Swiss postage stamp, issued in 1994 for the International Congress of Mathematicians in Zurich, featuring Jakob Bernoulli and illustrating his “golden theorem”.
Jakob Bernoulli, head of a dynasty of brilliant scholars, was one of the world’s leading mathematicians. Bernoulli’s great work, Ars Conjectandi, published in 1713, included a profound result that he established “after having meditated on it for twenty years”. He called it his “golden theorem”. It is known today as the law of large numbers, and it was the first limit theorem in probability, and the first attempt to apply probability outside the realm of games of chance [TM225 or search for “thatsmaths” at irishtimes.com].
Continue reading ‘Bernoulli’s Golden Theorem and the Law of Large Numbers’
for s=1.1 (red), s=1.01 (blue) and s=1.001 (black).
is chosen randomly with probability 
of being either plus one or minus one. It follows from the Kolmogorov three-series theorem that the series is “almost surely” convergent.
is hopelessly inefficient. With one million throws of the needle we might expect to get an approximation accurate to about three digits. The idea is more of philosophical than of practical interest. Buffon never envisaged it as a means of computing 
ThatsMaths 