Sum of the Squares of the Sides of a Projected Regular Tetrahedron
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Let be a regular tetrahedron with side
. Project
orthogonally to a plane
and let
,
, …,
be the lengths of the projections of the six sides of
in
. This Demonstration shows that
.
Contributed by: Izidor Hafner (June 2017)
Open content licensed under CC BY-NC-SA
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Details
This problem was posed in [1, pp. 20, 28].
Reference
[1] V. V. Prasolov and I. F. Sharygin, Problems in Stereometry (in Russian), Moscow: Nauka, 1989.
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