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The Double Subdivision-Network Method

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angle ϕ
0.897598
step 1
0.
step 2
0.
Two polygons
V
and
W
are equivalent (
V≅W
) if they have the same area. In the article "On the Degree of Equivalence of Polygons", Tarski defines the degree of equivalence
σ(V,W)
of two equivalent polygons
V
and
W
as the least integer
n
for which there exists an
n
-piece dissection of
V
to
W
.
He then gives a few elementary properties of this concept. For example, if
V≅X
and
W≅X
, then
σ(V,W)≤σ(V,X)σ(W,X)
.
This Demonstration shows an example where the limiting equality holds. A unit square
V
and a certain triangle
W
are both equivalent by dissection to a parallelogram
X
. Since
σ(V,X)=2
and
σ(W,X)=2
, there is four-piece dissection of
V
to
W
—that is,
σ(V,W)=4
.
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