## Blaise PascalJune 19, 2012
• Pascal's triangle, a triangular array of the binomialAs I wrote in a previous article (Extreme Intelligence, October 14, 2011) Pascal was a child prodigy who had an estimated intelligence quotient (IQ) of 195. As I wrote in that same article, Albert Einstein and Stephen Hawking are tied with estimated IQs of 160; while Richard Feynman had a measured IQ of "only" 126. Mathematics
Pascal's triangle, introduced in his 1654 Traité du triangle arithmétique (Treatise on the Arithmetical Triangle) is known to most high school mathematics students. It's easy to construct, and it's a simple way to remember the coefficients of a binomial expansion; viz.,
(x + y)
^{2}.
Hydrostatics
There's good reason that the unit of pressure, the pascal, which is a newton's force acting over a square meter, is named after him. Pascal conducted some critical experiments in hydrostatics, including his famous barrel experiment, in which he demonstrated the pressure exerted by a long, thin column of water. Pascal was able to burst a wooden barrel through pressure exerted by water in a ten meter pipe attached to it.
This experiment confirmed his principle that pressure exerted anywhere in a confined incompressible fluid is transmitted equally throughout the fluid. His observations are summarized in his law of hydrostatics,
ΔP = ρgΔhwhere ΔP is the pressure change in an incompressible fluid that results from a change in its height Δh. The constant ρ is the fluid density, and g is the gravitational acceleration. Inventions
In a previous article (Who Invented the Computer?, March 21, 2011), I wrote about a prized possession of mine when I was a child. This was a plastic pencil box with a mechanical calculator built into its sliding door. A pencil point could be used to rotate a row of gear-like wheels to add and subtract very large numbers.
Pascal invented this mechanical calculator, called a Pascaline, in 1642 (see photograph). Pascal invented this to help his father, who was a tax collector, do calculations. The mechanism was much more complicated than the decimal calculator in my pencil box, since French currency at the time had 20 sols in a livre and 12 deniers in a sol. In the decade since its invention, fifty of these machines had been built, but few were sold.[2]
Other Things Pascal
Many years ago I programmed extensively in Pascal, a language designed by famed computer scientist, Niklaus Wirth. This language was named in honor of Pascal, and Wirth cautioned everyone not to write it as PASCAL. I used this language on a VAX-11/780, and then migrated to personal computer versions when they became fast enough. Today, I write mostly in C.
There's a fairly large lunar crater (115 km diameter), named Pascal (see photograph).
"I would have written a shorter letter, but I did not have the time."[5] ( ## References:- D.R. Wilkins, Transcriber, "Blaise Pascal (1623 - 1662)," from "A Short Account of the History of Mathematics," (4th edition, 1908) by W. W. Rouse Ball.
- J. J. O'Connor and E. F. Robertson, "Blaise Pascal." School of Mathematics and Statistics, University of St. Andrews.
- Inventor of the Week, Lemelson-MIT Web Site, May 2003.
- July 1654: Pascal's Letters to Fermat on the "Problem of Points," This Month in Physics History, American Physical Society Web Site.
- "Je n'ai fait celle-ci plus longue que parce que je n'ai pas eu le loisir de la faire plus courte."
- Blaise Pascal, "To The Reverend Fathers, The Jesuits," Letter XVI of The Provincial Letters, December 4, 1656, at the University of Adelaide eBooks web site.
- Blaise Pascal quotations on Wikiquote.
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