Midpoint polygon
In geometry, the midpoint polygon of a polygon P is the polygon whose vertices are the midpoints of the edges of P.
It is sometimes called the Kasner polygon after Edward Kasner, who termed it the inscribed polygon "for brevity".
See also
References
- Gardner, Richard J. (2006), Geometric tomography, Encyclopedia of Mathematics and its Applications, 58 (2nd ed.), Cambridge University Press
- Gardner, Richard J.; Gritzmann, Peter (1999), "Uniqueness and Complexity in Discrete Tomography", in Herman, Gabor T.; Kuba, Attila, Discrete tomography: Foundations, Algorithms, and Applications, Springer, pp. 85–114
- Kasner, Edward (March 1903), "The Group Generated by Central Symmetries, with Application to Polygons", American Mathematical Monthly 10 (3): 57–63, http://www.jstor.org/stable/2968300
- Schoenberg, Isaac J. (1982), Mathematical Time Exposures, Mathematical Association of America
Further reading
- Berlekamp, Elwyn R.; Gilbert, Edgar N.; Sinden, Frank W. (March 1965), "A Polygon Problem", American Mathematical Monthly 72 (3): 233–241, http://www.jstor.org/stable/2313689
- Cadwell, J. H. (May 1953), "A Property of Linear Cyclic Transformations", The Mathematical Gazette 37 (320): 85–89, http://www.jstor.org/stable/3608930
- Clarke, Richard J. (March 1979), "Sequences of Polygons", Mathematics Magazine 52 (2): 102–105, http://www.jstor.org/stable/2689847
- Croft, Hallard T.; Falconer, K. J.; Guy, Richard K. (1991), "B25. Sequences of polygons and polyhedra", Unsolved Problems in Geometry, Springer, pp. 76–78
- Darboux, Gaston (1878), "Sur un problème de géométrie élémentaire", Bulletin des sciences mathématiques et astronomiques, Sér. 2 2 (1): 298–304, http://www.numdam.org/item?id=BSMA_1878_2_2_1_298_1
- Gau, Y. David; Tartre, Lindsay A. (April 1994), "The Sidesplitting Story of the Midpoint Polygon", Mathematics Teacher 87 (4): 249–256
External links