(*ThelinearGoldenRatioϕ,1-dimension,andtheplanarGoldenAngle2π/ϕ^2,2-dimensions,arebothwell-knownmathematicalquantitiesthathavebeenwrittenaboutforhundredsofyearsandarethesubjectofmanybooksandarticles.Itisthereforeverystrangethatnobody(untilnow)haseverdiscussedmovingupjustonemoredimensiontoformthe3-dimensionalGoldenSolidAngle.Bycreatingasphereoftotalsurfacearea1+ϕ,andthencalculatingthesolidanglesubtendedbytheunityarea,wefindthattheGoldenSolidAnglehasavalueof4π/ϕ^2steradians-recallthatthePlanarSolidAnglehasavalueof2π/ϕ^2radians.HenceanumericalvaluefortheGoldenSolidAngleis:*)
In[]:=
N[(4*Pi)/(GoldenRatio^2),20]
Out[]=
4.7999264594573066445
(*Orverynearly4.8steradians.ThisgivestheradiusoftheGoldenSphereas0.4564...whereastheradiusoftheGoldenCircleis0.4166...*)