Plenty of Pi to Go Around
Plenty of Pi to Go Around - supporting image
The parts of a circle can be rearranged to resemble a parallelogram. The more parts the circle is cut into, the closer it gets, BUT it will never make it. There is always a bit of curveture on the top and bottom. Therefore, pi is infinite. . .
The Paradoxically Infinite Slice of Pi
The Paradoxically Infinite Slice of Pi - supporting images
No matter what size circle, the ratio of circumference to diameter is always pi (3.14...). The black string above each circle shows the diameter length of the corresponding circle. That length fits 3 full times around the edge. The orange string on the edge shows this amount. The red lines that define angle A show the ends of a diameter length. Angle B measures the same in each circle, about 16.5 degrees. Angle B is 0.14 times the amount of angle A, and the blue section of the circumference is 0.14 times the amount of one diameter length. I like to angle B the paradoxically infinte slice of pi!
Pi are Squared? Pi IS Squared.
Pi are Squared? Pi IS Squared - supporting images
No matter the size of the circle, its area is just over 3 times the amount of the radius squared. The shaded square shows the radius squared. The green box around the circle shows what 4 times the radius squared would be. The area of the circle is clearly less than that because of the leftover space in each corner. The blue shape to the left shows how those leftover parts (outside the circle, but inside the box) compare to the radius squared. The leftovers are a little less than the radius squared. The area of the circle is a little more than 3 times the radius squared. . . maybe about 0.14 times more. . .