http://www.mapleprimes.com/questions/142591-How-To-Find-Vertices-Of-An-Equilateral en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 21:36:20 GMT Wed, 10 Jun 2026 21:36:20 GMT The latest answers and comments added to the Question, How to find vertices of an equilateral triangle knowing coordinates of centroid? http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/142591-How-To-Find-Vertices-Of-An-Equilateral http://www.mapleprimes.com/questions/142591-How-To-Find-Vertices-Of-An-Equilateral?ref=Feed:MaplePrimes:How to find vertices of an equilateral triangle knowing coordinates of centroid?:Comments#answer142594 <p>It is easy to prove that there are no such triangles in the plane. In space there are infinitely many such triangles. The smallest will be <strong>(3, 0, 0), (0, 3, 0), (0, 0, 3)</strong> .&nbsp;Its easy to find a simple search.</p> <p>PS.&nbsp;It can be found without brute force if you know that in any cube, there are 3 vertices of the cube, forming an equilateral triangle.</p> <p>It is easy to prove that there are no such triangles in the plane. In space there are infinitely many such triangles. The smallest will be <strong>(3, 0, 0), (0, 3, 0), (0, 0, 3)</strong> .&nbsp;Its easy to find a simple search.</p> <p>PS.&nbsp;It can be found without brute force if you know that in any cube, there are 3 vertices of the cube, forming an equilateral triangle.</p> 142594 Thu, 24 Jan 2013 23:13:59 Z Kitonum Kitonum http://www.mapleprimes.com/questions/142591-How-To-Find-Vertices-Of-An-Equilateral?ref=Feed:MaplePrimes:How to find vertices of an equilateral triangle knowing coordinates of centroid?:Comments#answer142595 See your question http://www.mapleprimes.com/questions/136025-How-Do-I-Find-Coordinates-Vertices-Of . An arbitrary equilateral triangle with integer coordinates can be translated by homothety and shift in such a way that its centroid becomes (1,1,1). See your question http://www.mapleprimes.com/questions/136025-How-Do-I-Find-Coordinates-Vertices-Of . An arbitrary equilateral triangle with integer coordinates can be translated by homothety and shift in such a way that its centroid becomes (1,1,1). 142595 Thu, 24 Jan 2013 23:16:05 Z Markiyan Hirnyk Markiyan Hirnyk http://www.mapleprimes.com/questions/142591-How-To-Find-Vertices-Of-An-Equilateral?ref=Feed:MaplePrimes:How to find vertices of an equilateral triangle knowing coordinates of centroid?:Comments#answer142617 <p>Thanks for all helps.</p> <p>Thanks for all helps.</p> 142617 Fri, 25 Jan 2013 11:39:00 Z toandhsp toandhsp http://www.mapleprimes.com/questions/142591-How-To-Find-Vertices-Of-An-Equilateral?ref=Feed:MaplePrimes:How to find vertices of an equilateral triangle knowing coordinates of centroid?:Comments#comment142596 The last step can easily be realized in Maple. Hint: (3/4,7/8,-9/5)*40-(29,34,-73)=(1,1,1). The last step can easily be realized in Maple. Hint: (3/4,7/8,-9/5)*40-(29,34,-73)=(1,1,1). 142596 Thu, 24 Jan 2013 23:37:36 Z Markiyan Hirnyk Markiyan Hirnyk