Midpoint polygon

In geometry, the midpoint polygon of a polygon P is the polygon whose vertices are the midpoints of the edges of P.^[1][2]

It is sometimes called the Kasner polygon after Edward Kasner, who termed it the inscribed polygon "for brevity".^[3][4]

See also

• Circulant matrix
• Midpoint-stretching polygon
• Varignon's theorem

References

1. ^ Gardner 2006, p. 36.
2. ^ Gardner & Gritzmann 1999, p. 92.
3. ^ Kasner 1903, p. 59.
4. ^ Schoenberg 1982, pp. 91, 101.

• 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

• Weisstein, Eric W., "Midpoint Polygon" from MathWorld.

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