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Architectural Geometry

Gothic arches, Islamic patterns, tensegrity, and structural beauty

Explore the mathematics behind architectural masterpieces. From the pointed arches of Gothic cathedrals to the intricate muqarnas vaults of Islamic architecture, every great building encodes deep geometric principles. These interactive demos let you manipulate the forces, proportions, and patterns that shape the built world.

Arches & Structural Forms

The geometry of load-bearing curves and force transfer in historic architecture.

01
Gothic Pointed Arches
Construct equilateral, lancet, drop, Tudor, and horseshoe arches with adjustable voussoirs and columns.
03
Gaudi Catenary Arches
Simulate Gaudi's hanging chain method. Drag anchor points, add weights, and flip to see the ideal compressive arch.
08
Flying Buttress Forces
Visualize how Gothic cathedrals transfer vault thrust through flying buttresses to external piers with force diagrams.

Islamic Geometric Art

Sacred geometry, tessellation, and three-dimensional ornament from the Islamic tradition.

02
Islamic Star Patterns
Generate interlacing star patterns with adjustable symmetry (6, 8, 10, 12-fold) inspired by girih tile geometry.
10
Muqarnas Vault Construction
Build 3D stalactite vaulting with cascading tiers of niche-like cells. Rotate and explore the honeycomb geometry.

Structural Systems

Modern structural geometry: tension, compression, and doubly-curved surfaces.

04
Tensegrity Structures
Explore floating compression within continuous tension. Build prisms, icosahedra, and towers in 3D.
05
Geodesic Dome Builder
Subdivide an icosahedron at frequencies 1V-4V. Toggle wireframe, solid, and dual hexagonal views.
07
Hyperbolic Paraboloid Shell
Rotate a saddle surface (z = x^2 - y^2) and view it as surface, ruled lines, contours, or wireframe.

Proportion & Pattern

Mathematical harmony in architectural design and organic facade generation.

09
Fibonacci in Architecture
See the golden ratio in facade proportions, spiral construction, Fibonacci grids, and floor plan layouts.
06
Voronoi Facade Generator
Generate organic Voronoi tessellation facades like the Beijing Water Cube. Click to add seed points.