## 1623 – Pascal – bio

Blaise Pascal was born in 1623 in Clermont, France. He is mostly known as being an outstanding mathematician, but also was a physicist and philosopher. He made significant contributions to the areas of conic sections and projective geometry. Pascal’s triangle is a number matrix in the shape of a triangle with the numbers staggered so that each number is the sum of the closest pair in the row immediately above it. The numbers also represent binomial coefficients, which are the coefficients you get when raising the polynomial equation “x + 1” to subsequent powers which are the row numbers in the triangle. (x+1) raised to the zero power is 1. (x+1) raised to the first power is 1 + x. (x+1) raised to the second power is 1 + 2x + x(squared). So, the first row is simply 1. The second row is 1 and 1. The third row is 1 and 2 and 1. This continues, giving:

The triangle can also be used to generate Fibonacci numbers by summing the numbers in diagonal rows. And it can be used to calculate how many combinations can be made from pairing objects in different sized groups. This is used in probability theory which was created by the work of Pascal and Fermat.

Even though Pascal has his name attached to the triangle of numbers, the theory behind it was developed over many years, by many mathematicians before him. The triangle of binomial coefficients was described by Pingala, an Indian who lived sometime around -0300 to -0400. In Persia, Al-Karaji (0953) and Al-Khayyam, Omar (1048) both did some work with the triangle and binomials. In China, Yang Hui (1238) drew the triangle and in Italy, Tartaglia (1500) worked with it.

Pascal invented the hydraulic press and the syringe. He continued the work of Torricelli with the barometer and advanced it, pressing for adoption of the idea of a vacuum, which was widely disbelieved at the time.

PRECURSOR:

Pingala

Euclid

Al-Karaji

Al-Khayyam

Yang Hui

Fibonacci

Torricelli

Tartaglia

**1588 – Mersenne**

**1596 – Descartes**

**1601 – Fermat**

**1629 – Huygens**

CONCURRENT:

SUBSEQUENT:

von Guericke

Laplace

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