Difference between revisions of "User:Afly"

Revision as of 22:23, 10 December 2023

About Afly

Friends with Yrock and ConfidentFlamingo

User # 1013218 Profile

Some of my asymptote creations

These are a random collection of diagrams and text that I have made. YOU ARE ALLOWED TO USE THESE IMAGES AND/OR TEXT IN YOUR PAGES OR USE THEM FOR REFERENCE.

Triangle

$[asy] pair A=(0,0); pair B=(2,0); pair C=(1,sqrt(3)); draw(A--B--C); draw(A--C--B); [/asy]$

$\text{That is a equilateral triangle with side length 2!}$

$\text{The height is } \sqrt{2^2-1^2} = \sqrt{3}$

$\text{The area is } 2 \cdot \sqrt{3} \cdot \frac{1}{2} = \boxed{\sqrt{3}}$

$\dots$

$[asy] pair A=(0,0); pair B=(0,2); pair C=(1,1); draw(A--B--C); draw(A--C--B); [/asy]$

$\text{Homework: calculate the area}$

ANSWER: LOOK ONLY WHEN THE PROBLEM IS COMPLETED >>> THIS IS ONLY TO CHECK YOUR ANSWER

$\text{This is an isosceles right triangle. It has side length }\sqrt{2}$

$\text{It has an height of } \frac{\sqrt{2}}{\sqrt{2}} = 1 \text{ and a base of } \sqrt{2} \cdot \sqrt{2} = 2$

$\text{The area is } 1 \cdot 2 \cdot \frac{1}{2} = \boxed{1}$ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Pythagorean

$[asy] pair A=(0,0); pair B=(0,3); pair C=(4,0); draw(A--B--C--A,black+linewidth(1)); pair D=(-3,0); pair E=(-3,3); draw(A--B--E--D--A,red+linewidth(1)); pair F=(0,-4); pair G=(4,-4); draw(A--C--G--F--A,orange+linewidth(1)); pair H=(7,4); pair I=(3,7); draw(B--C--H--I--B,yellow+linewidth(1)); draw(A--B--C--A,black+linewidth(1)); [/asy]$ $\text{The pythagorean theorem: red plus orange equals yellow}$

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Isosceles Trapezoid

$[asy] pair A=(0,0); pair B=(10,0); pair C=(6,8); pair D=(2,8); pair E=(30/7,40/7); draw(A--B--C--D--A,black+linewidth(5)); fill(A--E--D--cycle,red); fill(B--E--C--cycle,yellow); dot(A); dot(B); dot(C); dot(D); dot(E); label(A,'A',SW); label(B,'B',SE); label(C,'C',NE); label(D,'D',NW); label(E,'E',S); draw(A--E--C,blue+linewidth(2)); draw(B--E--D,blue+linewidth(2)); [/asy]$ $\text{Given that } \overline{AB} \parallel \overline{DC} \text{ , prove that } A_\triangle AED = A_\triangle BEC .$

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Hexagon (In AMC 2023 10A #24)

$[asy] unitsize(1cm); unitsize(5cm); draw(scale(3)*polygon(6)); filldraw(shift(dir(0)*2+dir(120)*3/7)*polygon(6), lightgray); filldraw(shift(dir(60)*2+dir(180)*3/7)*polygon(6), lightgray); filldraw(shift(dir(120)*2+dir(240)*3/7)*polygon(6), lightgray); filldraw(shift(dir(180)*2+dir(300)*3/7)*polygon(6), lightgray); filldraw(shift(dir(240)*2+dir(0)*3/7)*polygon(6), lightgray); filldraw(shift(dir(300)*2+dir(60)*3/7)*polygon(6), yellow); pair A = (0,0) + 3 * dir(300); pair B = A + 3/7 *dir(60); pair C = B + 1 * dir(180); pair D = C + 3/7 * dir(240); pair E = C + 4/7 * dir(120); pair F = E + 3/7 * dir(240); pair G = F + 4/7 * dir(240); pen p = red+linewidth(6); draw(A--B--C--D--cycle,p); draw(C--E--F--D--cycle,p); draw(F--G--D--cycle,p); label("1",(B + C)/2,dir(90)); label("1",(A + D)/2,dir(270)); label("3/7",(A + B)/2,dir(330)); label("3/7",(C + D)/2,dir(330)); label("4/7",(C+E)/2,dir(30)); label("3/7",(E+F)/2,dir(150)); label("4/7",(F+D)/2,dir(30)); label("4/7",(F+G)/2,dir(150)); label("4/7",(G+D)/2,dir(270)); [/asy]$

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Tiny 3D experiments

$[asy] unitsize(60); pair A = (0,0); pair B = A + dir(0); pair C = A + dir(60); pair D = A + dir(120); pair E = A + dir(180); pair F = A + dir(240); pair G = A + dir(300); filldraw(A--B--C--D--cycle,orange); filldraw(A--D--E--F--cycle,blue); filldraw(A--F--G--B--cycle,gray); [/asy]$

$[asy] unitsize(40); pair A = (0,0); pair B = A + dir(0); pair C = A + dir(60); pair D = A + dir(120); pair E = A + dir(180); pair F = A + dir(240); pair G = A + dir(300); filldraw(A--B--C--D--cycle,orange); filldraw(A--D--E--F--cycle,blue); filldraw(A--F--G--B--cycle,gray); [/asy]$

$[asy] unitsize(60); pair A = (0,0); pair B = A + dir(0); pair b = A + 2/3*dir(0); pair C = A + dir(60); pair c = A + 2/3*dir(60); pair D = A + dir(120); pair d = A + 2/3*dir(120); pair E = A + dir(180); pair e = A + 2/3*dir(180); pair F = A + dir(240); pair f = A + 2/3*dir(240); pair G = A + dir(300); pair g = A + 2/3*dir(300); filldraw(A--e--f--g--cycle,orange); filldraw(A--g--b--c--cycle,blue); filldraw(A--c--d--e--cycle,gray); filldraw(b--c--d--D--C--B--cycle,orange); filldraw(d--e--f--F--E--D--cycle,blue); filldraw(f--g--b--B--G--F--cycle,gray); [/asy]$

Circle diagrams

A collection of stuff having to do with circles

Intersection points

$[asy] unitsize(6); pair A1 = (0,0); pair A2 = A1 + dir(0)*30; pair A3 = A2 + dir(0)*30; pair B1 = (9,0); pair B2 = B1 + dir(0)*30; pair B3 = B2 + dir(0)*30; pair G1 = (9/2,-15/2); pair G2 = G1 + dir(0)*30; pair G3 = G2 + dir(0)*30; pair H1 = A1 + dir(90)*5; pair H2 = A2 + dir(90)*5; pair H3 = A3 + dir(90)*5; pair I1 = B1 + dir(90)*3; pair I2 = B2 + dir(90)*4; pair I3 = B3 + dir(90)*5; pair J1 = A1 + dir(120)*5; pair J2 = A2 + dir(120)*5; pair J3 = A3 + dir(120)*5; pair K1 = B1 + dir(60)*3; pair K2 = B2 + dir(60)*4; pair K3 = B3 + dir(60)*5; pair N1 = G1 + dir(270)*9/2; pair N2 = G2 + dir(270)*9/2; pair N3 = G3 + dir(270)*9/2; path E1 = circle(A1,5); path E2 = circle(A2,5); path E3 = circle(A3,5); path F1 = circle(B1,3); path F2 = circle(B2,4); path F3 = circle(B3,5); path L1 = A1--J1; path L2 = A2--J2; path L3 = A3--J3; path M1 = B1--K1; path M2 = B2--K2; path M3 = B3--K3; path O1 = A1--B1; path O2 = A2--B2; path O3 = A3--B3; draw(E1,red); draw(E2,red); draw(E3,red); draw(F1,green); draw(F2,green); draw(F3,green); draw(L1,red); draw(L2,red); draw(L3,red); draw(M1,green); draw(M2,green); draw(M3,green); draw(O1,blue); draw(O2,blue); draw(O3,blue); label("No points",G1); label("One point",G2); label("Two points",G3); label("$r_{A1}+r_{B1}<d_1$",N1); label("$r_{A2}+r_{B2}=d_2$",N2); label("$r_{A3}+r_{B3}>d_3$",N3); label("$r_{B1}$",M1,dir(330),green); label("$r_{B2}$",M2,dir(330),green); label("$r_{B3}$",M3,dir(330),green); label("$d_1$",O1,dir(240),blue); label("$d_2$",O2,dir(240),blue); label("$d_3$",O3,dir(240),blue); pair [] D1 = intersectionpoints(E2,F2); pair [] D2 = intersectionpoints(E3,F3); pair C1 = D1[0]; pair C2 = D2[0]; pair C3 = D2[1]; dot(C1,blue); dot(C2,blue); dot(C3,blue); label("$I_2$",C1,dir(0),blue); label("$I_{3a}$",C2,dir(0),blue); label("$I_{3b}$",C3,dir(0),blue); [/asy]$

Created files

(Using desmos)

Colored dodecagon

Original file:

5/6 size:

2/3 size:

1/2 size:

1/3 size:

1/6 size:

Pentagon 2023 12B Q25 dissmo

Original size:

4/5 size:

Page

Toolbox

Search

Difference between revisions of "User:Afly"

Revision as of 22:23, 10 December 2023

Contents

About Afly

Some of my asymptote creations

Triangle

Pythagorean

Isosceles Trapezoid

Hexagon (In AMC 2023 10A #24)

Tiny 3D experiments

Circle diagrams

Intersection points

Created files

Colored dodecagon

Pentagon 2023 12B Q25 dissmo

@@ Line 217: / Line 217: @@
 unitsize(6);
 pair A1 = (0,0);
-pair A2 = A1 + shift(dir(0))*30;
+pair A2 = A1 + dir(0)*30;
-pair A3 = A2 + shift(dir(0))*30;
+pair A3 = A2 + dir(0)*30;
 pair B1 = (9,0);
-pair B2 = B1 + shift(dir(0))*30;
+pair B2 = B1 + dir(0)*30;
-pair B3 = B2 + shift(dir(0))*30;
+pair B3 = B2 + dir(0)*30;
 pair G1 = (9/2,-15/2);
-pair G2 = (69/2,-15/2);
+pair G2 = G1 + dir(0)*30;
-pair G3 = (129/2,-15/2);
+pair G3 = G2 + dir(0)*30;
-pair H1 = A1 + (0,5);
+pair H1 = A1 + dir(90)*5;
-pair H2 = A2 + (0,5);
+pair H2 = A2 + dir(90)*5;
-pair H3 = A3 + (0,5);
+pair H3 = A3 + dir(90)*5;
-pair I1 = B1 + (0,3);
+pair I1 = B1 + dir(90)*3;
-pair I2 = B2 + (0,4);
+pair I2 = B2 + dir(90)*4;
-pair I3 = B3 + (0,5);
+pair I3 = B3 + dir(90)*5;
+pair J1 = A1 + dir(120)*5;
+pair J2 = A2 + dir(120)*5;
+pair J3 = A3 + dir(120)*5;
+pair K1 = B1 + dir(60)*3;
+pair K2 = B2 + dir(60)*4;
+pair K3 = B3 + dir(60)*5;
+pair N1 = G1 + dir(270)*9/2;
+pair N2 = G2 + dir(270)*9/2;
+pair N3 = G3 + dir(270)*9/2;
 path E1 = circle(A1,5);
 path E2 = circle(A2,5);
@@ Line 237: / Line 246: @@
 path F2 = circle(B2,4);
 path F3 = circle(B3,5);
+path L1 = A1--J1;
+path L2 = A2--J2;
+path L3 = A3--J3;
+path M1 = B1--K1;
+path M2 = B2--K2;
+path M3 = B3--K3;
+path O1 = A1--B1;
+path O2 = A2--B2;
+path O3 = A3--B3;
 draw(E1,red);
 draw(E2,red);
@@ Line 243: / Line 261: @@
 draw(F2,green);
 draw(F3,green);
+draw(L1,red);
+draw(L2,red);
+draw(L3,red);
+draw(M1,green);
+draw(M2,green);
+draw(M3,green);
+draw(O1,blue);
+draw(O2,blue);
+draw(O3,blue);
 label("No points",G1);
 label("One point",G2);
 label("Two points",G3);
-label("${\omega}_{A1}$",H1,N,red);
+label("$r_{A1}+r_{B1}<d_1$",N1);
-label("${\omega}_{A2}$",H2,N,red);
+label("$r_{A2}+r_{B2}=d_2$",N2);
-label("${\omega}_{A3}$",H3,N,red);
+label("$r_{A3}+r_{B3}>d_3$",N3);
-label("${\omega}_{B1}$",I1,N,green);
+label("$r_{B1}$",M1,dir(330),green);
-label("${\omega}_{B2}$",I2,N,green);
+label("$r_{B2}$",M2,dir(330),green);
-label("${\omega}_{B3}$",I3,N,green);
+label("$r_{B3}$",M3,dir(330),green);
+label("$d_1$",O1,dir(240),blue);
+label("$d_2$",O2,dir(240),blue);
+label("$d_3$",O3,dir(240),blue);
 pair [] D1 = intersectionpoints(E2,F2);
 pair [] D2 = intersectionpoints(E3,F3);
@@ Line 261: / Line 291: @@
 dot(C3,blue);
 label("$I_2$",C1,dir(0),blue);
-label("$I_{3A}$",C2,dir(0),blue);
+label("$I_{3a}$",C2,dir(0),blue);
-label("$I_{3B}$",C3,dir(0),blue);
+label("$I_{3b}$",C3,dir(0),blue);
 </asy>