Open AccessConstruction of parametric equation for equilateral triangle vertices with integer coordinates
Author(s) -
M. Yumia,
Hengki Tasman
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1442/1/012037
Subject(s) - equilateral triangle , integer (computer science) , combinatorics , mathematics , plane (geometry) , parametric statistics , diophantine equation , discrete mathematics , geometry , computer science , statistics , programming language
In this paper we explore equilateral triangles with integer coordinates vertices lying on the plane a x + b y + c z = 0 where coefficients a, b, c satisfy the Diophantine equation a 2 + b 2 + c 2 = 3d 2 for some integer!. If the plane is translated with any integer translation vector, we find planes which also containing equilateral triangles with integer coordinates vertices. Based on that knowledge from some previous studies, another parametric equations for integer coordinates vertices of equilateral triangle in ℝ 3 are constructed.