(12C Platinum) Length of An Ellipse

[Albert Chan]

(07-07-2019 04:06 PM)Albert Chan Wrote:  a=50, b=10, FIX 5, we get ellipse perimeter = 210.10028, absolute error = -0.00017

FYI, absolute error based on ellipse perimeter AGM2 method:

(50, 10) repeated AGM:
→ (30 , √(500) ≅ 22.36067977), gap = 7.63932023
→ (26.18033989, 25.90020064), gap = 0.28013825
→ (26.04027027, 26.03989355), gap = 0.00037672
→ (26.04008191, 26.04008191)

effective radius = (30² - (0.5)(7.63932023²) - (1)(0.28013825²) - (2)(0.00037672²)) / 26.04008191 = 33.43852445

ellipse perimeter = 2 * pi * 33.43852445 = 210.1004455 ≅ 210.10045