Blaise Pascal Essay, Research Paper

Blaise Pascal

Blaise Pascal was born at Clermont, Auvergne, France on June 19, 1628.

He was the son of ?tienne Pascal, his father, and Antoinette B?gone, his mother

who died when Blaise was only four years old. After her death, his only family

was his father and his two sisters, Gilberte, and Jacqueline, both of whom

played key roles in Pascal’s life. When Blaise was seven he moved from

Clermont with his father and sisters to Paris. It was at this time that his

father began to school his son. Though being strong intellectually, Blaise had

a pathetic physique.

Things went quite well at first for Blaise concerning his schooling.

His father was amazed at the ease his son was able to absorb the classical

education thrown at him and “tried to hold the boy down to a reasonable pace to

avoid injuring his health.” (P 74,Bell) Blaise was exposed to all subjects, all

except mathematics, which was taboo. His father forbid this from him in the

belief that Blaise was strain his mind. Faced with this opposition, Blaise

demanded to know ?what was mathematics?’ His father told him, “that generally

speaking, it was the way of making precise figures and finding the proportions

among them.” (P 39,Cole) This set him going and during his play times in this

room he figured out ways to draw geometric figures such as perfect circles, and

equilateral triangles, all of this he accomplished. Due to the fact that ?

tienne took such painstaking measures to hide mathematics from Blaise, to the

point where he told his friends not to mention math at all around him, Blaise

did not know the names to these figures. So he created his own vocab for them,

calling a circle a “round” and lines he named “bars”. “After these definitions

he made himself axioms, and finally made perfect demonstrations.” (P 39,Cole)

His progression was far enough that he reached the 32nd proposition of Euclid’s

Book one. Deeply enthralled in this task his father entered the room un-noticed

only to observe his son, inventing mathematics. At the age of 13 ?tienne began

taking Blaise to meetings of mathematicians and scientists which gave Blaise the

opportunity to meet with such minds as Descartes and Hobbes. Three years later

at the age of 16 Blaise amazed his peers by submitting a paper on conic sections.

His sister was quoted as having said “that it was considered so great an

intellectual achievement that people have said they have seen nothing as mighty

since the time of Archimedes.” (I:Pascal) This was his first real contribution

to mathematics, but not his last. Note:

www.nd.edu/StudentLinks/akoehl/Pascal.html

Pascal’s contributions to mathematics from then on were surmasing. From

a young age he was ?creating science.’ His first scientific work, an essay on

sounds he prepared at a very young age. Once at a dinner party someone tapped a

glass with a spoon. Pascal went about the house tapping the china with his fork

then dissappeard into his room only to emerge hours later having completed a

short essay on sound. He used the same approach to all of the problems he

encountered; working at them until he was satisfied with his understanding of

the problem at hand. A few of his disocoveries stood out more then others, of

them his calculating machine, and his contributions to combinatorial analysis

have made a signifigant contribution to mathematics.

The mechanical calculator was devised by Pascal in 1642 and was brought

to a commercial version in 1645. It was one of the earliest in the history of

computing. ?Side by side in an oblong box were places six small drums, round

the upper and lower halves chich the numbers 0 to 9 were written, in decending

and ascending orders respectively. According to whichever aritchmatical process

was currently in use, one half of each drum was shut off from outside view by a

sliding metal bar: the upper row of figures was for subtraction, the lower for

addition. Below each drum was a wheel consisting of ten (or twenty of twelve)

movable spokes inside a fixed rim numbered in ten (or more) equal sections from

0 to 9 etc, rather like a clockface. Wheels and rims were all visible on the

box lid, and indeed the numbers to be added or subtracted were fed into the

machine by means of the wheels: 4 for instance, being recorded by using a small

pin to turn the stoke opposite division 4 as far as a catch positioned close to

the outer edge of the box. The procedure for basic arithmatical process then as

follows.

To add 315+172, first 315 was recorded on the three (out of six) drums

closest to the right-hand side: 5 would appear in the sighting aperture to the

extremem right, 1 next to it, and 3 next to that again. To increase by one the

number showing in any aperture, it was necessary to turn the appropriate frum

forward 1/10th of a revolution. Tus in this sum, the drum on the extremem right

of the machine would be given two turns, the drum immediately to its left would

be moved on 7/10ths of a revolution, whilst the drum to its immediate left would

be rotated forward by 1/10th. Tht total of 487 could then be read off in the

appropriate slots. But, easy as thes operation was, a problem clearly arose

when the numbers to be added together involved totals needing to be carried

forward: say 315 + 186. At the perios at which Pascal was working, and because

there had been no previous attempt at a calculating-machine capable of carrying

column totals forward, this presened a serious technical challenge.(adamson p

23)

Pascal is also accredited with the advent of Pascal’s triangle; An

arrangement of numbers which were originally discovered by the chinese but named

after Pascal due to his furthur discoveries into the properties which it

possesed. ex. (Pascals Triangle)

1

1 1

1 2 1

1 3 3 1

.

.

.

`Pascal investigated binomial coefficients and laid the foundations of the

binomial theorem.’(adamson p37) ?A triangular array of numbers consists of ones

written on the vertical leg and on the hypotenuse of a right angled isosceled

triangle; each other element composing the triangle is the sum of the element

directly above it and of the element above it and to the left. Pascal proceeded

from this to demonstrate that the numbers in the (n+1)st row are the

coeffieients in the binomial expansion of (x+y)n. Due to the ease and clarity

of the formation of the problems involved, Pascal’s triangle, although not

original was one of his finest achievements. It has greatly influenced mandy

discoveries including the theoritical basis of the computer). It has also made

an essential contribution to the field of combinatory analysis. It also ?

through the work of John Wallis it led Isaac Newton to the discovery of the

binomial theorem for fractional and negative indices, and it was central to

Leibniz’s discovery of the calculus.’(adamson p37)

As stated looking closer at the triangle Pascal was able to deduce many

properties. First of all, the enteries in any row of the triangle are an equal

distance from each other.

He found another property can be derived from the triangle. He

discovered that any number in the triangle is the sum of the two numbers

directly above it. This hls true for both triangles, the solved and unsolved.

(3/1) + (3/2) = (4/2). Similarly, (5/1) + (5/2) = (6/2). The generalization

of this property is known as Pascal’s theorem.

Furthur studies in hydrodynamics, hydrostatic and atmospheric pressure

led Pascal to many dicoveries still in use today such as the syringe and

hydrolic press. Both these inventions came after years of him experimenting

with vacuum tubes. One such experiment was to ?Take a tube which is curved at

its bottom end, sealed at its top end A and open its extermity B. Another tube,

a completely straight one open at both extermities M and N, is joined into the

curved end of the first tube by its extermity M. Seal B, the opening of the

curved end of the first tube, either with your finger or in some other manner

and turn the entire apparatus upside down so that, in other words, the two

tubes really only consist of one tube, being interconnected. Fill this tube

with quicksilver and turn it the right way up again so that A is at the top;

then place the end N in a dishfull of quicksilver. The whole of the quicksilver

in the upper tube will fall down, with the result that it will all recede into

the curve unless by any chance part of it also flows through the aperture M into

the tube below. But the quicksilver in the lover tube will only partially

subside as part of it will also remain suspended at a heright of 26′-27′

according to the place and weather conditions in which the experiment is being

carried out.

The reason for this difference is because the air weights down on the

quicksilver in the dish beneath the lower tube, and thus the quicksilver which

is inside that tube is held suspened in balence.

But it does not weigh down upon the quicksilver at the curved end of the

upper tube, for the finger or bladder sealing this prevents any access to it, so

that, as no air is pressing down at this point, the quicksilver in the upper

tube drops freely because there is nothing to hold it up or to resist its fall.

All of these contibutions have made a lasting impact of all of mankind.

Everything that Pascal created is still in use today in someway or another. His

primative form of a syringe is still used in the medical field today to

administer drugs and remove blood. The work he did on combinatory mathematics

can be applied by anyone to ?figure out the odds’ concerning a situation, which

is exactly how he used it; by going to casinos and playing games smart.

Something that anyone can do today. The work he did concerning hydrolic

pressses are still in use today in factories, and car garages.

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