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Difference between revisions of "User:Afly"

(→‎Tiny 3D experiments)
(→‎Some of my asymptote creations)
Line 206: Line 206:
 
filldraw(d--e--f--F--E--D--cycle,blue);
 
filldraw(d--e--f--F--E--D--cycle,blue);
 
filldraw(f--g--b--B--G--F--cycle,gray);
 
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 + shift(dir(0))*30;
 +
pair A3 = A2 + shift(dir(0))*30;
 +
pair B1 = (9,0);
 +
pair B2 = B1 + shift(dir(0))*30;
 +
pair B3 = B2 + shift(dir(0))*30;
 +
pair G1 = (9/2,-15/2);
 +
pair G2 = (69/2,-15/2);
 +
pair G3 = (129/2,-15/2);
 +
pair H1 = A1 + (0,5);
 +
pair H2 = A2 + (0,5);
 +
pair H3 = A3 + (0,5);
 +
pair I1 = B1 + (0,3);
 +
pair I2 = B2 + (0,4);
 +
pair I3 = B3 + (0,5);
 +
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);
 +
draw(E1,red);
 +
draw(E2,red);
 +
draw(E3,red);
 +
draw(F1,green);
 +
draw(F2,green);
 +
draw(F3,green);
 +
label("No points",G1);
 +
label("One point",G2);
 +
label("Two points",G3);
 +
label("${\omega}_{A1}$",H1,N,red);
 +
label("${\omega}_{A2}$",H2,N,red);
 +
label("${\omega}_{A3}$",H3,N,red);
 +
label("${\omega}_{B1}$",I1,N,green);
 +
label("${\omega}_{B2}$",I2,N,green);
 +
label("${\omega}_{B3}$",I3,N,green);
 +
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>
 
</asy>
  

Revision as of 21:43, 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 + shift(dir(0))*30; pair A3 = A2 + shift(dir(0))*30; pair B1 = (9,0); pair B2 = B1 + shift(dir(0))*30; pair B3 = B2 + shift(dir(0))*30; pair G1 = (9/2,-15/2); pair G2 = (69/2,-15/2); pair G3 = (129/2,-15/2); pair H1 = A1 + (0,5); pair H2 = A2 + (0,5); pair H3 = A3 + (0,5); pair I1 = B1 + (0,3); pair I2 = B2 + (0,4); pair I3 = B3 + (0,5); 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); draw(E1,red); draw(E2,red); draw(E3,red); draw(F1,green); draw(F2,green); draw(F3,green); label("No points",G1); label("One point",G2); label("Two points",G3); label("${\omega}_{A1}$",H1,N,red); label("${\omega}_{A2}$",H2,N,red); label("${\omega}_{A3}$",H3,N,red); label("${\omega}_{B1}$",I1,N,green); label("${\omega}_{B2}$",I2,N,green); label("${\omega}_{B3}$",I3,N,green); 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:

Colored dodecagon.png






























5/6 size:

Colored dodecagon.png

























2/3 size:

Colored dodecagon.png




















1/2 size:

Colored dodecagon.png















1/3 size:

Colored dodecagon.png










1/6 size:

Colored dodecagon.png





Pentagon 2023 12B Q25 dissmo

Original size:

Pentagon 2023 12B Q25 dissmo.png
























4/5 size:

Pentagon 2023 12B Q25 dissmo.png
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