User:Negativebplusorminus
A AoPS member, National MathCounts qualifier, and USAJMO qualifier.
Contents
Contest Results
MathCounts
In 2011, as a 7th grader, I didn't qualified for the State Countdown Round. In 2012, as an 8th grader, I lost the National MathCounts.
In the National competition, and scores as the worst.
AMCs
2012: 17 on AMC 10A, 27.5 on AMC 10B, 1 on AIME, 37.5 index for USAJMO. The cutoff was a 999.5, so I did not qualify for the USAJMO. However, I got 0 on the USAJMO. That thing is hard.
Equations for the Roots of the Complex
![\[\sqrt{a+bi}=\sqrt{\frac{a+\sqrt{a^2+b^2}}{2}}+i\sqrt{\frac{-a+\sqrt{a^2+b^2}}{2}}\]](http://latex.artofproblemsolving.com/1/1/5/115b79b994447d87745338438f7a8dc8bf2c25ad.png)
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. I have also found various roots of unity in their radical forms during my spare time.
Spirographs
I have created a great number of spirographs, each interesting and unique. More can be found on my AoPS blog (but you might have to look through a few pages of other stuff, too). To view the entire collection, please visit negativebplusorminus.blogspot.com, but again, you might have to scroll down a bit. Here are some samples:
![[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)
![[asy] import graph; size(300); string s="for(real t,real u){return t^2u^3, store as f};"; real f(real t) {return floor(t);} int p=25; int n=45+p; path g=polargraph(f,-100pi,100pi,281, operator --); draw(g, blue);[/asy]](http://latex.artofproblemsolving.com/9/9/1/991f1fbb461dc3aa2a412ddd6842ec73d7f9ecda.png)
Inspirographs
Another amazing creation of mine. More can be found here (but you might have to look through a few pages of other stuff, too). To view the entire collection, please visit negativebplusorminus.blogspot.com in the near future (the site will be updated soon). Below are a few samples. <asy2> import graph3; import grid3; import palette; size(400,300,IgnoreAspect); defaultrender.merge=true; real f(pair z) {return sin(z.y)*(z.x^2+1)^(0.1*log(z.y^2+1));} surface s=surface(f,(-30,-30),(30,30),70,Spline); s.colors(palette(s.map(zpart),Rainbow())); draw(s,render(compression=Low,merge=true)); grid3(XYZgrid);</asy2> <asy2> import graph3; import grid3; import palette;currentprojection=orthographic(1,5,0.2); size(400,300,IgnoreAspect); defaultrender.merge=true; real f(pair z) {return sin(z.x^2+z.y^2);} surface s=surface(f,(-2.95,-2.95),(2.95,2.95),70,Spline); s.colors(palette(s.map(zpart),Rainbow())); draw(s,render(compression=Low,merge=true)); grid3(XYZgrid);</asy2>
