Structure with Rings of Proportionally Identical Arched Vaults

2002 Arches

2002 ArchesPoster of cutaway view of proportional arch structure surrounded with a pattern of other views

2002 ArchesView from ground level into and across the proportional arch structure center

Aesthetic & Mathematical Inspiration

Escher and Coxeter

M. C. Escher responded to the some of the mathematician H. S. M. Coxeter’s work. Specifically, Escher was fascinated with a figure which “depicts a tessellation of the hyperbolic plane by right triangles” Coxeter Tesselation (Wikipedia). The Circle Limit III, 1959 was a result of M. C. Escher’s ‘Limit’ tesselations. Another is the print Square Limit, 1964. It is in the National Gallery of Art. In both the upper size ‘Limit’ is obvious. Both Escher’s and Coxeter’s creations of limit tesselations of the plane are two dimensional. I was aware of some of Escher’s ‘Limit’ pieces, but not Coxeter’s. In conclusion, my arched form displays how this hyperbolic limit approach can be applied three dimensionally in real world architecture.

The Two Types of Arch Springs in 2002 Arches

Major & Minor

2002 ArchesMajor Column Springing

The major column springing has pairs of primary (1), secondary (2), tertiary (3), and quaternary (4) arch sizes in the order 12344321.

2002 ArchesPlan view of a proportional arched structure

Each vault is a regular 45° 90° 45° right triangle. The result is arches whose sizes are related by the square root of 2. This plan view has one additional outer ‘ring’ of even smaller arched vaults than the arched model. This demonstrates that the ‘rings’ can be extended at will until their relative size is impractically small.

2002 ArchesMinor Column Springing

The minor column springing has pairs of secondary (2), tertiary (3), and quaternary (4) arch sizes in the order 22344322.

2002 ArchesView of vaults

2002 ArchesView of Major Vault Springing

Short Animation of 2002 Arches

Angel’s Eye View