Sphericon
Encyclopedia
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The sphericon is a three-dimensional solid with one side and two edges, discovered by Colin Roberts, of Hertfordshire
Hertfordshire
Hertfordshire is a ceremonial and non-metropolitan county in the East region of England. The county town is Hertford.The county is one of the Home Counties and lies inland, bordered by Greater London , Buckinghamshire , Bedfordshire , Cambridgeshire and...
, England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
.
It may be constructed from a bicone
Bicone
A bicone or dicone is the three-dimensional geometric shape swept by revolving an isosceles triangle around its edge of unequal length. Alternatively, one can view a bicone as the surface created by joining two identical right circular cones base-to-base....
(a double cone
Cone (geometry)
A cone is an n-dimensional geometric shape that tapers smoothly from a base to a point called the apex or vertex. Formally, it is the solid figure formed by the locus of all straight line segments that join the apex to the base...
) with an apex
Apex (geometry)
In geometry, an apex is the vertex which is in some sense the highest of the figure to which it belongs.*In an isosceles triangle, the apex is the vertex where the two sides of equal length meet, opposite the unequal third side....
of 90 degrees, by splitting the bicone along a plane through both apexes, rotating one of the two halves by 90 degrees, and reattaching the two halves.
Alternatively, the surface of a sphericon can be formed by cutting and gluing a paper template in the form of four circular wedges (with angles of
degrees) joined edge-to-edge http://www.pjroberts.com/sphericon/images/nets/4n.jpg.
Ian Stewart
Ian Stewart (mathematician)
Ian Nicholas Stewart FRS is a professor of mathematics at the University of Warwick, England, and a widely known popular-science and science-fiction writer. He is the first recipient of the , awarded jointly by the LMS and the IMA for his work on promoting mathematics.-Biography:Stewart was born...
of the University of Warwick
University of Warwick
The University of Warwick is a public research university located in Coventry, United Kingdom...
and Tony Phillips of Stony Brook University have also investigated the sphericon, and it has helped the latter develop theories about maze
Maze
A maze is a tour puzzle in the form of a complex branching passage through which the solver must find a route. In everyday speech, both maze and labyrinth denote a complex and confusing series of pathways, but technically the maze is distinguished from the labyrinth, as the labyrinth has a single...
s.
External links
- Sphericon Homepage. It contains images, text and animation that give a fuller view of the sphericon family.
- Paper model of a sphericon Make a sphericon
- Sphericon variations using regular polygonRegular polygonA regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...
s with different numbers of sides - A Sphericon in Motion showing the characteristic wobbly motion as it rolls across a flat surface