|
|
This is only a preview of the paper
Click here to register and get the full text.
Existing members click here to login
|
|
|
1708). Among the wide range of Mathematics pertaining to the Bernoullis are Bernoulli Numbers, Bernoulli Differential Equation, Bernoulli's Principle of Fluid Dynamics, Bernoulli Trial, Bernoulli Inequality, etc. Jacob (1654-1705) is the first of the Bernoullis to make Mathematics a career, despite pressure to seek a career elsewhere. He contributed greatly to Calculus, Infinite Series and Probability. In particular, he published the Law of Large Numbers in 1689. This Law states that if an experiment of an event is carried out a large number of times, then the relative frequency of the event occurring equals the corresponding probability. He also solved what is now called Bernoulli Differential Equation: y' = p(x)y + q(x)yn Among his other works are: A general method to determine evolutes of a curve as the envelope of its circles of curvature. Caustic curves of parabola, logarithmic spiral and epicycloids (1692-93) Lemniscate of Bernoulli (1694). The Drawbridge Problem: what is the curve such that a weight sliding along the cable always keeps the bridge in balance? (1695) Jacob and Johann are responsible for promoting Gottfried William Leibniz's work on Calculus, as they were among the first to comprehend the theory of infinitestimals put forward by Leibniz. However, the two brothers are in constant rivalry over who is the better mathematician, so much so that their rivalry was known to the public community. One of the reason that the rivalry is so intense is that Johann could not ascend the chair of Mathematics in Basel because Jacob was holding it.
Approximate Word count = 993
Approximate Pages = 4
(250 words per page double spaced)
|
|
|
|
|
|