Tetrad (geometry Puzzle) on:
[Wikipedia]
[Google]
[Amazon]
In
/ref>
by Walter Trump However, their placement surrounds an uncovered hole in the plane. Among solutions without holes, the ones with the fewest possible sides are given by a hexagon identified by Scott Kim as a student at Stanford University. It is not known whether five-sided solutions without holes are possible. :
Kim's solution has 16 vertices, while some of the pentagon solutions have as few as 11 vertices. It is not known whether fewer vertices are possible.
Tetrad-solution6.svg, 11 squares
Tetrad_solution3.svg, 12 squares
Tetrad_solution2.svg, 10 triangles
Tetrad_solution5.svg, 22 triangles
Tetrad_solution4.svg, 26 triangles
Tetrad_solution1.svg, 4 hexagons
Polyform Tetrads
an
7 April 2020
Application of IT in Mathematical Proofs and in Checking of Results of Pupils’ Research
Tetrads and their Counting
Juris ČERŅENOKS, Andrejs CIBULIS {{Geometry-stub * Tessellation
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a tetrad is a set of four simply connected
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the spac ...
disjoint planar regions in the plane, each pair sharing a finite portion of common boundary. It was named by Michael R. W. Buckley in 1975 in the Journal of Recreational Mathematics
The ''Journal of Recreational Mathematics'' was an American journal dedicated to recreational mathematics, started in 1968. It had generally been published quarterly by the Baywood Publishing Company, until it ceased publication with the last issue ...
. A further question was proposed that became a puzzle, whether the 4 regions could be congruent, with or without ''holes'', other enclosed regions.Martin Gardner, ''Penrose Tiles to Trapdoor ciphers'', 1989, p.121-12/ref>
Fewest sides and vertices
The solutions with four congruent tiles include some with five sides.Further Questions about Tetradsby Walter Trump However, their placement surrounds an uncovered hole in the plane. Among solutions without holes, the ones with the fewest possible sides are given by a hexagon identified by Scott Kim as a student at Stanford University. It is not known whether five-sided solutions without holes are possible. :
Kim's solution has 16 vertices, while some of the pentagon solutions have as few as 11 vertices. It is not known whether fewer vertices are possible.
Congruent polyform solutions
Gardner offered a number of polyform ( polyomino,polyiamond
A polyiamond (also polyamond or simply iamond, or sometimes triangular polyomino) is a polyform whose base form is an equilateral triangle. The word ''polyiamond'' is a back-formation from ''diamond'', because this word is often used to describe ...
, and polyhex) solutions, with no holes.
References
External links
Polyform Tetrads
an
7 April 2020
Application of IT in Mathematical Proofs and in Checking of Results of Pupils’ Research
Tetrads and their Counting
Juris ČERŅENOKS, Andrejs CIBULIS {{Geometry-stub * Tessellation