Mathematics and Optimal Form

Scientific American Library Series #13

by Stefan Hildebrandt, Anthony Tromba

Book by Hildebrandt, Stefan, Tromba, Anthony J.

Genres: Mathematics, Science

215 pages, Hardcover

First published December 1, 1984

Reviews

[Curtis Penner · Rating 2 out of 5]

The book was very good with historical information, but the focus is on bubbles.

This is a mathematical book, not meant for the mathematical as it had very little mathematics. It was a publication derived from the Scientific American magazine.

[Michael · Rating 5 out of 5]

The german edition of 'Mathematics and Optimal Form' is a fascinating and well explained excursion into the world of optimal 2D and 3D shapes. It does not contain formal proofs but many concise informal proofs, not neglecting the discussion of difficulties such as the neccessity to prove the existence of optima.
The shortest path problem, Steiner tree problem, geodesics and shapes of constant curvature with minimal tension get special attention. Also applications and historical discussions take a broad place in this popular science book. The last chapter, on dynamics, is to my taste however not well written and difficult to follow for someone who is not trained in physics. Perhaps it was not very wise to confine this very broad topic to only a single chapter.
But all in all, an inspiring popular science book that can widely be understood by laymen without loosing precision.

[Tadeusz Pudlik]

Beautifully illustrated and occasionally informative, but quite light on the actual mathematics. The book's subject matter falls somewhere in between Philip Ball's The Self Made Tapestry: Pattern Formation in Nature and Courant's What Is Mathematics?: An Elementary Approach to Ideas and Methods. I found it less enjoyable than either of those classics, though.

The principal focus is on the calculus of variations, and especially minimal surfaces as physical models for soap films.