Archimedes' π — Polygon Bounds Explorer
Inscribed and circumscribed regular
n
-gons squeezing in on π from both sides
Inscribed — lower bound
Circle
Circumscribed — upper bound
Number of sides
n
6
3
4
6 ★
12
24
48
96 ★
Lower bound
inscribed perimeter ÷ d
3.000000
True π
exact value
3.141593
Upper bound
circumscribed perimeter ÷ d
3.464102
3.0000
< π <
3.4641
Gap:
0.4641
— shrinks toward 0 as
n
grows
▶ Watch the bounds converge