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# Gauss' work in his life watch

1. Can anyone list as many mathematical topics you can think of that is related to Gauss? I'm currently producing an essay and have provided many of his work, but i'm running out of ideas on what I can have in it.
Heres a list of what i have:
his 17 sided polygon can be constructed with ruler and compass
his proof of the fundamental theorem of algebra
Every number can be represented by at most the sum of 3 triangle numbers.
summing a series using Gauss's method (writing series out twice but the second one is in reverse order)
These are all that I can think of and was wondering does anyone know any more topics, that i havent mentioned and can include in my essay and I can research about?
Thanks.
2. (Original post by Zhen Lin)
List of topics named after Gauss.
Thanks
3. It's hardly visible on that list by Zhen, but the Divergence theorem is a hugely important result by Gauss.
4. Complex numbers.
5. Theorem Egregium
6. Elliptical curves and p dic arithmetic.
7. Thanks guys
8. Complex analysis, set theory.
9. Hey, as I went deeper into my research I came across a complex number referred to as Gaussian integer. I was just wondering why is it named after Gauss? What exactly did he do? I'm trying to find out right now but haven't found anything so far.
10. (Original post by JBKProductions)
Hey, as I went deeper into my research I came across a complex number referred to as Gaussian integer. I was just wondering why is it named after Gauss? What exactly did he do? I'm trying to find out right now but haven't found anything so far.
Gaussian integers are complex numbers a+bi such that a and b are both integers (so essentially the lattice/integer points in the Argand plane). From the wiki page it looks like he used them for quartic reciprocity.
11. (Original post by GHOSH-5)
Gaussian integers are complex numbers a+bi such that a and b are both integers (so essentially the lattice/integer points in the Argand plane). From the wiki page it looks like he used them for quartic reciprocity.
Thanks
12. I think I'm too young to have really studied it very much, but didn't he prove that any polynomial with it's highest power being n have n roots? The most amazing thing is, he proved it when he was like 17 I think?
13. (Original post by Tallon)
I think I'm too young to have really studied it very much, but didn't he prove that any polynomial with it's highest power being n have n roots? The most amazing thing is, he proved it when he was like 17 I think?
You mean the Fundamental Theorem of Algebra? I think he was around 21 when he proved it, but I could easily be wrong.
14. (Original post by GHOSH-5)
You mean the Fundamental Theorem of Algebra? I think he was around 21 when he proved it, but I could easily be wrong.

im sure it was 17/18. I remember reading it in an fp2 book and then realising how much I havn't done in my life compared to him at the same age lol
15. (Original post by Tallon)
im sure it was 17/18. I remember reading it in an fp2 book and then realising how much I havn't done in my life compared to him at the same age lol
One that I found quite amazing was, when he was 18 or 19, he showed that you can construct any regular n-gon, where n is a Fermat prime (and also where n is a product of distinct Fermat primes and a power of 2).
16. (Original post by Tallon)
im sure it was 17/18. I remember reading it in an fp2 book and then realising how much I havn't done in my life compared to him at the same age lol
He was born in 1777 and the date for the FTA (which was the subject of his doctorate) is usually given as 1799.

http://www-gap.dcs.st-and.ac.uk/~his...ies/Gauss.html
http://en.wikipedia.org/wiki/Fundame...rem_of_algebra

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