Text 7. Blaise Pascal

Blaise Pascal (June 19, 1623-August 19,1662) was a French mathematician, physicist, religious philosopher. Pascal was a child prodigy, who was educated by his father. Pascal's earliest work was in the natural and applied sciences, where he made important contributions to the construction of mechanical calculators and the study of fluids, and clarified the concepts of pressure and vacuum by expanding the work of Evangelista Torricelli. Pascal also wrote powerfully in defence of the scientific method.

He wrote a significant treatise on the subject of projective geometry at the age of sixteen and corresponded with Pierre de Fermat from 1654 on probability theory, strongly influencing the development of modern economics and social sciences.

At age eighteen Pascal constructed a mechanical calculator, called Pascal's calculator or the Pascaline, capable of addition and subtraction, to help his father with this work. The Zwinger museum, in Dresden, Germany, exhibits one of his original mechanical calculators. Though these machines stand near the head of the development of computer engineering, the calculator failed to be a great commercial success. Pascal continued to make improvements to his design through the next decade and built a total of fifty machines.

In addition to the childhood marvels recorded above, Pascal continued to influence mathematics throughout his life. In 1653 Pascal wrote his ''Traité du triangle arithmétique'' in which he described a convenient tabular presentation for binomial coefficients, the "arithmetical triangle", now called Pascal's triangle. (It should be noted, however, that Yang Hui, a Chinese mathematician of the Qin dynasty, had independently worked out a concept similar to Pascal's triangle four centuries earlier.)

Mathematical symbols and expressions

+	plus, addition sign
-	minus, subtraction sign
	plus or minus (minus or plus)
	multiplied by, multiplication sign
/	divided by, division sign
:	divided by, ratio sign
<	less than
>	greater than
	equal to or less than
	equal to or greater than
	approximately equal
=	equals
	not equal to
	infinity
	square root
	cube root
	nth root
an	the nth root
a1	a sub 1
an	a sub n
a'	a prime
a"	a double prime
a2	a square, a to the second power
a3	a cube, a cubed, a to the third power
a-n	a to the minus nth power
log or log10	common logarithm
loge	natural logarithm
sin	sine
cos	cosine
tan	tangent
sec	secant
f (x)	function of x
x	increment of x, delta x
	summation of, sigma
	integral of
	integral between the limits a and b
dx	differential of x
dy/dx	derivative of y with respect to x
d2y/dx2	second derivative of y with respect to x