Grade 11 Math Essay - Blaise Pascal

by Toni Lintunen

Introduction

Blaise Pascal was born on June 19, 1623 in Clermont Ferrand. His

nationality was french. He died in 1662. He was credited for his

imaginative and subtle work in geometry and other branches of mathematics.

His work influenced later generations of theologians and philosophers,

helping make mathematics what it is today. Blaise Pascal is considered part

of the foundation of the very heart of mathematics.

History

At age 12 he mastered Euclid\'s Elements. In 1645, he invented and

sold the first adding machine. His study of hydrostatics led to the

invention of the syringe and hydraulic press. At age 16, he formulated the

basic theorems of projective geometry. These theorems became known as

Pascal\'s theorem. He proved that the level of mercury column in a

barometer is determined by the increase or decrease in the surrounding

atmospheric pressure. This discovery verified the hypothesis of the Italian

physicist Evangelista Torricelli, concerning the effect of atmospheric

pressure on the equilibrium of liquids.

After publishing Essay pour les coniques (Essay on conic sections),

Pascal temporarily abandoned the study of mathematics due to poor health.

He lived in Paris for a while in a frivolous manner as a break. His

interest in probability theory of the odds in gambling games lead him to

discover the Theory of probability in conjunction with Pierre de Fermat.

This theory dealt with the actuarial, mathematical, social statistics, and

calculations used in today\'s modern theoretical physics. At the end of

1654, after several months of depression, Pascal had a life altering

religious experience. He entered the Jansenist monastery in Port Royal.

Here, he never published his own name again in his mathematical studies.

He wrote a pseudonym to help in the struggle against the Jesuits for the

defense of the Jansenist, Antoine Arnauld. In 1658, he broke with the

Jansenists, and left the monastery. Pascal died on August 19, 1662 from

cancer, at age 39. In his life, his most famous work was perhaps Pensees

(thoughts). This was a set of deeply personal meditations in a somewhat

fragmented form on human suffering and faith in God. Another famous work

of his was called "Pascal\'s Wager." This expressed the conviction that

belief in God is rational: If God does not exist, one stands to lose

nothing by believing in him anyway, whereas if he does exist, one stands to

lose everything by not believing.

Pascal\'s Gears

Pascal\'s Gears were the first mechanical computing machine ever

invented. It was invented in 1642. This machine consisted of a series of

interlocking discs and gears, hence the name Pascal\'s Gears. Each gear had

one of the digits from 0 to 9 engraved on it. A complete turn of any gear

caused the gear to its left to make one-tenth of a turn, displaying the

next highest number. This mechanism was used in calculators and adding

machines up until the 1960\'s. The concept of Pascal\'s Gears is still being

used today in mechanical car odometers.

Pascal\'s Law

This was perhaps his most important piece of work he has ever done.

Written in 1653, it stated that in a fluid at rest, pressure on any surface

exerts a force perpendicular to the surface and independent of the

direction of orientation of the surface. The law is sometimes assumed to

include the principle that any additional pressure applied to a fluid will

be transmitted equally to every point in the fluid. This law is the basis

of machines involving hydraulic systems.

Conclusion

Pascal has proven to be a very unique individual in the time that he

had lived. He discovered very essential concepts of mathematics making it

the way it is today. At the same time, he dwelled in philosophical and

religious ideas and concepts. One common trend in both areas he studied,

is the use of logic. The use of logic, being the heart of mathematics, was

the basis of his philosophical and religious aspects of his life. These

parts of his life revolved around logic and order. Logic, what answered

his mathematical ponderings, also answered the questions he asked about

life itself.

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