A proof of a relation between the numbers of singularities of a closed polygon
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Let (P) denote a closed plane polygon, te and ti the numbers of exterior and interior double supporting lines, respectively, d the number of double points and i the number of inflectional edges of (P). T.F. Banchoff has shown that these numbers satisfy the relation te−ti=d+1/2i.
A new and simple proof of this equation is presented.
KeywordsSimple Proof Double Point Supporting Line Double Supporting Closed Polygon
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