Tuesday, June 24, 2014

BLAISE PASCAL - Inventor of the first calculator 


“We sail within a vast sphere, ever drifting in uncertainty, driven from end to end” - Blaise Pascal

Blaise Pascal - Image from google.com

Blaise Pascal (1623 – 1662) was a French mathematician, physicist, inventor, writer and philosopher. Pascal was probably one of the greatest mathematicians of all time.  He was known to be first inventor of the mechanical calculator. His other contributions to the mathematics field that we are still using today were the Pascal Theorem and the Pascal’s triangle (Encyclopedia, 2008)

           

Pascal Theorem


Illustration of Pascal Theorem. 
Retrieved from HowStuffWorks.com 
When Pascal was 16 (1940), he was able to prove a basic theorem in projective geometry. This theorem was later named after him. According to the Pascal theorem, "the three points of intersection of the pairs of opposite sides of a hexagon inscribed in a conic plane are collinear"(Encyclopedia, 2008). In other words, if you take any plane intersecting a cone and draw a hexagon inside it, the lines extending from the opposite sides of the hexagon meet in three points lying on the same line.


Pascaline


The Pascaline.
 Picture taken at Musée des Arts et Métiers in Paris.
When Pascal was 18 (1942), he designed the first calculator that was used to perform addition and subtraction. The machine required complicated wheel arrangements and was very difficult to built given the rudimentary techniques available at the time. After fifty prototypes, Pascal was able to produce the first working model - the Pascaline - three years later. Today there are only eight Pascalines known to have survived.



Pascal's triangle


Pascal's triangle.
 Animated GIF retrieved from Wikipedia.com.



Another demonstration of Pascal's genius is the Pascal's triangle. In Pascal’s triangle, each number is the sum of the two directly above it. The triangle represents binomial coefficients in a polynominal equation of the format (x + y)n.









Pascal's law 

Image retrieved from google.com
In addition to Pascal’s work in the mathematics field, Pascal also made significant contributions to the study of pressure and vacuum in physics. Pascal's law is a the fundamental law in hydrostatic. It states that "a change in the pressure at any point of an enclosed incompressible fluid is conveyed undiminished to every part of the fluid and to the surfaces of its container” (Pascal, n.d.)

Today, we can see the application of Pascal’s law in hydraulic brakes, car lifts, hydraulic jacks, and forklifts (PascalTeam, 2012). Using Pascal's law, we can use very a small force to lift a very heavy object! 

In honor of Pascal’s contributions to the study of pressure, his name is used as a unit of pressure measurement.

Unfortunately, Pascal died at a young age of 39. He devoted the majority of his later life to religion. However, he left a legend behind him. We still use many of his discoveries today. Personally I learned about Pascal 40 years ago in Vietnam. I was taught Pascal's triangle when I was in middle school and Pascal's law when I was in high school. For me, he was one of the greatest minds in science and math. What about you? Who do you think is the greatest mathematicians? 

Reference


Pascal, Blaise. (2008). Complete Dictionary of Scientific Biography. Retrieved from http://www.encyclopedia.com/doc/1G2-2830903299.html

Pascal's Law - Pascal's Principle. (2012). Retrieved from http://pascalteam.hu/en_pascal_law.php

2 comments:

  1. Personally, I'm a big fan of Euclid. I've always really loved geometric proofs because they don't really require heavy mathematical background to understand. You see them and they make sense. Because of that, I really like flipping through my friend's copy of Euclid's Elements whenever I'm in his car. Related to that, have you seen Euclid The Game? It's a browser-based game that gives you certain mathematical tools (like the ability to use a compass to draw a circle around a point and to draw a line segment between two points) and you have to use these to figure out additional tools (like how to find a perpendicular line through a point) and it's incredibly interesting and fun to use. http://euclidthegame.org/ (I'm currently stuck on level 19)

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  2. I like your blog a lot, Thuy; the layout is very attractive. I learned a lot more about Pascal from reading your blog than I did in high school. I remember my math teacher briefly mentioning Pascal’s triangle, but I never heard of his theorem or law. It sounds like you had a better learning experience in Vietnam. I think Oliver Heaviside is one of the greatest mathematicians. He was also an electrical engineer as well as a physicist. When he 16 years old he dropped out of school and began to teach himself; much of what he learned was through self-study. He is known for making great contributions to math, physics, and electrical engineering.

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