Interesting Esoterica

Pascal's Pyramid Or Pascal's Tetrahedron

Web page by Jim Nugent
  • Published in 1990
  • Added on
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A lattice of octahedra and tetrahedra (oct-tet lattice) is a useful paradigm for understanding the structure of Pascal's pyramid, the 3-D analog of Pascal's triangle. Notation for levels and coordinates of elements, a standard algorithm for generating the values of various elements, and a ratio method that is not dependent on the calculation of previous levels are discussed. Figures show a bell curve in 3 dimensions, the association of elements to primes and twin primes, and the values of elements mod(x) through patterns arranged in triangular plots. It is conjectured that the largest factor of any element is less than the level index.

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keywords
3-D,Galton Board,JimNugent,Pascal,Pascal's tetrahedron,Pascal's triangle,Sierpinski,Stephen Mueller,True BASIC,bell curve,binomial,expansion,geometry,mathematics,oct-tet,octahedron,prime numbers,taxicab,taxicab geometry,tetrahedron,three dimensional,trinomial,twin prime,twin primes

BibTeX entry

@online{item31,
	title = {Pascal's Pyramid Or Pascal's Tetrahedron},
	author = {Jim Nugent},
	url = {https://web-beta.archive.org/web/20160410142410/http://buckydome.com/math/Article2.htm http://buckydome.com/math/Article2.htm},
	urldate = {2013-06-25},
	abstract = {A lattice of octahedra and tetrahedra (oct-tet lattice) is a useful paradigm for understanding the structure of Pascal's pyramid, the 3-D analog of Pascal's triangle. Notation for levels and coordinates of elements, a standard algorithm for generating the values of various elements, and a ratio method that is not dependent on the calculation of previous levels are discussed. Figures show a bell curve in 3 dimensions, the association of elements to primes and twin primes, and the values of elements mod(x) through patterns arranged in triangular plots. It is conjectured that the largest factor of any element is less than the level index.},
	comment = {},
	keywords = {3-D,Galton Board,JimNugent,Pascal,Pascal's tetrahedron,Pascal's triangle,Sierpinski,Stephen Mueller,True BASIC,bell curve,binomial,expansion,geometry,mathematics,oct-tet,octahedron,prime numbers,taxicab,taxicab geometry,tetrahedron,three dimensional,trinomial,twin prime,twin primes},
	collections = {easily-explained},
	year = 1990
}