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 a2 + b2 + c2 = 3d2 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 3 are constructed.
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - 29 Jan 2020|
|Event||Basic and Applied Sciences Interdisciplinary Conference 2017, BASIC 2017 - , Indonesia|
Duration: 18 Aug 2017 → 19 Aug 2017