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Can 8 Gothic Arches Forge an Imperial Crown?
Curves & geometry

Can 8 Gothic Arches Forge an Imperial Crown?

BEHIND THE WORK

Can pure mathematical equations forge a 3D Imperial Royal Crown? Tracing across 8 Gothic spire peaks, Fleur-de-lis trefoil crests, 4 transverse dome arches, and a summit Imperial Monde—all drawn in a single unbroken 3D luminous line with exact 0.000mm closure.

Artismathic turns equations into visual art—one function at a time.

#MathArt #ImperialCrown #Geometry #3DArt #DifferentialGeometry #Architecture #Mathematics #Blender3D #Shorts

THE MATHEMATICAL RULE

Rising spire flanks of the composite crown\text{Rising spire flanks of the composite crown}ϕk(u)=kπ4+πu8,r(u)=2.2+0.18sin⁡(πu)\phi_k(u)=\frac{k\pi}{4}+\frac{\pi u}{8},\quad r(u)=2.2+0.18\sin(\pi u)z(u)=−0.8+1.8sin⁡1.6(πu/2),0≤u≤1, k=0,…,7z(u)=-0.8+1.8\sin^{1.6}(\pi u/2),\quad0\leq u\leq1,\ k=0,\ldots,7(x,y,z)=(rcos⁡ϕk,rsin⁡ϕk,z(u))(x,y,z)=(r\cos\phi_k,r\sin\phi_k,z(u))
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