View source for User:Johnxyz1

Favorite topic: <cmath>\text{Counting \& Probability}</cmath>for which I am reading AOPS intermediate book on

Favorite color: <cmath>\text{\textcolor{green}{Green}}</cmath>

Favorite software: <cmath>MS\ \text{Excel}</cmath>

Favorite Typesetting Software: <cmath>\text{\LaTeX}</cmath>

Favorite Operating System: Linux (although I am rarely on one)

Below are some stuff I am doing to practice <math>\text{\LaTeX}</math>. That does not mean I know all of it (actually the only ones I do not know yet is the cubic one and the <math>e^{i\pi}</math> one)

<cmath>\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</cmath>
<cmath>e^{i\pi}+1=0</cmath>
<cmath>\sum_{x=1}^{\infty} \frac{1}{x}=2</cmath>
<cmath>\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*}
</cmath>


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>


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!