Wednesday, July 24, 2019

Aesthetics in Mathematics by Christopher Havens

I made a picture for any of you to look at, so long as you graph it by computer or graphing utility first. This bunch of mess is beautiful. It's a graphical version of the Sierpinski triangle, but I used only circles to achieve what appear to be triangles. You'll notice some straight lines forming rectangles. These serve to border, or "frame" my art. To see the picture, view all equations in the same window... In other words, let them overlap. Enjoy.

let sqrt(x) be the square root of x. Stuff like 26^2 means 26 squared (26 times 26)

1) x^2+y^2=26^2
2) x^2+(y+26)^2=26^2
3) x^2+y^2=13^2
4) x^2+(y+13)^2=(13/2)^2
5) (x-13sqrt(3))^2+(y+13)^2=26^2
6) (x-13sqrt(3))^2+(y-13)^2=26^2
7) x^2+(y-26)^2=26^2
8) (x+13sqrt(3))^2+(y-13)^2=26^2
9) (x+13sqrt(3))^2+(y+13)^2=26^2
10) (x-(13sqrt(3))/2)^2+(y-(13/2))^2=(13/2)^2
11) (x+(13sqrt(3))/2)^2+(y-(13/2))^2=(13/2)^2
12) (x+(39sqrt(3))/4)^2+(y-(39/4))^2=(13/4)^2
13) (x-(39sqrt(3))/4)^2+(y-(39/4))^2=(13/4)^2
14) (x+(13sqrt(3))/4)^2+(y-(39/4))^2=(13/4)^2
15) (x-(13sqrt(3))/4)^2+(y-(39/4))^2=(13/4)^2
16) x^2+(y+(39/4))^2=(13/4)^2
17) (x-(13sqrt(3))/2)^2+y^2=(13/4)^2
18) (x+(13sqrt(3))/2)^2+y^2=(13/4)^2
19) (x+(13sqrt(3))/4)^2+(y+(39/4))^2=(13/4)^2
20) (x-(13sqrt(3))/4)^2+(y+(39/4))^2=(13/4)^2
21) (x+(91sqrt(3))/8)^2+(y-(91/8))^2=(13/8)^2
22) x^2+(y+(91/4))^2=(13/8)^2
23) (x-(91sqrt(3))/8)^2+(y-(91/8))^2=(13/8)^2
24) (x+(65sqrt(3))/8)^2+(y-(91/8))^2=(13/8)^2
25) (x+(39sqrt(3))/8)^2+(y-(91/8))^2=(13/8)^2
26) (x+(13sqrt(3))/8)^2+(y-(91/8))^2=(13/8)^2
27) (x-(13sqrt(3))/8)^2+(y-(91/8))^2=(13/8)^2
28) (x-(39sqrt(3))/8)^2+(y-(91/8))^2=(13/8)^2
29) (x-(65sqrt(3))/8)^2+(y-(91/8))^2=(13/8)^2
30) (x+(13sqrt(3))/4)^2+(y-(13/2))^2=(13/8)^2
31) (x+(39sqrt(3))/4)^2+(y-(13/2))^2=(13/8)^2
32) (x-(13sqrt(3))/4)^2+(y-(13/2))^2=(13/8)^2
33) (x-(39sqrt(3))/4)^2+(y-(13/2))^2=(13/8)^2
34) (x+(13sqrt(3))/2)^2+(y+(13/4))^2=(13/8)^2
35) (x-(13sqrt(3))/2)^2+(y+(13/4))^2=(13/8)^2
36) (x+(65sqrt(3))/8)^2+(y-(13/8))^2=(13/8)^2
37) (x-(65sqrt(3))/8)^2+(y-(13/8))^2=(13/8)^2
38) (x+(39sqrt(3))/8)^2+(y-(13/8))^2=(13/8)^2
39) (x-(39sqrt(3))/8)^2+(y+(65/8))^2=(13/8)^2
40) (x+(39sqrt(3))/8)^2+(y+(65/8))^2=(13/8)^2
41) (x-(39sqrt(3))/8)^2+(y-(13/8))^2=(13/8)^2
42) (x+(13sqrt(3))/8)^2+(y+(65/8))^2=(13/8)^2
43) (x-(13sqrt(3))/8)^2+(y+(65/8))^2=(13/8)^2
44) (x+(13sqrt(3))/4)^2+(y+13)^2=(13/8)^2
45) (x-(13sqrt(3))/4)^2+(y+13)^2=(13/8)^2
46) (x+(13sqrt(3))/8)^2+(y+(143/8))^2=(13/8)^2
47) (x-(13sqrt(3))/8)^2+(y+(143/8))^2=(13/8)^2
48) x^2+y^2=29^2
49) x^2+y^2=33^2
50) x^2+y^2=39^2
51) x^2+y^2=41^2
52) x^2+y^2=43^2
53) x^2+y^2=45^2
54) x^2+y^2=47^2
55) x^2+y^2=52^2
56) y=44
57) y=-44
58) y=30
59) y=-30
60) y=36
61) y=-36
62) x=48
63) x=-48
64) x=54
65) x=-54
66) x= 62
67) x=-62

Christopher

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