1. bookVolumen 9 (2022): Edición 16 (June 2022)
Detalles de la revista
License
Formato
Revista
eISSN
2182-1976
Primera edición
16 Apr 2016
Calendario de la edición
2 veces al año
Idiomas
Inglés
access type Acceso abierto

Arithmetic Billiards

Publicado en línea: 14 Jun 2022
Volumen & Edición: Volumen 9 (2022) - Edición 16 (June 2022)
Páginas: 43 - 54
Detalles de la revista
License
Formato
Revista
eISSN
2182-1976
Primera edición
16 Apr 2016
Calendario de la edición
2 veces al año
Idiomas
Inglés
Abstract

Arithmetic billiards show a nice interplay between arithmetics and geometry. The billiard table is a rectangle with integer side lengths. A pointwise ball moves with constant speed along segments making a 45° angle with the sides and bounces on these. In the classical setting, the ball is shooted from a corner and lands in a corner. We allow the ball to start at any point with integer distances from the sides: either the ball lands in a corner or the trajectory is periodic. The length of the path and of certain segments in the path are precisely (up to the factor √2 or 2√2) the least common multiple and the greatest common divisor of the side lengths.

[Gar84] Martin Gardner, Sixth Book of Mathematical Diversions from “Scientific American”, University of Chicago Press, Paperback 1984, ISBN: 0226282503. (See pp. 211–215) Search in Google Scholar

[GF13] Hema Gopalakrishnan and Stephanie Furman, Pool Table Geometry, Math Circle Poster and Activity Session, JMM2013 San Diego, http://sigmaa.maa.org/mcst/PosterActivitySessions/documents/PoolTableActivity.pdf. Search in Google Scholar

[Lap04] Glenda Lappan, James T. Fey, William M. Fitzgerald, Susan N. Friel, and Elizabeth Difanis Phillips, Comparing and Scaling: Ratio, Proportion, and Percent in Connected Mathematics Project, Upper Saddle River NJ, Pearson Prentice Hall, 2004. ISBN: 0131656352. (See pp. 64–66.) Search in Google Scholar

[Pap] Paper Pool Game, NCTM (National Council of Teachers of Mathematics) Illuminations, https://illuminations.nctm.org/Unit.aspx?id=6527. Search in Google Scholar

[Per18] Antonella Perucca, Arithmetic billiards, Plus Magazine, 24 April 2018, University of Cambridge, https://plus.maths.org/content/arithmetic-billiards-0. Search in Google Scholar

[Ste99] Hugo Steinhaus, Mathematical Snapshots, Dover Recreational Math. Series, Courier Corporation, 1999. ISBN:0486409147. (See p. 63.) Search in Google Scholar

[Tan12] James Tanton, Mathematics Galore!: The First Five Years of the St. Mark’s Institute of Mathematics (Classroom Resource Materials), The Mathematical Association of America, 2012. ISBN: 0883857766. (See pp. 145–156.) Search in Google Scholar

[Tho08] Blake Thornton, Greatest common divisor, The Washington University Math Teachers’ Circle, 2008, http://www.dehn.wustl.edu/~blake/courses/WU-Ed6021-2011-Summer/handouts/Greatest%20Common%20Divisor-sols.pdf. (See pp. 5–8.) Search in Google Scholar

[Wik] Wikipedia contributors, Arithmetic billiards, Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/w/index.php?title=Arithmetic_billiards&oldid=889358328 (accessed June 30, 2021). Search in Google Scholar

[Zuc07] Joshua Zucker, The Bouncing Ball Problem, San Jose Math Circle, 2007, http://sanjosemathcircle.org/handouts/2007-2008/20071003.pdf. (See p. 1.) Search in Google Scholar

Artículos recomendados de Trend MD

Planifique su conferencia remota con Sciendo