f90fde8c-2f31-4a56-ba52-7c3ea03241ca 7 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

a 1 : b 0.5 : 21 line

General parametric equation x y Ellipse x 2^a 2^/ y 2^b 2^/ + 1 - :

ε = eccentricity ε 1 b 2^a 2^/ - sqrt : 0.866025

3 sqrt 2 / 0.866025

point on ellipse [±]

θ X a b * b 2^a 2^θ tan (2^* + sqrt / :

θ Y a b * a 2^b 2^θ tan (2^/ + sqrt / :

Geometric construct

θ 0.25 π * :

C 0 0.125 0 0.125 - 00 0.125 - 0 0.125 052 mat :

XY 00 θ X θ Y 22 mat :

b 000 b 22 mat :

a 00 a 022 mat :

p θ X θ Y 12 mat :

p 0.447214 0.447214 12 mat

plot Ellipse XY C p b a 61 sys :

plot

Ellipse Perimeter

Ellipse Area

a 1 :

b 0.5 :

ε 1 b 2^a 2^/ - sqrt :

b

A π a * b * :

a

p 4 a * 1 ε 2^t sin (2^* - sqrt t 0 π 2 / int * :

A 1.570796

p 4.84422411027381

For more "Ellipse maths": read from literature. In Smath, we don't use perimeter approximations !