Lemniscates and How Not to Square the Circle

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Lemniscates and How Not to Square the Circle Empty Lemniscates and How Not to Square the Circle

Post  John on Thu Feb 09, 2012 1:03 pm

The symbol for infinity "∞" is almost identical to the Cartesian graph of a lemniscate (Lt. lemniscatus, decorated by ribbons) and exactly identical to an intoxicated "8." The symbol was first introduced by the English mathematician John Wallis in his 1665 Arithmetica Infinitorum. Conjectures abound as to the reason for Wallis' choice. Some argue that the figure resembled a Roman symbol for 'many,' others believe that the Greek omega "ω" was the inspiration as the final letter of their alphabet. Still others speculate that Wallis was simply tired of attempting to finish his first infinite series...

Despite Wallis' obvious patience, his last nerve was repeatedly sauntered over by our old friend Thomas Hobbes. Hobbes thought himself a capable mathematician and attempted to solve several intractable problems, most famously, the squaring of the circle. His many attempts led to ridicule by illustrious mathematicians of the day, the most vehement being Wallis. My favorite example, compliments of former NCSU faculty member, Douglas Jesseph's Squaring the Circle:

In a dispute with Hobbes over the use of an infinite series to produce a quarter ratio, Wallis claimed that he need not believe in the infinite to use it in a proof, but could simply suppose it as a
material conditional. Furthermore, in direct response to Hobbes, Wallis stated,

Whether a thing be or not be is not concerned, but whether they can be supposed, as in, when I say, if Hobbes were a mathematician, he would argue otherwise; I do not affirm that he is...only that if he were what he is not, he would not do as he doeth!

Wallis, "thou art the man!"

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