Hexlet
Also called Soddy's Hexlet. Consider three mutually tangent Spheres 
, 
, and 
. Thenconstruct a chain of Spheres tangent to each of , , and threading and interlocking with the
ring. Surprisingly, every chain closes into a ``necklace'' after six Spheres regardless of wherethe first Sphere is placed. This is a special case of Kollros' Theorem. The centers of a Soddy hexlet always lie on an Ellipse (Ogilvy 1990, p. 63).
References
Coxeter, H. S. M. ``Interlocking Rings of Spheres.'' Scripta Math. 18, 113-121, 1952. Gosset, T. ``The Hexlet.'' Nature 139, 251-252, 1937. Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., pp. 49-50, 1976. Morley, F. ``The Hexlet.'' Nature 139, 72-73, 1937. Ogilvy, C. S. Excursions in Geometry. New York: Dover, pp. 60-72, 1990. Soddy, F. ``The Bowl of Integers and the Hexlet.'' Nature 139, 77-79, 1937. Soddy, F. ``The Hexlet.'' Nature 139, 154 and 252, 1937.
- Oscillation
- Oscillation Land
- Osculating Circle
- Osculating Curves
- Osculating Interpolation
- Osculating Plane
- Osculating Sphere
- Osedelec Theorem
- Ostrowski's Inequality
- Ostrowski's Theorem
- Otter's Tree Enumeration Constants
- Outdegree
- Outer Automorphism Group
- Outer Product
- Oval
- Oval of Descartes
- Ovals of Cassini
- Overlapping Resonance Method
- Oversampling
- Ovoid
- Paasche's Index
- Packing
- Packing Density
- p-adic Number
- Padovan Sequence