Difference between revisions of "User:Johnxyz1"

Revision as of 20:30, 4 July 2024

Favorite topic: $\text{Counting \& Probability}$ for which I am reading AOPS intermediate book on

Favorite color: $\text{\textcolor{green}{Green}}$

Favorite software: $MS\ \text{Excel}$

Favorite Typesetting Software: $\text{\LaTeX}$

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

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

$\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $e^{i\pi}+1=0$ $\sum_{x=1}^{\infty} \frac{1}{x}=2$ $\begin{align*} x &= \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) + \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} \\ & + \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) - \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} - \frac{b}{3a} \\ &\text{(I copied it from another website but I typeset it myself;}\\ &\text{I am pretty sure those are not copyrightable. I still need \textit{years} to even understand this.)}\\ &\text{This is the cubic formula, although it is \textit{rarely} actually used and memorized a lot. The equation is}\\ &ax^3+bx^2+cx+d=0 \end{align*}$

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$",Y_min,Y_max,Ticks(l,Y_tick_density,(Y_tick_density/2),NoZero),Arrows);// if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));} real t, T1, T2; for (T1 = X_min ; T1 <= X_max ; T1 += resolution){ while (! ib(T1) && T1 <= X_max){T1 += resolution;} if(T1 > X_max){break;} T2 = T1; while ( ib(T1) && T1 <= X_max){T1 += resolution;} T1 -= resolution; draw(graph(f,T2,T1,n=2400),graph_color+linewidth(line_width),Arrows); } if (mark_lattice){ for (t = X_min; t <= X_max; ++t){ if (f(t)%1==0 && ib(t)){ dot((t,f(t)),graph_color+linewidth(line_width*4)); } } } dot((0,0));[/asy]$

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Difference between revisions of "User:Johnxyz1"

Revision as of 20:30, 4 July 2024

@@ Line 28: / Line 28: @@
 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>