Difference between revisions of "User:Negativebplusorminus"
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Discovered <math>\sqrt{a+bi}</math> in terms of <math>a</math> and <math>b</math>, without trigonometry (not even using DeMoivre's theorems), and is noted for using mostly correct punctuation, capitalization, and spelling in the [[Art of Problem Solving]] classes (see [[AoPS Online School]] for how this classroom operates). | Discovered <math>\sqrt{a+bi}</math> in terms of <math>a</math> and <math>b</math>, without trigonometry (not even using DeMoivre's theorems), and is noted for using mostly correct punctuation, capitalization, and spelling in the [[Art of Problem Solving]] classes (see [[AoPS Online School]] for how this classroom operates). | ||
==Spirographs== | ==Spirographs== | ||
| + | I have created a great number of spirographs, each interesting and unique. They are contained on my blog. Below is a sample: | ||
<asy> | <asy> | ||
string s="Spirograph by user negativebplusorminus of the Art of Problem Solving forum. Please to not plagiarize; it is illegal and insulting."; | string s="Spirograph by user negativebplusorminus of the Art of Problem Solving forum. Please to not plagiarize; it is illegal and insulting."; | ||
Revision as of 09:18, 3 December 2011
A AoPS member.
Reaper
I got 9th place in the longest game of Reaper, Game 18, and 16th in Game 19. In game 20, I was 20th. I also managed to get a score of 2797 in Boxy, the temporary game that existed on October 4th.
negativebplusorminus
My username is from the quadratic formula, which states that the roots of the equation 
are
![\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]](http://latex.artofproblemsolving.com/d/0/1/d01fd749d6550b117a645c357f01b3c9377e5756.png)
which, when read aloud, is "negativebplusorminus..."
Signature
Signature as of September 1st, 2011:
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![\[\sqrt{a+bi}=\sqrt{\frac{a+\sqrt{a^2+b^2}}{2}}+i\sqrt{\frac{-a+\sqrt{a^2+b^2}}{2}}\]](http://latex.artofproblemsolving.com/1/1/5/115b79b994447d87745338438f7a8dc8bf2c25ad.png)
Pride goes before destruction, a haughty spirit before a fall.
I swear on my honor that my work and my answers are my own; if I received help, credit is given.
Equation
I derived that equation myself, and I am quite proud of it. I have a similar one for the fourth roots of 
which can be derived from inputting that equation into itself.
Notable Work
Discovered 
in terms of 
and 
, without trigonometry (not even using DeMoivre's theorems), and is noted for using mostly correct punctuation, capitalization, and spelling in the Art of Problem Solving classes (see AoPS Online School for how this classroom operates).
Spirographs
I have created a great number of spirographs, each interesting and unique. They are contained on my blog. Below is a sample:
![[asy] string s="Spirograph by user negativebplusorminus of the Art of Problem Solving forum. Please to not plagiarize; it is illegal and insulting."; import graph; size(300); string s="for(real t,real u){return t^2u^3, store as f};"; real f(real t) {return t+log(t^2+t^4+1);} int p=15; int n=45+p; path g=polargraph(f,-200pi,200pi,10000, operator --); draw(g, orange);[/asy]](http://latex.artofproblemsolving.com/a/5/3/a53f363cc7a774840a58ada7d8754d4f9c51fb23.png)
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