'" he recalled in an interview over Skype last week. "It was an amazing moment. I'll never have another moment like that in my life."

Aczel was born, as he likes to tell people, on the high seas. The son of a cruise ship captain, he was raised around an eclectic and transient community and grew up to speak a host of different languages. But his interest in the history of numerals began while studying at the University of California, Berkeley. He went on to write 14 books about mathematics and physics, several of which have become international bestsellers.

His latest, Finding Zero tells the story of his recent search for proof that the concept of the numeric zero was invented in Asia, and possibly Cambodia - a eureka moment he goes so far as to call "the greatest invention of the human mind". The book will be published by MacMillian early next year.

The story, which sees the author - in the words of the publisher - "doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross-examining so-called scholars", starts in India. The first zero was once believed to have been found at the Chatur-bujha temple in the city of Gwalior. "I saw a lot of things there; then somebody told me that there was an earlier zero than the one in India," said Aczel.

That zero was uncovered by George Cœdès, a 20th-century French scholar who dedicated his life's work to Southeast Asian archaeology and history. An expert in ancient Khmer script, married to a Cambodian princess, Cœdès transcribed and translated thousands of inscriptions from monuments found in the region then known as Indochina.

At the time, most scholars agreed that the numerical zero was probably either a European or an Arab invention. One of the proponents of this theory was a British scholar named G.R Kaye, who launched searing attacks on Cœdès, who contended that the numeral came not from the West but from the East and, in particular, Cambodia. "It was pretty confrontational - the conflict between them," said Aczel.

The first known use of a numerical zero in India was dated to the mid-ninth century, an era that coincided with the Arab Caliphate - so Kaye's theory, which posited that the numeral had passed to the East via Arab traders, stood. "But Cœdès had a feeling that the zero had to come from Asia," explained Aczel, adding that the researcher was more Asian in his thinking than Western.

It was Cœdès who coined the term "Indianised civilisation" to refer to the countries of Indochina. The phrase is frequently used to describe Angkor. Many of the illustrations on the walls of the ancient temple complex are drawn from the Ramayana and Mahabharata stories.

During his research, Cœdès heard about a stone among the ruins of a seventh-century Cambodian temple which was said to be inscribed with a numeric zero. In the early 1900s, he hunted it down to Sambor on Mekong, in present-day Kratie, and translated the text on the stone almost in full. On the slab is written a long list of the names of slaves to be given to the king with their children, alongside five pairs of bulls and white rice, by the "respectable people living here".

But the key phrase is a date marker: "The Chaka era reached 605 in the year of the waning moon." The date uses a numerical zero, and the Chaka era began in AD78, meaning the inscription was made in AD 683 - placing it a full two centuries earlier than the Indian zero. Cœdès' paper was published in 1931 and put to rest the theories about European and Arab sources.

"The significance of K-127 to Cambodia is that it indicates that at present knowledge, the first zero - the most important number - is an ancient Khmer invention," said Aczel. "Someone may find an earlier zero in India, but I personally bet against it."

As for the stone, it was moved to the National Museum of Cambodia and then, in the late 1960s, to the Conservation d'Angkor. But when Aczel arrived, on the trail of Cœdès nearly four decades later, there was no guarantee the stone had survived the turbulent events of the preceding years.

During the nearly four years the Khmer Rouge was in power, the ultra-Maoist regime enslaved and plundered the country. Thousands of ancient artefacts were destroyed. In the aftermath of the regime, looting continued to plague the country's ancient sites - the Conservation d'Angkor was among the targets.

When Aczel arrived in Phnom Penh in search of K-217, Hab Touch, the director of the National Museum, could confirm it had been there, but whether or not it remained there was unknown.

In a twist of fate, immediately after Aczel re-discovered it among the debris, the stone was removed by a pair of students who took it to a laboratory for restoration.

"From out of the blue, two women walked in - nobody goes in there! - speaking Italian and I told them about it," said Aczel.

"One of them, she said, 'Well, in that case we'll take it!'"

The mathematician, who believes the stone belongs in a museum, considers its removal a bitter blow. Aczel said he hopes the book will persuade the authorities to take some action to retrieve it.

"Seeing is believing - K-127 can be felt, touched, scrutinised, learned from, admired, celebrated. It is immensely important."

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Did ancient Cambodians invent the zero? A little way outside Siem Reap, a few sheds and a makeshift office house thousands of ancient relics rarely seen by the millions who pass through the city to see the temples each year.

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Aim 8: Who really invented “Pythagoras’ Theorem”?

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Aim 8: Who really invented “Pythagoras’ Theorem”?

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Hipparchus, Menelaus and Ptolemy. The first recorded use is in China, known as the "Gougu theorem" (勾股定理) and in India known as the Bhaskara Theorem.

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IM Ancient clay tablets from Babylonia indicate that the Babylonians in the second millennium B.C., 1000 years before Pythagoras, had rules for generating Pythagorean Triples, understood the relationship between the sides of a right triangle, and, in solving for the hypotenuse of an isosceles right triangle, came up with an approximation of accurate to five decimal places.