Given four distinct parallel planes, prove that there exists a regular tetrahedron with one vertex in each of the planes.
https://www.desmos.com/calculator/ihybvlhvtp
The four parallel planes are parallel to the x-y plane and have equations Z=0, Z=1, Z=c, Z=d with 1<c<d.
The c and d sliders control the heights of the highest two planes.
Point A=(0,0), B=(a,0) and can be dragged back and forth.
The gray circles are the possible points for C.
The blue, red, and pink circles are the possible locations for D.
These must coincide to make a regular tetrahedron.
To prove: There exists a value of b for any choice of c and d.
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Posted by Jer
on 2024-08-13 16:55:41 |
graphical demonstration, no proof