The conic geometry of rectangles inscribed in lines
Authors:
Bruce Olberding and Elaine A. Walker
Journal:
Proc. Amer. Math. Soc. 149 (2021), 2625-2638
MSC (2020):
Primary 51N10; Secondary 11E10
DOI:
https://doi.org/10.1090/proc/15374
Published electronically:
March 18, 2021
MathSciNet review:
4246812
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We develop a circle of ideas involving pairs of lines in the plane, intersections of hyperbolically rotated elliptical cones and the locus of the centers of rectangles inscribed in lines in the plane.
- Keith Kendig, Conics, The Dolciani Mathematical Expositions, vol. 29, Mathematical Association of America, Washington, DC, 2005. With 1 CD-ROM (Windows NT/2000, XP, Macintosh). MR 2146621
- Benjamin Matschke, A survey on the square peg problem, Notices Amer. Math. Soc. 61 (2014), no. 4, 346–352. MR 3184501, DOI https://doi.org/10.1090/noti1100
- Mark D. Meyerson, Balancing acts, Topology Proc. 6 (1981), no. 1, 59–75 (1982). MR 650481
- B. Olberding and E. A. Walker, Supplementary graphics, 2021, http://ziaspace.com/math/
- B. Olberding and E. A. Walker, Paths of rectangles inscribed in lines over fields, submitted, arXiv:2006.14424.
- R. Schwartz, Four lines and a rectangle, Exp. Math. (2020), 1–8, DOI: 10.1080/10586458.2019.1671923.
- Richard Evan Schwartz, A trichotomy for rectangles inscribed in Jordan loops, Geom. Dedicata 208 (2020), 177–196. MR 4142923, DOI https://doi.org/10.1007/s10711-020-00516-8
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 51N10, 11E10
Retrieve articles in all journals with MSC (2020): 51N10, 11E10
Additional Information
Bruce Olberding
Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003-8001
MR Author ID:
333074
Email:
bruce@nmsu.edu
Elaine A. Walker
Affiliation:
1801 Imperial Ridge, Las Cruces, New Mexico 88011
Email:
miselaineeous@yahoo.com
Received by editor(s):
August 14, 2019
Received by editor(s) in revised form:
August 16, 2019, and September 24, 2020
Published electronically:
March 18, 2021
Communicated by:
Matthew Papanikolas
Article copyright:
© Copyright 2021
American Mathematical Society
