Proof of Pi

[BMAD]

Assume we know nothing of Pi's actual value. Apparently, we think it is some random number generated by a calculator every time the Pi button is pressed. All we know that is 2*Radius*Pi is the circumference of a circle and pi*radius*radius is area. Use a unit circle to prove that Pi is >3 and <4.

[LVan Toren]

Circumference of circle < perimeter of circumscribed square

2*Radius*Pi < 4* Side
but Side=2*Radius
so Pi < 4
Circumference of circle > Perimeter of inscribed regular hexagon
2*Radius*Pi > 6 * Side
but Side = Radius
thus Pi > 3

[bonanova]

<tongue in cheek>

Since it has long been accepted that the proof is in the pudding, not in the pi, perhaps the puzzle is not solvable.

<remove tongue from cheek>