Dissection of a Square to a Parallelogram with the Same Base
Dissection of a Square to a Parallelogram with the Same Base
Two polygons of the same area are said to be equivalent. In [1], Tarski defines the degree of equivalence of two equivalent polygons and as the smallest natural number for which there exists a dissection of to using pieces. The function is denoted as .
V
W
n
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n
σ(V,W)
Later he defines , where is a unit square and is a parallelogram with the same base and altitude with angle . He states that and leaves the proof as an exercise for the readers.
T(ϕ)=σ(V,W)
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ϕ
⌈cscϕ⌉≤T(ϕ)≤⌈cotϕ⌉