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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
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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