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Right Tetrahedron: de Gua Theorem
In a right triangle with legs
and
and hypotenuse
,
(Pythagorean theorem).
In a right tetrahedron with right triangle faces of area
,
and
,
(de Gua theorem).
Equivalently, the
cuboid has diagonals of length
, where
.
Contributed by:
Ed Pegg Jr
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RELATED LINKS
de Gua's Theorem
(
Wolfram
MathWorld
)
Pythagorean Theorem
(
Wolfram
MathWorld
)
Trirectangular Tetrahedron
(
Wolfram
MathWorld
)
Right-Angled Tetrahedron
(
Wolfram Demonstrations Project
)
Pythagorean Theorem 3D
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Ed Pegg Jr
"
Right Tetrahedron: de Gua Theorem
"
http://demonstrations.wolfram.com/RightTetrahedronDeGuaTheorem/
Wolfram Demonstrations Project
Published: November 21, 2018
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