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Jacob Bernoulli |
On August 16
th we celebrated 300 years anniversary of passing away of Jacob Bernoulli, a Swiss mathematician considered to be one of the most important founders of calculus of variations and probability theory.One of his most important works was Ars Conjectandi, published in 1713. It contains the general theory of permutation and combination, the weak law of large numbers, the binomial theorem and multinomial theorem, the analysis of properties of (introduced in this work) Bernoulli numbers. Also a lot of space is devoted to the analysis of the amount of money that one should expect to win playing games of chance.
Here is only a selection of the fundamental for mathematics achievements of
Jacob Bernoulli:
• a construction how to divide any triangle into four equal parts with two
perpendicular lines,
• works on infinite series (e.g. the convergence of
∑(1/n), ∑(1/n2)) ,
• proof that the problem of determining the isochrone is equivalent to solving a
first-order nonlinear differential equation,
• finding the solution of y' = p(x)y + q(x)yn (now called the Bernoulli
equation),
• analysis of such curves as parabola, logarithmic spiral, lemniscate.
Jacob Bernoulli had always been impressed by the properties of the logarithmic
spiral. He had requested to carve on his tombstone the Latin inscription Eadem
Mutata Resurgo meaning I shall arise the same though changed.
For a variety of historical information about the life of Jacob Bernoulli please
visit e.g.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Bernoulli_Jacob.html.