## 330 Reputation

7 years, 100 days

## How can I select four vertices of a list...

Maple

I have a list L:=[[0,0,0], [1,0,0], [1,1,0], [0,1,0], [0,0,1], [1,0,1], [1,1,1], [0,1,1]] (8 vertices of a cube). How can I select four vertices of the list to make a regular tetrahedron?

## How do I write the equation of the phere...

I see from here http://www.mapleprimes.com/questions/220829-How-Do-I-Write-The-Equation-Of-The-Plane to write the equation of a sphere. I tried
restart; L := [[[0, 0, 0], [2, 0, 0], [0, 2, 0], [2, 2, 0]], [[0, 0, 0], [2, 0, 0], [0, 2, 0], [0, 0, 2]], [[0, 0, 0], [2, 0, 0], [0, 2, 0], [2, 0, 2]], [[0, 0, 0], [2, 0, 0], [0, 2, 0], [0, 2, 2]], [[0, 0, 0], [2, 0, 0], [0, 2, 0], [2, 2, 2]], [[0, 0, 0], [2, 0, 0], [2, 2, 0], [0, 0, 2]], [[0, 0, 0], [2, 0, 0], [2, 2, 0], [2, 0, 2]], [[0, 0, 0], [2, 0, 0], [2, 2, 0], [0, 2, 2]], [[0, 0, 0], [2, 0, 0], [2, 2, 0], [2, 2, 2]], [[0, 0, 0], [2, 0, 0], [0, 0, 2], [2, 0, 2]], [[0, 0, 0], [2, 0, 0], [0, 0, 2], [0, 2, 2]], [[0, 0, 0], [2, 0, 0], [0, 0, 2], [2, 2, 2]], [[0, 0, 0], [2, 0, 0], [2, 0, 2], [0, 2, 2]], [[0, 0, 0], [2, 0, 0], [2, 0, 2], [2, 2, 2]], [[0, 0, 0], [2, 0, 0], [0, 2, 2], [2, 2, 2]], [[0, 0, 0], [0, 2, 0], [2, 2, 0], [0, 0, 2]], [[0, 0, 0], [0, 2, 0], [2, 2, 0], [2, 0, 2]], [[0, 0, 0], [0, 2, 0], [2, 2, 0], [0, 2, 2]], [[0, 0, 0], [0, 2, 0], [2, 2, 0], [2, 2, 2]], [[0, 0, 0], [0, 2, 0], [0, 0, 2], [2, 0, 2]], [[0, 0, 0], [0, 2, 0], [0, 0, 2], [0, 2, 2]], [[0, 0, 0], [0, 2, 0], [0, 0, 2], [2, 2, 2]], [[0, 0, 0], [0, 2, 0], [2, 0, 2], [0, 2, 2]], [[0, 0, 0], [0, 2, 0], [2, 0, 2], [2, 2, 2]], [[0, 0, 0], [0, 2, 0], [0, 2, 2], [2, 2, 2]], [[0, 0, 0], [2, 2, 0], [0, 0, 2], [2, 0, 2]], [[0, 0, 0], [2, 2, 0], [0, 0, 2], [0, 2, 2]], [[0, 0, 0], [2, 2, 0], [0, 0, 2], [2, 2, 2]], [[0, 0, 0], [2, 2, 0], [2, 0, 2], [0, 2, 2]], [[0, 0, 0], [2, 2, 0], [2, 0, 2], [2, 2, 2]], [[0, 0, 0], [2, 2, 0], [0, 2, 2], [2, 2, 2]], [[0, 0, 0], [0, 0, 2], [2, 0, 2], [0, 2, 2]], [[0, 0, 0], [0, 0, 2], [2, 0, 2], [2, 2, 2]], [[0, 0, 0], [0, 0, 2], [0, 2, 2], [2, 2, 2]], [[0, 0, 0], [2, 0, 2], [0, 2, 2], [2, 2, 2]], [[2, 0, 0], [0, 2, 0], [2, 2, 0], [0, 0, 2]], [[2, 0, 0], [0, 2, 0], [2, 2, 0], [2, 0, 2]], [[2, 0, 0], [0, 2, 0], [2, 2, 0], [0, 2, 2]], [[2, 0, 0], [0, 2, 0], [2, 2, 0], [2, 2, 2]], [[2, 0, 0], [0, 2, 0], [0, 0, 2], [2, 0, 2]], [[2, 0, 0], [0, 2, 0], [0, 0, 2], [0, 2, 2]], [[2, 0, 0], [0, 2, 0], [0, 0, 2], [2, 2, 2]], [[2, 0, 0], [0, 2, 0], [2, 0, 2], [0, 2, 2]], [[2, 0, 0], [0, 2, 0], [2, 0, 2], [2, 2, 2]], [[2, 0, 0], [0, 2, 0], [0, 2, 2], [2, 2, 2]], [[2, 0, 0], [2, 2, 0], [0, 0, 2], [2, 0, 2]], [[2, 0, 0], [2, 2, 0], [0, 0, 2], [0, 2, 2]], [[2, 0, 0], [2, 2, 0], [0, 0, 2], [2, 2, 2]], [[2, 0, 0], [2, 2, 0], [2, 0, 2], [0, 2, 2]], [[2, 0, 0], [2, 2, 0], [2, 0, 2], [2, 2, 2]], [[2, 0, 0], [2, 2, 0], [0, 2, 2], [2, 2, 2]], [[2, 0, 0], [0, 0, 2], [2, 0, 2], [0, 2, 2]], [[2, 0, 0], [0, 0, 2], [2, 0, 2], [2, 2, 2]], [[2, 0, 0], [0, 0, 2], [0, 2, 2], [2, 2, 2]], [[2, 0, 0], [2, 0, 2], [0, 2, 2], [2, 2, 2]], [[0, 2, 0], [2, 2, 0], [0, 0, 2], [2, 0, 2]], [[0, 2, 0], [2, 2, 0], [0, 0, 2], [0, 2, 2]], [[0, 2, 0], [2, 2, 0], [0, 0, 2], [2, 2, 2]], [[0, 2, 0], [2, 2, 0], [2, 0, 2], [0, 2, 2]], [[0, 2, 0], [2, 2, 0], [2, 0, 2], [2, 2, 2]], [[0, 2, 0], [2, 2, 0], [0, 2, 2], [2, 2, 2]], [[0, 2, 0], [0, 0, 2], [2, 0, 2], [0, 2, 2]], [[0, 2, 0], [0, 0, 2], [2, 0, 2], [2, 2, 2]], [[0, 2, 0], [0, 0, 2], [0, 2, 2], [2, 2, 2]], [[0, 2, 0], [2, 0, 2], [0, 2, 2], [2, 2, 2]], [[2, 2, 0], [0, 0, 2], [2, 0, 2], [0, 2, 2]], [[2, 2, 0], [0, 0, 2], [2, 0, 2], [2, 2, 2]], [[2, 2, 0], [0, 0, 2], [0, 2, 2], [2, 2, 2]], [[2, 2, 0], [2, 0, 2], [0, 2, 2], [2, 2, 2]], [[0, 0, 2], [2, 0, 2], [0, 2, 2], [2, 2, 2]]];
getEq := proc (L1::listlist) local p, S, expr; seq(geom3d:-point(p || j, L1[j]), j = 1 .. 4); geom3d:-Equation(geom3d:-sphere(S, [p1, p2, p3, p4], [x, y, z])) end proc; map(getEq, L);

But I couldn't get the result. How can get the result?

## How can I get a point in list of point t...

I want to write a plane passing through a point (in list) and parallel to a plane.

L := [[-14, 2, 3], [-13, -3, 1], [-13, -3, 5], [-13, 0, -2]]:
with(geom3d):
point(A, L[1]):
plane(P, 2*x+3*y+z = 0, [x, y, z]):
n := NormalVector(P):
Equation(plane(Q, [A, n], [x, y, z]));

I tried
t[i] := ([seq])(point(M, pt[]), pt in L):
Equation( plane(Q,t[i],n],[x,y,z]),i=1..nops(L));

It is not true. How can I repair it?

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