Difference between revisions of "User:Negativebplusorminus"

(Spirographs)
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I derived that equation myself, and I am quite proud of it.  I have a similar one for the fourth roots of <math>a+bi</math> 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.
 
I derived that equation myself, and I am quite proud of it.  I have a similar one for the fourth roots of <math>a+bi</math> 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==
 
==Spirographs==
I have created a great number of spirographs, each interesting and unique.  More can be found on my [http://www.artofproblemsolving.com/Forum/blog.php?u=93546& AoPS blog] (but you might have to look through a few pages of other stuff, too).  To view the entire collection, please visit [http://www.negativebplusorminus.blogspot.com negativebplusorminus.blogspot.com].  Here are some samples:
+
I have created a great number of spirographs, each interesting and unique.  More can be found on my [http://www.artofproblemsolving.com/Forum/blog.php?u=93546& AoPS blog] (but you might have to look through a few pages of other stuff, too).  To view the entire collection, please visit [http://www.negativebplusorminus.blogspot.com negativebplusorminus.blogspot.com], but again, you might have to scroll down a bit.  Here are some samples:
 
<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.";
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path g=polargraph(f,-100pi,100pi,281, operator --);
 
path g=polargraph(f,-100pi,100pi,281, operator --);
 
draw(g, blue);</asy>
 
draw(g, blue);</asy>
 +
 
==Inspirographs==
 
==Inspirographs==
 
Another amazing creation of mine.  More can be found [http://www.artofproblemsolving.com/Forum/blog.php?u=93546& here] (but you might have to look through a few pages of other stuff, too).
 
Another amazing creation of mine.  More can be found [http://www.artofproblemsolving.com/Forum/blog.php?u=93546& here] (but you might have to look through a few pages of other stuff, too).

Revision as of 09:23, 12 April 2012

A AoPS member, National MathCounts qualifier, and USAJMO qualifier.

Contest Results

MathCounts

In 2011, as a 7th grader, I qualified for the State Countdown Round. In 2012, as an 8th grader, I qualified for National MathCounts. Hopefully, this page will be updated when I know the results of the National competition.

AMCs

2012: 117 on AMC 10A, 127.5 on AMC 10B, 8 on AIME, 207.5 index for USAJMO. The cutoff was a 204.5, so I qualified for the USAJMO. Hopefully, this page will be updated when I know the results of the USAJMO.

negativebplusorminus

My username is from the quadratic formula, which states that the roots of the equation $ax^2+bx+c=0$ are \[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\] which, when read aloud, is "negativebplusorminus..."

Equations for the Roots of the Complex

\[\sqrt{a+bi}=\sqrt{\frac{a+\sqrt{a^2+b^2}}{2}}+i\sqrt{\frac{-a+\sqrt{a^2+b^2}}{2}}\] I derived that equation myself, and I am quite proud of it. I have a similar one for the fourth roots of $a+bi$ 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] [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]

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. 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>