Equilateral Triangles in 3D with Integer Coordinates
Equilateral Triangles in 3D with Integer Coordinates
The number of equilateral triangles with integer coordinates in a cube of size depends on the "minimal" equilateral triangles defined in such a cube and all the transformations of such triangles. This Demonstration shows the minimal triangles along with the total number of equilateral triangles for = 1 to 5.
n
n
Details
Details
For more information, see:
E. J. Ionascu, "A Parametrization of Equilateral Triangles Having Integer Coordinates," Journal of Integer Sequences, 10(6), 2007 Article 07.6.7, www.cs.uwaterloo.ca/journals/JIS.
E. J. Ionascu, "Counting All Equilateral Triangles in {0, 1,..., n}^3," math.colstate.edu/ejionascu. (Oct 18, 2007)
"Number of Equilateral Triangles with Coordinates (x, y, z) in the Set {0, 1, ..., n}," (sequence A102698), in The On-Line Encyclopedia of Integer Sequences (copyright N. J. A. Sloane), www.research.att.com/~njas/sequences. (Oct 18, 2007)
External Links
External Links
Permanent Citation
Permanent Citation
Rodrigo A. Obando, Eugen Ionascu
"Equilateral Triangles in 3D with Integer Coordinates"
http://demonstrations.wolfram.com/EquilateralTrianglesIn3DWithIntegerCoordinates/
Wolfram Demonstrations Project
Published: October 19, 2007