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The mathematical secrets of Pascal’s triangle

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It’s known as Pascal’s triangle in the Western world, but centuries before that, it was the Staircase of Mount Meru in India, the Khayyam Triangle in Iran, and Yang Hui’s Triangle in China. It can look complicated at first, but when you start to spend time with some of the incredible patterns hidden within this infinite mathematical work of art — diagonals, odds and evens, horizontal sums, exponents of 11, squares, the Fibonacci Sequence, and so much more — you may never look at a triangle in the same way again.

Note: Before you watch the mathematical secrets of Pascal’s triangle, above, you may want to try this simplified worksheet (updated pdf) for a hands-on understanding of how some of the numbers, patterns, and secrets of Pascal’s triangle works. Update: Additional worksheets here.

Another quick visual: Check out Jenny Eather’s Pascal’s triangle images below, one of many entries in her Maths Dictionary for Kids.


Related reading: The Sierpinski Triangle.

In the archives, watch more math, more shapes, and these site favorites: Mathematica – A World of Numbers… and Beyond, Vi Hart’s Hexaflexagon, Why do honeybees love hexagons?

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