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purplemath.com
Limits and infinity are weird.

#limits #area #perimeter #circle #square #approximation #circumference #pi #piequals4 #purplemath
A six panel comic, with two frames in each of three rows. Panel 1: Draw a circle. (A circle is shown, with diameter d = 1, having a red perimeter, and filled in with light blue.) Panel 2: Draw a square around it. Perimeter equals 4. (A black square has been drawn around the circle.] Panel 3: Remove corners. Perimeter is still 4. (Each of the corners of the original square has been cut out, with the "corner" of the removed portion touching the circle.) Panel 4: Remove more corners. Perimeter is still 4. (The process is repeated between each pair of points that touches the circle.( Panel 5: Repeat to infinity. (The corner-removal process is shown at a much later stage, with the black jagged-edged rectilinear line now very close to the red circumference of the circle.) Panel 6: π = 4. Problem, Archimedes? (A grinning cartoon face is shown.)
November 13, 2025 at 5:50 PM