Born: 19 June 1623 in Clermont (now Clermont-Ferrand), Auvergne, France
Died: 19 Aug 1662 in Paris, France

Blaise Pascal worked on conic sections and produced important theorems in projective geometry. In correspondence with Fermat he laid the foundation for the theory of probability.

Pascal's father, Étienne Pascal, had unorthodox educational views and decided to teach his son himself. He decided that Pascal was not to study mathematics before the age of 15 and all mathematics texts were removed from their house.

Pascal however, his curiosity raised by this, started to work on geometry himself at the age of 12. He discovered that the sum of the angles of a triangle are 2 right angles and, when his father found out he relented and allowed Pascal a copy of Euclid.
At the age of 14 Pascal started to attend Mersenne's meetings. Mersenne belonged to the religious order of the Minims, and his cell in Paris was a frequent meeting place for Fermat, Pascal, Gassendi, and others.

At the age of 16 Pascal presented a single piece of paper to one of Mersenne's meetings. It contained a number of projective geometry theorems, including Pascal's mystic hexagon.

Pascal invented the first digital calculator (1642) to help his father. The device, called the Pascaline, resembled a mechanical calculator of the 1940's.

Further studies in geometry, hydrodynamics, and hydrostatic and atmospheric pressure led him to invent the syringe and hydraulic press and to discover Pascal's law of pressure.

He worked on conic sections and produced important theorems in projective geometry. In correspondence with Fermat he laid the foundation for the theory of probability.

His most famous work in philosophy is Pensées , a collection of personal thoughts on human suffering and faith in God. 'Pascal's wager' claims to prove that belief in God is rational with the following argument.

If God does not exist, one will lose nothing by believing in him, while if he does exist, one will lose everything by not believing .
His last work was on the cycloid, the curve traced by a point on the circumference of a rolling circle.

Pascal died at the age of 39 in intense pain after a malignant growth in his stomach spread to the brain.

Blaise Pascal

Frankie Ferreira

Presented 5/12/95
Received  6/7/95

Name: Blaise Pascal. Also worked under the pseudonym Lovis de Montalte, or it's anagram, Amos Dettonville. Born: June 19, 1623. Clermont, Auvergne, France. Health:

1. Known as the "greatest might-have-been" in the history of mathematics. 2. At the age of one became seriously ill with either tuberculosis or rickets. Doctors found that the sight of water made him hysterical, and he would often throw tantrums when he saw his father and mother together. From the age of 17, acute dyspepsia made his days a torment and chronic insomnia made his nights half-waking nightmares. At 23 his whole digestive track went bad and he suffered a temporary paralysis. 3. Father forbade him to pursue math because it might worsen his health. Naturally, that only piqued his curiosity. 4. Later in life, became a religious fanatic. Believed that his pursuit of mathematics displeased God and that his pain had been sent from God as a form of punishment. Accomplishments: 1. First spectacular feat was to prove, entirely on his own initiative, and without a hint from any book, that the sum of the angles of a triangle is equal to two right angles. Realizing that his son was a gifted mathematician, Etienne gave his son a copy of Euclid's Elements. Apparently, he had found out and proved several of Euclid's propositions for himself before he ever saw the book. In fact, his sister, Gilberte, declared that her brother had rediscovered for himself the first 32 propositions of Euclid, and that he had found them in the same order as that in which Euclid sets them forth. This is believed by historians to be highly unlikely. 2. At 16, he introduces Pascal's theorem, which states that by taking any conic section, say an ellipse, and on it marking any six points (A through E) and joining them up, in this order, by straight lines, the 6 sided figure inscribed in the conic section ( known as the "mystic hexagram" ), in which AB and DE, BC and EF, CD and FA are pairs of opposite sides, will produce 2 lines in each of these pairs intersecting in a point and the 3 points of intersection lie on a straight line. This theorem is said to have influenced Leibniz in his study of tangents. Amazingly, Pascal's theorem is invariant under conical projection (unlike right angles). 3. At 18 he invented and made the first calculating machine in history. The adding machine was devised to assist his father in the auditing of government accounts. It was able to handle numbers not exceeding 6 digits. It contained a sequence of engaging dials, each marked from 0 to 9, so designed that when one dial of the sequence turned from 9 to 0 the preceding dial of the sequence automatically turned one unit. Thus, the "carrying" process of addition was mech- anically accomplished. He manufactured over 50 machines, some of which are still preserved in the Conservatoire des Arts et Metiers at Paris. He has also been credited with the invention of the one-wheeled wheelbarrow. Pascal's Triangle: Row 0 1 Row 1 1 1 Row 2 1 2 1 Row 3 1 3 3 1 Row 4 1 4 6 4 1 Row 5 1 5 10 10 5 1 1. Used by Chu Sh•-kiŽ in 1303. Chu speaks of the triangle as already ancient in his time. 2. The numbers in the nth row are the coefficients in the expansion of (1+x)4n by the binomial theorem, thus for n = 4, (1+x)4 = 1 + 4x + 6x2 + 4x3 + 1x4. 3. The sum of the numbers in between the diagonals produces the Fibonacci sequence. 4. Each row represents the corresponding power of 11 (the top row being the 0th row). Example: Row 5 is 1 5 10 10 5 1 115 = 1 6 1, 0 5 1 Exercise: 1. Using Pascal's triangle, find 119.

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