[VA] SRC#004- Fun with Sexagesimal Trigs

[Albert Chan]

Prove A = 2^29 = 536870912:

Checking the edges, using shorthand t# = tan(#°):

tan(A°+B°) = (tA + tB) / (1 - tA tB)

(t60 + tA) (t60 + tB), where A+B=30°
= t60^2 + t60*(tA + tB) + tA tB
= t60^2 + t60*t30*(1 - tA tB) + tA tB
= 3 + 1 - tA tB + tA tB
= 2^2

t15 = tan(45° - 30°)
= (t45 - t30) / (1 + t45 t30)
= (1 - 1/√3) / (1 + 1/√3)
= (√3 - 1) / (√3 + 1)
= (√3 - 1)^2 / (3 - 1)
= (3 + 1 - 2*√3) / 2

-> t15 = 2 - √3
-> center = t60 + t15 = 2

14 pairs of edges and 1 center, all can considered value of 2, thus A = 2^29