llipse Circumference "Did you know that the 20-sided polygon provides a more accurate value than Ramanujan's approximation formula?"

 

Ellipse Circumference "Did you know that the 20-sided polygon provides a more accurate value than Ramanujan's approximation formula?"

From the perspective of elliptic integration

Test when the semi-major axis is 1 and the semi-minor axis is 0.5.

16-sided ratio → (2π (circle perimeter) / regular 16-sided perimeter) × 16-sided perimeter = 4.844242023

20-sided ratio → (2π / regular 20-sided perimeter) × 20-sided perimeter = 4.84422551

Ramanujan's approximation formula = 4.8442105

Ellipse integral = 4.84422508

 

Ellipse > 3600-sided > 20-sided ratio > Integral > Ramunujan's approximation formula