Blaise Pascal was born at Clermont, Auvergne, France on June 19, 1628. He was the son of
Etienne Pascal, his father, and Antoinette Begone, 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 Etienne 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 Etienne
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.
|