How did the letters between Fermat and Pascal contribute to this theory?
July 1654: Pascal’s Letters to Fermat on the “Problem of Points” In the mid-17th century, an exchange of letters between two prominent mathematicians–Blaise Pascal and Pierre de Fermat–laid the foundation for probability, thereby changing the way scientists and mathematicians viewed uncertainty and risk.
What is Pascal’s probability theory?
One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value. The problem concerns a game of chance with two players who have equal chances of winning each round.
What is the history of Pascal’s triangle?
Pascal’s Triangle is named after the seventeenth century mathematician and philosopher, Blaise Pascal. Pascal’s Triangle was also known to the Chinese in the 11th century. The Chinese Mathematician, Jia Xian devised a triangular representation of the coefficients of the binomial theorem in the 11th century.
What is Fermat Pascal system?
Fermat’s method was essentially to lay out all possible paths to the needed number of wins and count how many went to each player. This method works but gets cumbersome as the number needed to win increases. Pascal’s approach made use of his arithmetic triangle, which we now call Pascal’s triangle.
What did Pierre de Fermat discover?
Independently of Descartes, Fermat discovered the fundamental principle of analytic geometry. His methods for finding tangents to curves and their maximum and minimum points led him to be regarded as the inventor of the differential calculus.
What did Pierre de Fermat do for math?
Pierre de Fermat was one of the most brilliant and productive mathematicians of his time, making many contributions to the differential and integral calculus, number theory, optics, and analytic geometry, as well as initiating the development of probability theory in correspondence with Pascal.
Why was Pascal’s triangle made?
Pascal’s triangle, in algebra, a triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression, such as (x + y)n. Chinese mathematician Jia Xian devised a triangular representation for the coefficients in the 11th century. …