Difference between revisions of "User:Negativebplusorminus"
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− | A AoPS member. | + | A AoPS member, National MathCounts qualifier, and USAJMO qualifier. |
− | + | ==Contest Results== | |
− | == | + | ===MathCounts=== |
− | I | + | 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== | ==negativebplusorminus== | ||
My username is from the [[Quadratic formula | quadratic formula]], which states that the roots of the equation <math>ax^2+bx+c=0</math> are | My username is from the [[Quadratic formula | quadratic formula]], which states that the roots of the equation <math>ax^2+bx+c=0</math> are | ||
<cmath>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</cmath> | <cmath>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</cmath> | ||
which, when read aloud, is "negativebplusorminus..." | which, when read aloud, is "negativebplusorminus..." | ||
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− | <cmath>\sqrt{a+bi}=\sqrt{\frac{a+\sqrt{a^2+b^2}}{2}}+i\sqrt{\frac{-a+\sqrt{a^2+b^2}}{2}}</cmath> | + | ==Equations for the Roots of the Complex== |
− | + | <cmath>\sqrt{a+bi}=\sqrt{\frac{a+\sqrt{a^2+b^2}}{2}}+i\sqrt{\frac{-a+\sqrt{a^2+b^2}}{2}}</cmath> | |
− | + | 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. | |
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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. | ||
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==Spirographs== | ==Spirographs== | ||
− | I have created a great number of spirographs, each interesting and unique. More can be found | + | 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: |
<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,-200pi,200pi,10000, operator --); | path g=polargraph(f,-200pi,200pi,10000, operator --); | ||
draw(g, orange);</asy> | 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 [http://www.artofproblemsolving.com/Forum/blog.php?u=93546& here] (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]. 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> | |
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Revision as of 08:21, 12 April 2012
A AoPS member, National MathCounts qualifier, and USAJMO qualifier.
Contents
[hide]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 are which, when read aloud, is "negativebplusorminus..."
Equations for the Roots of the Complex
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. Here are some samples:
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>