๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Rational tetrahedra with edges in arithmetic progression

โœ Scribed by C. Chisholm; J.A. MacDougall

Book ID
104024486
Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
315 KB
Volume
111
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

โœฆ Synopsis

This paper discusses tetrahedra with rational edges forming an arithmetic progression, focussing specifically on whether they can have rational volume or rational face areas. Several infinite families are found which have rational volume, a face can have rational area only if its edges are themselves in arithmetic progression, and a tetrahedron can have at most one such rational face area.

๐Ÿ“œ SIMILAR VOLUMES

Arithmetic Progressions in Sequences wit
Arithmetic Progressions in Sequences with Bounded Gaps
โœ Tom C Brown; Donovan R Hare ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 528 KB

Let G(k, r) denote the smallest positive integer g such that if 1=a 1 , a 2 , ..., a g is a strictly increasing sequence of integers with bounded gaps a j+1 &a j r, 1 j g&1, then [a 1 , a 2 , ..., a g ] contains a k-term arithmetic progression. It is shown that G(k, 2) > -(k & 1)ร‚2 ( 43 ) (k&1)ร‚2 ,