Happy Birthday!
Happy Birthday Abraham de Moivre, I'm so sorry that I didn't celebrate your birthday until this year!
A few snippets from Wikipedia, sorry that I didn't write them myself:
Born May 26, 1667 in Vitry-le-François, Champagne, France, Died November 27, 1754 in London, England
de Moivre was a Calvinist. He left France after the revocation of the Edict of Nantes (1685) and spent the remainder of his life in England.
It is reported in all seriousness that De Moivre correctly predicted the day of his own death. Noting that he was sleeping 15 minutes longer each day, De Moivre surmised that he would die on the day he would sleep for 24 hours. A simple mathematical calculation quickly yielded the date, November 27, 1754. He did indeed pass away on that day. (Yet another factoid you can use on next year's precalc class, Mr. Karafiol, and I'm sorry if you said this to us and I forgot).
He first discovered the "closed form" expression for Fibonacci numbers linking the nth power of phi to the nth Fibonacci number.
http://en.wikipedia.org/wiki/Abraham_de_Moivre
In honor of his 340th birthday, I'm going to recap all the fun stuff you can do with de Moivre's theorem, I'm so sorry if this isn't enough:
First of all, de Moivre's theorem states that (in complex form): r(cos(θ)+isin(θ))n=rn(cos(nθ)+isin(nθ))
In polar form, it becomes
(r,θ)n=(rn,nθ)
But remember, it also works backwards to find roots of polar coordinates!
So,
*nrt(r,θ)=(nrt(r),((θ+2kπ)/n)
Remember the +2kπ !
*nrt=nth root, unfortunately I can't write it in pretty print, sorry!
I'm sorry if I forgot anything else you can do with de Moivre's theorem.
Oh, it's also National sorry day in Australia, sorry I didn't mention that at the beginning.
A few snippets from Wikipedia, sorry that I didn't write them myself:
Born May 26, 1667 in Vitry-le-François, Champagne, France, Died November 27, 1754 in London, England
de Moivre was a Calvinist. He left France after the revocation of the Edict of Nantes (1685) and spent the remainder of his life in England.
It is reported in all seriousness that De Moivre correctly predicted the day of his own death. Noting that he was sleeping 15 minutes longer each day, De Moivre surmised that he would die on the day he would sleep for 24 hours. A simple mathematical calculation quickly yielded the date, November 27, 1754. He did indeed pass away on that day. (Yet another factoid you can use on next year's precalc class, Mr. Karafiol, and I'm sorry if you said this to us and I forgot).
He first discovered the "closed form" expression for Fibonacci numbers linking the nth power of phi to the nth Fibonacci number.
http://en.wikipedia.org/wiki/Abraham_de_Moivre
In honor of his 340th birthday, I'm going to recap all the fun stuff you can do with de Moivre's theorem, I'm so sorry if this isn't enough:
First of all, de Moivre's theorem states that (in complex form): r(cos(θ)+isin(θ))n=rn(cos(nθ)+isin(nθ))
In polar form, it becomes
(r,θ)n=(rn,nθ)
But remember, it also works backwards to find roots of polar coordinates!
So,
*nrt(r,θ)=(nrt(r),((θ+2kπ)/n)
Remember the +2kπ !
*nrt=nth root, unfortunately I can't write it in pretty print, sorry!
I'm sorry if I forgot anything else you can do with de Moivre's theorem.
Oh, it's also National sorry day in Australia, sorry I didn't mention that at the beginning.
posted by Kevin S. at 5:19 PM
2 Comments:
haha, nicely done.
For those of you keeping track, 340 = 20 * 17.
== pjk
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