A proof of a relation between the numbers of singularities of a closed polygon
- 22 Downloads
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
Unable to display preview. Download preview PDF.
- Banchoff, T.F., Global geometry of polygons I, The Theorem of Fabricius-Bjerre, Proc. Amer. math. Soc. 45 (1974), 237–241.Google Scholar
- Fabricius-Bjerre, Fr., On the double tangents of plane curves, Math. Scand. 11 (1962), 113–116.Google Scholar
- Fabricius-Bjerre, Fr., A theorem on closed polygons in the projective plane, Nord. Mat. Tids. 10 (1962), 143–146.Google Scholar
- Fabricius-Bjerre, Fr., A relation between the numbers of singular points and singular lines of a plane closed curve, Math. Scand. 40 (1977), 20–24.Google Scholar
- Halpern, B., Double normals and tangent normals for polygons, Proc. Amer. Math. Soc. 51 (1975), 434–437.Google Scholar