lune of Hippocrates,

Anything goes, but keep it seemly...

lune of Hippocrates,

Postby StrmCkr » Thu Aug 13, 2020 9:44 pm

cap 2.PNG
initial quarry
cap 2.PNG (199.65 KiB) Viewed 68 times


lune of Hippocrates: many a brave souls wonder into the FALSE mans hopes of squaring the circle....

this entire construct is created using a circle with the radius of 1.

the light green triangle by shape{see 2nd attachment for clearer lines of separation} has the same area of the dark orange shapes = the purple arc has the same area of the green triangle - the dark orange + purple arc triangle. {thus the purple arc is square-able}

from here the fun begins:
the dark purple arc = dark green arch + dark yellow shape : prove the area of Green and yellow arc sections are both square-able.

dark green portion x 2 has the same surface area of the light blue ellipse and is potentially square-able

light blue ellipse = dark red semi sphere shape in area {just below the black triangle}

what does all that translate too ?
= the area of a circle is potentially square-able.

8 x light blue ellipse + 8x black triangle + 4 x light grey triangle = area of a circle.

the number remains transcendental as the light blue ellipse happens to be the square of a square product and rounding errors will always extrapolate as its a multiplied by a factor of 8.


area of a elipse2.PNG
added lines to match shapes
area of a elipse2.PNG (166.06 KiB) Viewed 68 times
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 1163
Joined: 05 September 2006

Re: lune of Hippocrates,

Postby Mathimagics » Sat Aug 22, 2020 11:48 pm

This is what happens when you put 5 lunatics together in the same (square) room ...
User avatar
Mathimagics
2017 Supporter
 
Posts: 1575
Joined: 27 May 2015
Location: Canberra

Re: lune of Hippocrates,

Postby StrmCkr » Sun Aug 23, 2020 5:15 am

Nice one math magic, but on the more serious side i did find potential proof of the area of the blue area as square of area =
0.009786........ Infinite repeating

Fun fun
Some do, some teach, the rest look it up.
User avatar
StrmCkr
 
Posts: 1163
Joined: 05 September 2006


Return to Coffee bar