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Inscribing triangles to compute area. Proposition. Suppose k, l L(Rm
 

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