Simulating symmetry composition in GeoGebra to simplify the Diamond theory in Carom billiard practice
DOI:
https://doi.org/10.21803/pensam.v10i19.29Keywords:
Billar a tres bandas; Composición de simetrías; Teoría de los diamantes; Software de geometría dinámica; GeoGebra; reeband billiard; Composition of isometriesAbstract
En este arti?culo se muestra una simulacio?n del juego del billar a tres bandas apoyada en el uso de geometri?a ba?sica y la utilizacio?n de un so ware de geometri?a dina?mica llamado Geogebra, para la visualizacio?n de propiedades de las transformaciones en el plano; esta simulacio?n permite simpli car el me?todo de pra?ctica de billar a tres bandas conocido como la “Teori?a de los diamantes para sistemas a tres bandas”. Haciendo uso de movimientos ri?gidos en el plano y las propiedades de la re exio?n de los cuerpos, se obtiene la “composicio?n de rebotes” que no es ma?s que la composicio?n de isometri?as, especi? camente de simetri?as axiales, para determinar con anticipacio?n el recorrido de la bola tiradora en tiros especiales, llamados bricoles (Berri?o, 2104).
Palabras clave: Billar a tres bandas, Composicio?n de simetri?as, Teori?a de los diamantes, Software de geometri?a dina?mica, GeoGebra.
Abstract
is paper works a simulation of the game of billiards (Carom billiard) based on the use of basic geometry and the use of a so ware of dynamic geometry called GeoGebra, for the visualization of properties of the transformations. is simulation makes possible to simplify the billiards practice method known as the “Diamond theory for Caron Billiard system”. Making use of rigid movements and the properties of the reflection of the bodies, we obtain the “composition of rebounds”. is composition is not more than an isometric composition, specifically of axial symmetries, to determine in advance the course of the ball in special shots, called bricoles (Berri?o, 2104).
Keywords: ree-band billiard, Composition of isometries, theory of diamonds, Dynamic geometry software, GeoGebra.
Resumo
Este artigo mostra uma simulac?a?o do jogo de bilhar a tre?s tabelas com base no uso da geometria ba?sica e o uso de um so ware de geometria dina?mica chamado GeoGebra, para a visualizac?a?o das propriedades das transformac?o?es. Esta simulac?a?o permite simpli car o me?todo de pra?tica de bilhar conhecido como “Teoria dos diamantes para sistemas de tre?s tabelas”. Fazendo uso de movimentos ri?gidos no plano e as propriedades do re exo dos corpos, obtemos a “composic?a?o dos rebotes” que na?o e? mais do que a composic?a?o das isometrias, especi camente de simetrias axiais, para determinar antecipadamente o curso da bola lmado em tiros especiais, chamados bricoles (Berri?o, 2104).
Palavras-chave: Bilhar a tre?s tabelas, Composic?a?o de simetrias, Teoria dos diamantes, Software de geometria dina?mica, GeoGebra.
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References
Berri?o, J. (2014). De la geometri?a ba?sica y el billar a tres bandas para principiantes. Revista Matua, 1(2), 40-50.
Bosch, C. (2010). El billar no es de vagos. Me?xico: Editorial Fondo de Cultura ITAM (Instituto Tecnolo?gico Auto?nomo de Me?xico).
Colo?n, C. (2008). Potenciacio?n de las tecnologi?as de informacio?n y las comunicaciones (TIC) en los procesos de docencia. Revista Pensamiento Americano, 1(1), 49-54.
Coriolis, G. (1835). Te?orie mathe?matique des efets de jeu de billard. Paris: Carilian-Gouery Libraire.
Coss Bu, R. (1998). Simulacio?n un enfoque pra?ctico. Me?xico: Limusa.
Everton, C. (1986). e History of Snooker and Billiards. United Kingdom: Partridge.
Henri?quez, C. (2009). Software libre u?til para las pequen?as empresas. Revista Pensamiento Americano, 2(3), 33-37.
Krehl, P. (2008). History of shock waves, explosions and impacts. A Chronological and Biographical Reference. Nimburg: Springer.
Godino, J. D. & Ruiz, F. (2002). Geometri?a y su dida?ctica para maestros. Granada: Gami S.L.
Miranda, R. (2008). Geometri?a del Pool. Geometri?a dina?mica. Recuperado de http:// www.geometriadinamica.cl/2008/07/ geometria-del-pool/
Orriols, D. (s.f.). Billar monitor, Teori?a de las tres bandas por el sistema de diamantes. Recuperado de http://www.javiercaceres.com/dir/billar/Diamantes/diamantes.htm
Tabachnikov, S. (2005). Billiards and geome- try. Pennsylvania: Penn State University Press.
Turizo, L., Orozco, S. & Sa?nchez, D. (2011). Modelando el juego tradicional la Cuarta, practicado por los jo?venes de la regio?n Caribe colombiana. Revista Pensamiento Americano, 4(7), 41-46.
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