Difference between revisions of "User:Johnxyz1"
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If you want to typeset your own LaTeX equation in a STANDALONE PDF like AOPS does (although they do images), use the standalone documentclass. | If you want to typeset your own LaTeX equation in a STANDALONE PDF like AOPS does (although they do images), use the standalone documentclass. | ||
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| + | ==Miscellaneous=== | ||
| + | On an AMC 8, you can use a ruler to measure things out. Sometimes that works! | ||
Revision as of 15:38, 6 September 2024
Favorite topic: ![\[\text{Counting \& Probability}\]](http://latex.artofproblemsolving.com/b/c/c/bcc448ef67345b970329c6e4921492fb5e4261cc.png)
for which I am reading AOPS intermediate book on
Favorite color: ![\[\text{\textcolor{green}{Green}}\]](http://latex.artofproblemsolving.com/6/c/8/6c8a353f688e76bb1ed7de3f8a0640984e6070c1.png)
Favorite software: ![\[MS\ \text{Excel}\]](http://latex.artofproblemsolving.com/e/2/2/e22328b2e74d53ca51923df707336ccc00545712.png)
Favorite Typesetting Software: ![\[\text{\LaTeX}\]](http://latex.artofproblemsolving.com/6/6/c/66cd718efc440a635cf4cf51cb4f64ecfa2af622.png)
Favorite Operating System: Linux (although I am rarely on one)
Below are some stuff I am doing to practice 
. That does not mean I know all of it (actually the only ones I do not know yet is the cubic one and the 
one)
![\[\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]](http://latex.artofproblemsolving.com/7/c/b/7cbf48dbdce18ee42c347668a9314410de651207.png)
![\[e^{i\pi}+1=0\]](http://latex.artofproblemsolving.com/2/6/c/26cc6b1c790a7db2144e4f5948158479292c55e6.png)
![\[\sum_{x=1}^{\infty} \frac{1}{x}=2\]](http://latex.artofproblemsolving.com/e/e/5/ee5784ec0e67d8ddb8d721443e25e5a727e1cf76.png)
![\begin{align*} x &= \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) + \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} \\ & + \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) - \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} - \frac{b}{3a} \\ &\text{(I copied it from another website but I typeset it myself;}\\ &\text{I am pretty sure those are not copyrightable. I still need \textit{years} to even understand this.)}\\ &\text{This is the cubic formula, although it is \textit{rarely} actually used and memorized a lot. The equation is}\\ &ax^3+bx^2+cx+d=0 \end{align*}](http://latex.artofproblemsolving.com/f/0/8/f08f932bc16a96f0869fb3aafcfc578fde10bda5.png)
Source code for equations:
https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm
Asymptote test (with autoGraph):
![[asy]/* AUTO-GRAPH V-4 beta by PythonNut*/ /* Customizations: feel free to edit */ import math; import graph; /* x maximum and minimum */ int X_max = 10; int X_min =-10; /* y maximum and minimum */ int Y_max = 10; int Y_min = -10; /* linewidth */ real line_width = 0.75; /* graph color */ pen graph_color = magenta; /* special */ bool mark_lattice = false; bool show_grid = true; real X_tick_density = 1; real Y_tick_density = 1; real ratio = 1; real resolution = 0.0001; int size = 300; /* graph function */ real f(real x) { return sin(x)*sin(x); /* type function to be graphed here */ } /* The Code. Do not disturb unless you know what you are doing */ bool ib(real t){ return (Y_min <= f(t) && f(t) <= Y_max); } size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6); xaxis("$x$",X_min,X_max,Ticks(l,X_tick_density,(X_tick_density/2),NoZero),Arrows); yaxis("$y$",Y_min,Y_max,Ticks(l,Y_tick_density,(Y_tick_density/2),NoZero),Arrows);// if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));} real t, T1, T2; for (T1 = X_min ; T1 <= X_max ; T1 += resolution){ while (! ib(T1) && T1 <= X_max){T1 += resolution;} if(T1 > X_max){break;} T2 = T1; while ( ib(T1) && T1 <= X_max){T1 += resolution;} T1 -= resolution; draw(graph(f,T2,T1,n=2400),graph_color+linewidth(line_width),Arrows); } if (mark_lattice){ for (t = X_min; t <= X_max; ++t){ if (f(t)%1==0 && ib(t)){ dot((t,f(t)),graph_color+linewidth(line_width*4)); } } } dot((0,0));[/asy]](http://latex.artofproblemsolving.com/d/2/a/d2ac85a7a4174cadc3d62edf70c10b86c43ea503.png)
If you want to typeset your own LaTeX equation in a STANDALONE PDF like AOPS does (although they do images), use the standalone documentclass.
Miscellaneous=
On an AMC 8, you can use a ruler to measure things out. Sometimes that works!
