Summary: Inscribing triangles to compute area.
Proposition. Suppose k, l L(Rm
, Rn
) and v1, . . . , vm Rm
. Then
|
m
k + l (v1 · · · vm) -
m
l (v1 · · · vm)|
m
p=1
m
p
||l||m-p
||k||p
|v1| · · · |vm|.
Proof. For each (p, m) let ^ (m - p, m) be such that rng ^ = {1, . . . , m} rng and let
s() {±1} be such that
v1 · · · vm = s()v v^.

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics