Imagine 'gluing together two tetrahedra with a common interior face that is removed. The resulting polyhedron has 6 triangular faces (hexahedron). Show that the sum of the outward pointing area vectors is zero. This result and pro- cedure extend to more complex polyhedra and even to curved surfaces as can be shown with the 'gradient' theorem in vector calculus.
Imagine 'gluing together two tetrahedra with a common interior face that is removed. The resulting polyhedron has 6 triangular faces (hexahedron). Show that the sum of the outward pointing area vectors is zero. This result and pro- cedure extend to more complex polyhedra and even to curved surfaces as can be shown with the 'gradient' theorem in vector calculus.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:7. Imagine 'gluing together two tetrahedra with a common interior face that is
removed. The resulting polyhedron has 6 triangular faces (hexahedron). Show
that the sum of the outward pointing area vectors is zero. This result and pro-
cedure extend to more complex polyhedra and even to curved surfaces as can
be shown with the 'gradient' theorem in vector calculus.
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