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occurred Aug 22, 2023 at 12:20

deleted 4 characters in body

edited Aug 22, 2023 at 9:56

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I want to select four points lie on the sphere (x-1)^2 + (y-3)^2 + (z-5)^2 = (5* Sqrt[3])^2 so that its coordinates are integer numbers to make a regular tetrahedron. I tried

ClearAll[a, b, r, c]; a = 1; b = 3; c = 5; r = (5* Sqrt[3])^2;Sqrt[3]; ss = Subsets[{x, y, z} /. Solve[{(x - a)^2 + (y - b)^2 + (z - c)^2 == r^2}, {x, y, z}, Integers], {4}]; list = Select[ ss, ( EuclideanDistance[#[[1]], #[[2]]] == EuclideanDistance[#[[1]], #[[3]]] == EuclideanDistance[#[[1]], #[[4]]] == EuclideanDistance[#[[2]], #[[4]]] == EuclideanDistance[#[[2]], #[[3]]] == EuclideanDistance[#[[3]], #[[4]]] && Det[{#[[1]] - #[[2]], #[[1]] - #[[3]], #[[1]] - #[[4]]}] != 0 &) ]

About ten minutes, I can not get the result? How can I get the result?

I want to select four points lie on the sphere (x-1)^2 + (y-3)^2 + (z-5)^2 = (5* Sqrt[3])^2 so that its coordinates are integer numbers to make a regular tetrahedron. I tried

ClearAll[a, b, r, c]; a = 1; b = 3; c = 5; r = (5* Sqrt[3])^2; ss = Subsets[{x, y, z} /. Solve[{(x - a)^2 + (y - b)^2 + (z - c)^2 == r^2}, {x, y, z}, Integers], {4}]; list = Select[ ss, ( EuclideanDistance[#[[1]], #[[2]]] == EuclideanDistance[#[[1]], #[[3]]] == EuclideanDistance[#[[1]], #[[4]]] == EuclideanDistance[#[[2]], #[[4]]] == EuclideanDistance[#[[2]], #[[3]]] == EuclideanDistance[#[[3]], #[[4]]] && Det[{#[[1]] - #[[2]], #[[1]] - #[[3]], #[[1]] - #[[4]]}] != 0 &) ]

About ten minutes, I can not get the result? How can I get the result?

I want to select four points lie on the sphere (x-1)^2 + (y-3)^2 + (z-5)^2 = (5* Sqrt[3])^2 so that its coordinates are integer numbers to make a regular tetrahedron. I tried

ClearAll[a, b, r, c]; a = 1; b = 3; c = 5; r = 5* Sqrt[3]; ss = Subsets[{x, y, z} /. Solve[{(x - a)^2 + (y - b)^2 + (z - c)^2 == r^2}, {x, y, z}, Integers], {4}]; list = Select[ ss, ( EuclideanDistance[#[[1]], #[[2]]] == EuclideanDistance[#[[1]], #[[3]]] == EuclideanDistance[#[[1]], #[[4]]] == EuclideanDistance[#[[2]], #[[4]]] == EuclideanDistance[#[[2]], #[[3]]] == EuclideanDistance[#[[3]], #[[4]]] && Det[{#[[1]] - #[[2]], #[[1]] - #[[3]], #[[1]] - #[[4]]}] != 0 &) ]

About ten minutes, I can not get the result? How can I get the result?

added 30 characters in body; edited title

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edited Aug 22, 2023 at 9:50

Laurenso

1.3k
4
14

How can I select four points on a sphere to make a regular tetrahedron so that its coordinates are integer numbers?

I want to select four points lie on the sphere (x-1)^2 + (y-3)^2 + (z-5)^2 = 15^2(5* Sqrt[3])^2 so that its coordinates are integer numbers to make a regular tetrahedron. I tried

ClearAll[a, b, r, c]; a = 1; b = 3; c = 5; r = 15;(5* Sqrt[3])^2; ss = Subsets[{x, y, z} /. Solve[{(x - a)^2 + (y - b)^2 + (z - c)^2 == r^2}, {x, y, z}, Integers], {4}]; list = Select[ ss, ( EuclideanDistance[#[[1]], #[[2]]] == EuclideanDistance[#[[1]], #[[3]]] == EuclideanDistance[#[[1]], #[[4]]] == EuclideanDistance[#[[2]], #[[4]]] == EuclideanDistance[#[[2]], #[[3]]] == EuclideanDistance[#[[3]], #[[4]]] && Det[{#[[1]] - #[[2]], #[[1]] - #[[3]], #[[1]] - #[[4]]}] != 0 &) ]

About ten minutes, I can not get the result? How can I get the result?

How can I select four points on a sphere to make a tetrahedron so that its coordinates are integer numbers?

I want to select four points lie on the sphere (x-1)^2 + (y-3)^2 + (z-5)^2 = 15^2 so that its coordinates are integer numbers. I tried

ClearAll[a, b, r, c]; a = 1; b = 3; c = 5; r = 15; ss = Subsets[{x, y, z} /. Solve[{(x - a)^2 + (y - b)^2 + (z - c)^2 == r^2}, {x, y, z}, Integers], {4}]; list = Select[ ss, ( EuclideanDistance[#[[1]], #[[2]]] == EuclideanDistance[#[[1]], #[[3]]] == EuclideanDistance[#[[1]], #[[4]]] == EuclideanDistance[#[[2]], #[[4]]] == EuclideanDistance[#[[2]], #[[3]]] == EuclideanDistance[#[[3]], #[[4]]] && Det[{#[[1]] - #[[2]], #[[1]] - #[[3]], #[[1]] - #[[4]]}] != 0 &) ]

About ten minutes, I can not get the result? How can I get the result?

How can I select four points on a sphere to make a regular tetrahedron so that its coordinates are integer numbers?

I want to select four points lie on the sphere (x-1)^2 + (y-3)^2 + (z-5)^2 = (5* Sqrt[3])^2 so that its coordinates are integer numbers to make a regular tetrahedron. I tried

ClearAll[a, b, r, c]; a = 1; b = 3; c = 5; r = (5* Sqrt[3])^2; ss = Subsets[{x, y, z} /. Solve[{(x - a)^2 + (y - b)^2 + (z - c)^2 == r^2}, {x, y, z}, Integers], {4}]; list = Select[ ss, ( EuclideanDistance[#[[1]], #[[2]]] == EuclideanDistance[#[[1]], #[[3]]] == EuclideanDistance[#[[1]], #[[4]]] == EuclideanDistance[#[[2]], #[[4]]] == EuclideanDistance[#[[2]], #[[3]]] == EuclideanDistance[#[[3]], #[[4]]] && Det[{#[[1]] - #[[2]], #[[1]] - #[[3]], #[[1]] - #[[4]]}] != 0 &) ]

About ten minutes, I can not get the result? How can I get the result?

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asked Aug 22, 2023 at 2:43

Laurenso

1.3k
4
14

How can I select four points on a sphere to make a tetrahedron so that its coordinates are integer numbers?

I want to select four points lie on the sphere (x-1)^2 + (y-3)^2 + (z-5)^2 = 15^2 so that its coordinates are integer numbers. I tried

ClearAll[a, b, r, c]; a = 1; b = 3; c = 5; r = 15; ss = Subsets[{x, y, z} /. Solve[{(x - a)^2 + (y - b)^2 + (z - c)^2 == r^2}, {x, y, z}, Integers], {4}]; list = Select[ ss, ( EuclideanDistance[#[[1]], #[[2]]] == EuclideanDistance[#[[1]], #[[3]]] == EuclideanDistance[#[[1]], #[[4]]] == EuclideanDistance[#[[2]], #[[4]]] == EuclideanDistance[#[[2]], #[[3]]] == EuclideanDistance[#[[3]], #[[4]]] && Det[{#[[1]] - #[[2]], #[[1]] - #[[3]], #[[1]] - #[[4]]}] != 0 &) ]

About ten minutes, I can not get the result? How can I get the result?

diophantine-equations