Geodesic Math and How to Use It

Geodesics is a technique for making shell-like structures that hold themselves up without supporting columns, by exploiting a three-way grid of tensile forces. They are very strong and can be very large — the geodesic bubble built for the United States exhibits at Expo '67 in Montréal encloses some 6 million cubic feet, roughly three-fourths of a sphere 250 feet in diameter, yet weighs only about 600 tons. Despite their potential, in the quarter-century since Fuller introduced them they had not been used widely.

Core structure

• What This Book Is
• Weight vs. Tension
• Appendix to Chapter 1: Tensegrity Prisms
• Spherical Tensegrities
• Equilibrium
• Elasticity Multiplication

Main ideas

• Geodesics make shell-like structures that stand without columns by exploiting a three-way grid of tensile forces.
• Conventional structure relies on beams supported by posts; geodesic/tensegrity structure replaces this with distributed tension.
• The simplest tensegrity (Diagram 1.5) consists of 3 compressive struts and 9 tensile tendons (a tendon being the portion of the tensile network between two adjacent strut ends).
• The three-strut tensegrity of Chapter 1 is asymmetrical, with triangular ends and rhomboidal sides.
• When the tension members of a tensegrity are taut, the structure is in a state of equilibrium.

Why it matters

The book turns Fuller's geometric intuitions into usable engineering mathematics, giving builders the equations behind geodesic domes and tensegrity structures. Its illustrations — from the Montréal Expo bubble to the thought-experiment of a half-mile sphere that would float on a one-degree temperature difference — make the extraordinary strength-to-weight ratios of these forms concrete.

See Also

• Synergetics — the foundational geometry behind geodesic and tensegrity structures

• Introduction to Geometry — companion classical-geometry reference in the corpus

• Dome Cookbook of Geodesic Geometry — Kruschke's hand-lettered builder's primer deriving the same chord-factor math jargon-free

• People connected to this geodesic mathematics: Kenneth Snelson, Joseph Clinton, Peter Jon Pearce

• Hugh Kenner — author of this manual

• Geoship (Geoship) — related organization

• Artifacts of R. Buckminster Fuller, Vol. 3: The Geodesic Revolution, Part 1, 1947–1959 (Artifacts of R. Buckminster Fuller, Vol. 3: The Geodesic Revolution, Part 1, 1947–1959) — related work

• A Fuller Explanation (A Fuller Explanation) — related work

• Artifacts of R. Buckminster Fuller, Vol. 4: The Geodesic Revolution, Part 2, 1960-1983 (Artifacts of R. Buckminster Fuller, Vol. 4: The Geodesic Revolution, Part 2, 1960-1983) — related work

• Duncan Stuart (Duncan Stuart) — related figure

• Goldberg–Coxeter Construction (Goldberg–Coxeter Construction) — related concept

• Geodesic Structures (Geodesic Structures) — related concept

• Montreal Biosphère (Expo '67 U.S. Pavilion) (Montreal Biosphère (Expo '67 U.S. Pavilion)) — related place

Sources

• geodesic_math_and_how_to_use_it/ — book project directory (repo-local source tree)
• geodesic_math_and_how_to_use_it/index.md — synthesis index for the source project