Continuous proportion relations and functions

✍ Scribed by Walter Benz

• Book ID: 104643503
• Publisher: Springer
• Year: 1990
• Tongue: English
• Weight: 345 KB
• Volume: 36
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00150784

✦ Synopsis

Dedicated to HeImut Salzmann on the occasion of his 60th birthday

ABSTRACT. Continuous proportion functions in three or more dimensions are classical.

. Let Z" be the set of all n-dimensional boxes of R" (n ~> 2) and let '~' be an equivalence relation on E". Two boxes Q, Q'e z" are called reciprocal if they are homothetic and if there exists an edge of Q which is congruent to an edge of Q'. Reciprocal rectangles are important in architecture; examples can be found in many building designs since ancient times (see, among others, Le Corbusier [8]). The following theorem will be proved: THEOREM 1. Suppose that (Z", ,-~) satisfies: