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History of DeMoivre's Theorem

Date: 11/14/97 at 16:18:29
From: Steven Berman
Subject: DeMoivre's theorem

What is the history behind DeMoivre's theorem?  Did he base it on the 
work of predecessors?

Date: 11/23/97 at 18:01:47
From: Doctor Bill
Subject: Re: DeMoivre's theorem


Demoivre discovered his theorem about the same time as it was 
discovered by Johann Lambert (1728-1777), a German mathematician.  
Demoivre and Lambert knew of each other's work, so they may have 
collaborated on it, but for some reason the theorem is named for 

DeMoivre was born in 1667 in France and his family moved to England 
when he was a boy. He was a teacher and in the course of his work he 
got a copy of Isaac Newton's _Principia Mathematica_ and he was 
intrigued by the work of Newton. He would tear out pages of the book 
and carry them around with him so he could study them in his spare 
time from teaching. It was this work by Newton that got him more 
interested in doing mathematical research because he realized that 
Newton's _Principia_ was a major breakthrough in the fields of math 
and the other sciences.

DeMoivre knew Newton and others such as Edmond Halley, and he 
corresponded with them on many topics, including his theorem.  
DeMoivre also did a lot of work in probability and astronomy, which 
includes work in complex numbers, so his theorem may have been a 
result of work in these fields or he may have found his theorem first, 
which then helped him develop his work in these two areas. I don't 
know which came first. So yes, the discovery of his theorem, and a lot 
of his other work, was based on the work of his predecessors, and also 
his contemporaries.

An interesting story about DeMoivre's death is that as he got older he 
realized that he had to sleep about 10 or 15 minutes longer each 
night. The day when that total reached somewhat over 23 hours he slept 
up to the limit of 24 hours and then died in his sleep. It's a story 
that all math historians tell, but do you think it's really true? I 
don't know, but it is an interesting story. He died in 1754.

-Doctor Bill,  The Math Forum
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