Generalized Intrinsic and Extrinsic Lengths in Submanifolds

Abstract

Lamé curves are not some strange specimen in the field of mathematics. Considering them as pure numbers—the outermost values of any row of Pascal’s Triangle—they are dual to the common “geometric mean” approach.

The search for differences or fundamental contrasts between the phenomena of organic or inorganic, of animate or inanimate things, has occupied many men’s minds, while the search for community of principles or essential similitudes has been pursued by few.

D’Arcy Wentworth Thompson