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1623 – 1662Clermont-Ferrand, France

Blaise Pascal

The binomial coefficients of $(a + b)^{n}$ form a triangle of pure pattern.

A short story

A French thinker (mathematician, physicist, philosopher) who wrote a small treatise on the arithmetical triangle at the age of thirty-one. The triangle's rows give the coefficients of $(a + b)^{n}$ for every $n$ : $1$ ; $1, 1$ ; $1, 2, 1$ ; $1, 3, 3, 1$ ; $1, 4, 6, 4, 1$ . The third row ( $1, 2, 1$ ) is exactly the formula $a^{2} + 2 ab + b^{2}$ . Tile Lab's picture-proof is one of countless ways to see it.

In their own words

It is so beautiful in its origin and its properties that I do not believe a thing of higher beauty could exist.

Paraphrased: from Pascal's Traité du triangle arithmétique, 1654, on the arithmetical triangle that bears his name.

The lab their idea turned into

Tile Lab

$(a + b)^{2}$ : see it as a square.

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