Alternative way of computing the squareroot using acos+sin

squareroot.rb

# Mesolabe Compass and Square Roots - Numberphile
# https://www.youtube.com/watch?v=9VVPBS_flOI

v=4; Math.sin(Math.acos(2.0 / (v + 1) - 1.0)) * (v + 1) / 2.0
# 2.0000000000000004 

v=9; Math.sin(Math.acos(2.0 / (v + 1) - 1.0)) * (v + 1) / 2.0
# 3.0 

v=16; Math.sin(Math.acos(2.0 / (v + 1) - 1.0)) * (v + 1) / 2.0
# 4.000000000000002 

v=25; Math.sin(Math.acos(2.0 / (v + 1) - 1.0)) * (v + 1) / 2.0
# 4.999999999999999 

v=36; Math.sin(Math.acos(2.0 / (v + 1) - 1.0)) * (v + 1) / 2.0
# 5.9999999999999964 

v=49; Math.sin(Math.acos(2.0 / (v + 1) - 1.0)) * (v + 1) / 2.0
# 7.000000000000008 

v=100; Math.sin(Math.acos(2.0 / (v + 1) - 1.0)) * (v + 1) / 2.0
# 10.00000000000001 

v=10000; Math.sin(Math.acos(2.0 / (v + 1) - 1.0)) * (v + 1) / 2.0
# 100.00000000000786