- initial quarry
- cap 2.PNG (199.65 KiB) Viewed 1062 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.
- added lines to match shapes
- area of a elipse2.PNG (166.06 KiB) Viewed 1062 times
