Presentació del taller

Al llarg d'aquest taller es proposa resseguir el contingut d'un treball de recerca que van realitzar Joan Bertomeu Balagueró, Lluís Borràs Vila, Lluís Caballol Angelats, Maria Gas de Cid i Àngels Miralles Verge, alumnes de COU de l'Institut de Batxillerat de Tortosa durant el curs 1982-1983. El títol original és [i]Traient suc d'un tetràedre (Estudi dels punts notables del tetràedre)[/i] i aporta idees innova­dores sobre la geometria del tetràedre i permet una reflexió sobre l'ús eficaç dels recursos informàtics actuals i els de fa 33 anys, a partir de l'actualització que n'ha fet Antoni Gomà Nasarre (Associació Catalana de GeoGebra) amb l'ús del programa GeoGebra.[br][br]El treball va ser premiat en la convocatòria 1983 dels [i]Premis CIRIT[/i] (actualment [i]Premis de Recerca Jove[/i],que convoca anualment el Govern de la Generalitat de Catalunya).   [br]El treball original i els comentaris per a la presentació com a taller en el C2EM, que valoren alguns aspectes crucials del treball, es poden descarregar de  [url=http://www.xtec.cat/~agoma/tetraedre]http://www.xtec.cat/~agoma/tetraedre[br][br][br][/url]

Intersecció de tres plans i sistemes 3 x 3

Al llarg d'aquest taller construirem plans geomètricament i de seguida en veurem l'equació. També podem definir els plans directament escrivint-ne l'equació a la línia d'entrada. I també podem pensar en el CAS per a resoldre un sistema d'equacions. Cada tipus de treball té particularitats que l'experiència ens ensenyarà a valorar i triar el més adequat.[br][br][b]Intersecció de tres plans[/b][br][br][list][*]Obrim el GeoGebra (o un fitxer nou) i escrivim a la línia d'entrada les equacions de tres plans que es tallin en un punt (ja sabeu que si poseu els coeficients més o menys "aleatòriament" gairebé segur que els plans es tallaran).[/*][*]El GeoGebra té un comandament [b]Intersecció[/b] que, tanmateix, només es pot aplicar a dos objectes. Com ho farem per a trobar el punt d'intersecció dels tres plans? Assageu-ho![/*][*]Per a visualitzar bé la situació potser voldreu "fer-ho bonic": acoloriu els plans i feu que es vegin les tres rectes intersecció dels plans per parelles. [br][/*][*]És bo de comentar que en la intersecció de dos plans o d'un pla i una recta, encara que natros fem servir el comandament Intersecció, el GeoGebra ho emmagatzema com si haguéssim fet servir un comandament anàleg que està definit com [b]InterseccióComALínia[/b].[br][br][br][b]Fem una macro (eina pròpia)?[/b][br][br]Si pensem que volem fer servir en diverses ocasions aquest procediment de calcular el punt d'intersecció de tres plans pot ser bo crear una eina pròpia que ho faci. [br][/*][*]Durant el taller no es va generar l'eina pròpia. Si ara ho vol fer la persona que practica amb aquest llibre de GeoGebra sàpiga que ha de triar com a objectes d'entrada els tres plans dels quals vol calcular la intersecció i com a objecte de sortida, naturalment, el punt d'intersecció.[/*][*]Tanmateix, per si es vol fer fer servir l'autor ha compartit un fitxer .ggb amb el nom de [i]Eines Tetràedre (Taller c2em) [/i]que té creada aquesta macro i algunes altres i també ha guardat les macros en format .ggt ([url=http://www.xtec.cat/~agoma/tetraedre/eines-tetraedre-c2em.zip]enllaç per descarregar-les[/url]). Per fer servir aquestes eines podeu obrir el fitxer .ggb i després començar el vostre treball o bé, si ja teniu a mig fer l'applet, podeu incorporar la macro (Fitxer-->Obre, desa la feina, i obrir el corresponent fitxer .ggt; la macro queda incorporada a la vostra feina). [br],[br][b]Sistema de tres equacions amb tres incògnites[/b][br]El calculador simbòlic és l'eina adequada per a la resolució de sistemes d'equacions. Visualitzeu, doncs, el CAS[/*][*] Escriviu tres equacions, però "donant-los-hi nom". Per exemple [size=150][b]a:= 2x+3y-5z=0[/b][/size][b][/b] i així amb les altres, dieu-los hi [size=150][b]b[/b][/size][b][/b] i [size=150][b]c[/b][/size][b][/b]. Veureu que es dibuixen els plans corresponents.[br][/*][*]Ara podeu fer [b]Resol[a,b,c] [/b] i ja tindreu la solució del sistema. Si voleu que e svegi el punt activeu el botonet corresponent. La solució es converteix en una llista d'un punt, la oslució del sistema, punt comú als plans.[/*][/list]Nota: en aquest cas, si voleu visualitzar les rectes intersecció dels plans per parelles, al CAS no es pot fer servir el comandament Intersecció. S'ha de fer forçosament amb InterseccióComALínia.

Consulta de recursos a l'abast

La recerca d'informació ha variat tan substancialment en els darrers 30 anys que, per als que tenim una certa edat, costa fins i tot d'imaginar. [br][br]Segur que avui dia començaríem per una recerca a Internet i, en concret, com que estem parlant del GeoGebra, buscaríem en l'entorn dels materials compartits a www.geogebra.org/materials.[br][br]Ja ho hem fet prèviament i hem trobat un llibre del mestre Manuel Sada sobre el tema, [br]Podeu accedir-hi si feu clic en el títol o en la imatge que s'adjunta tot seguit. [br][br][url=https://www.geogebra.org/m/LPS1Ng6M?doneurl=%2Fsearch%2Fperform%2Fsearch%2FManuel%2BSada%2]Buscando la recta de Euler en un tetraedro[/url][br][url=https://www.geogebra.org/m/LPS1Ng6M?doneurl=%2Fsearch%2Fperform%2Fsearch%2FManuel%2BSada%2][img width=595,height=302]data:image/png;base64,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[/img][/url][br][br]Treballem-hi una estona, fem-nos preguntes, investiguem... i ho comentarem. [br]Alguns aspectes ja actualitzen en part el treball de recerca que es presenta, però, tanmateix, al llarg del taller veurem que podrem aprofundir-ne alguns altres.

Investigando con GeoGebra (2)

En la hoja de trabajo del libro del profesor Manuel Sada sobre los tetraedros ortocéntricos se pueden mover los vértices (el applet está pensado para que [i]A, B[/i] i [i]C[/i] estén siempre en el plano horizontal. Conviene no alterar esta idea). [br]Ahora bien, es interesante conjeturar en qué condiciones el autor "nos deja" mover el punto D para que el tetraedro tenga ortocentro. Como nos tiene acostumbrados el applet está diseñado para sugerir ideas y para hacernos pensar. [br][br][list][*][b]Conjetura sobre la creación de tetraedros ortocénticos[/b][/*][/list][br]En el taller del c2em, después de un rato de geometria dinámica se formuló la conjectura que en el modelo general de los tetraedros ortocéntricos, el punto D queda siempre "en la vertical" del ortocentro de la base. [br][br]Para practicar y comprobar la conjetura se sugirió una construcción que constituye el applet siguiente y que detallamos a continuación en sus aspectos esenciales por si la persona que lee este libro quiere reproducirla. [br]Se trata de abrir desde GeoGebra el fichero compartido [i]Herramientas Tetraedro (RRR2)[/i] que, como ya se ha comentado tiene creada una macro que construye el ortocentro de un triángulo en 3D (herramienta que también se puede descargar en formato .ggt ([url=http://www.xtec.cat/~agoma/tetraedro/herramientas-castro.zip]enlace[/url]) .[br][list][*]Construir un triángulo ABC en el plano horizontal XY de la ventana gràfica 3D. [br][/*][*]Con la herramienta propia [i]OrtocentroTriángulo,[/i] clicar en los punts A, B y C así se obtiene el ortocentro de la base. Podéis llamarlo G, por ejemplo.[/*][*]Trazar por el ortocentre de la base una perpendicular a la cara ABC . Es una de las alturas del tetraedro. [br][/*][*]Definir un punto D sobre esta recta que acabamos de crear .[/*][*]Construir el tetraedro ABCD . [br][/*][/list]¿Será cierta la conjetura y este tetraedro en el que una altura pasa por el ortocentro de la cara opuesta es, efectivamente, un tetraedro ortocéntrico? Investiguemos y razonemos. [br][br][list][*]Crear ahora el ortocentro G2 de la cara BCD. [br][/*][*]La recta que pasa por A y por G2 ¿es una de las alturas del tetraedro? ¿se corta con la altura "vertical"?[br]o bien[/*][*]Trazar la recta que pasa por A y es perpendicular a la cara BCD. Esta recta ¿pasa por el punto G2? ¿se corta con la altura vertical?[/*][*]Repitamos el proceso para todas las caras.[/*][/list][br]El applet siguiente tiene hecha esta construcción.

Treball analític acurat

[img width=719,height=203]data:image/png;base64,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[/img][br][br]Seria un bon moment per a escriure en el CAS del GeoGebra les equacions de les mitjanes del tetràedre (recta que uneix cada vèrtex amb el baricentre de la cara oposada) i comprovar que tenen un punt en comú... però no està implementat adequadament encara en el CAS el càlcul geomètric 3D.[br]Fem-ho doncs a la línia d'entrada i deduïm quin és el baricentre.[br][img]data:image/png;base64,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[/img][br]Interpretem el resultat! [br][br]Ara, si escau, és un bon moment per practicar una mica la visió gràfica:[br]dibuixem un tetràedre[br]construïm el punt G amb el resultat que acabem d'obtenir [br]construïm el baricentre GC d'una cara[br]comprovem que la recta que uneix el vèrtex oposat a aquesta cara amb el punt G passa per GC.

Raonem

[b]El circumcentre d'un tetràedre[/b] (centre de l'esfera que passa pels quatre vèrtexs) existeix sempre. [br]El lloc geomètric dels punts de l'espai que equidisten de dos punts donats és un pla, que el GeoGebra ens permet calcular directament [i] [b]PlaMitger[,][/b].[/i] ([b]Alerta!!![/b] si algú és afeccionat a fer servir altres idiomes: aquest comandament en castellà és [i]PlanoBisector[/i]; en anglès [i]BisectorPlane[/i]...) [br]Deduïu tres possibles plans que poden servir per determinar el circumcentre i raoneu que realment tenen intersecció i que és un punt a la mateixa distància dels quatre vèrtexs del tetràedre.[br][br][br][b]L'incentre d'un tetràedre[/b] (centre de l'esfera tangent a les quatre cares) existeix sempre. [br]El lloc geomètric dels punts de l'espai que equidisten dels dos plans que formen un angle diedre és un pla, que no té un comandament propi en el GeoGebra (i que, si el tingués, se n'hauria de dir quelcom semblant a [i]PlaBisectorDeDosPlans[/i] o, per aplicar-ho a un tetràedre, [i]PlaBisectorCares[/i]) . [br]Deduïu tres possibles plans que poden servir per determinar l'incentre i raoneu que realment tenen intersecció i que és un punt a la mateixa distància dels quatre vèrtexs del tetràedre.

Quin punt és el centre d'aquesta esfera? Reflexionem

Observeu el tetràedre següent (que es presenta per mirar amb les ulleres 3D; desactiveu l'opció si no en disposeu)[br]Quina propietat diríeu que té té l'esfera que apareix?[br]Quina propietat ha de tenir el centre d'aquesta esfera?[br][br]Podreu girar la figura però no podreu moure els punts, que són molt especials els tetràedres amb aquesta propietat
Quin és el lloc geomètric dels punts que estan a la mateixa distància de dues rectes?[br]És un pla que es podria dir "pla bisector de dues rectes". Vegeu com es pot construir.[br][img width=369,height=182]data:image/png;base64,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[/img][br]Ho provem amb el GeoGebra?[br][br]Si fem els plans bisectors, per parelles, de les tres rectes que concorren en el vèrtex d'un tetraedre, quina propietat tindrà la recta intersecció? Comentem-ho, que resol geomètricament un problema interessant.[br][br]Perquè es pugui donar el cas d'una esfera com la que hem vist en l'applet anterior, el centre d'aquesta esfera ha d'estar a la mateixa distància de les sis arestes. La figura de l'applet deixa ben clar per què d'aquest punt els autors del treball en van dir [b]filcentre[/b]: va bé imaginar-se el tetràedre amb les arestes "de filferro".[br][br]Ben aviat es pot veure que no tots els tetràedres tenen filcentre. En la bibliografia, els tetràedres filcèntrics reben el nom de [i]tetràedres de Crelle[/i] o [i]esquelets[/i]. [br][br]El filcentre, si existeix, ha de ser la intersecció de tots els plans bisectors que acabem de comentar. [br]En sabríem triar tres que ja ens donessin el filcentre, cas d'existir?[br][br]En l'apartat següent suggerim alguns càlculs,

Bibliografia

[br][br][1] Ancochea, Bernat; Gomà, Antoni. [i]Geogebra 3D, un pas endavant[/i]. Taller a[br]les VIII Jornades de l'ACG. [i]Acostem (més)[br]el GeoGebra a l'aula[/i]. Barcelona, 19 i 20 de febrer de 2016. El material del[br]taller es pot descarregar de [br][url=https://app.box.com/s/iaxqpqjbhyn9a1bp84mumixhh559qlju]https://app.box.com/s/iaxqpqjbhyn9a1bp84mumixhh559qlju[/url][br][br][2]  Bellot Rosado, Francisco. [i]Geometría del tetraedro[/i]. Artícle a la Revista Escolar de la Olimpíada Iberoamericana de Matemática.[br]Edita OEI. Publicada a Internet. Juny 2008.[br]Es pot descarregar de [url=http://www.oei.es/oim/revistaoim/numero32/Tetraedro.pdf]http://www.oei.es/oim/revistaoim/numero32/Tetraedro.pdf[/url] [br][br][3] Bertomeu, Joan; Borràs, Lluís; Caballol,[br]Lluís; Gas de Cid, Maria; Miralles, Àngels. [i]Traient[br]suc d'un tetràedre (Estudi dels punts notables del tetràedre)[/i].  Institut de Batxillerat de Tortosa, per als[br]premis CIRIT 1983.  Es pot descarregar de  [url=http://www.xtec.cat/~agoma/tetraedre]http://www.xtec.cat/~agoma/tetraedre[/url][br]juntament amb la proposta raonada del taller.[br] [br][4] Casals, Rafael et al.  [i]Matemàtica[br]COU[/i].  Editorial Teide. Barcelona[br]1994.[br][br] [5] Euclides.  [i]Elementos[/i].  Biblioteca Clásica Gredos. Libros I-IV,[br]LIbros V-IX, Madrid 1991.  Libros X-XIII,[br][b]ISBN:[/b]9788424918309[br][br][6] Gomà, Antoni. [i]El tetràedre, un gran desconegut[/i]. Article a SCM/Notícies,[br]número 6, juliol 1997. Societat Catalana de Matemàtiques. Es pot descarregar de[br][url=http://blogs.iec.cat/scm/wp-content/uploads/sites/20/2011/02/N6.pdf]http://blogs.iec.cat/scm/wp-content/uploads/sites/20/2011/02/N6.pdf[/url][br][br][7] Marcos, C., Martínez, J.  [i]Matemáticas[br]4º Bachillerato[/i]. Ediciones SM. Madrid 1960.[br][br][8] Negro, A. et al.  [i]Curso[br]de Matemáticas. Orientación Universitaria[/i]. Editorial Alhambra. Madrid[br]1978.  Proyecto MT62.[br][br][9] Royanes, Eugenio. [i]Introducción a la geometria[/i]. Editorial Anaya. Madrid 1979. [br][br][10] Sada Allo, Manuel. (1/4/2015). [i]Buscando la recta de Euler en un tetraedro[/i].[br][Llibre del GeoGebraTube].  [br]Recuperat de [url=https://www.geogebra.org/m/LPS1Ng6M?doneurl=%2Fmanuel%2Bsada%23]https://www.geogebra.org/m/LPS1Ng6M?doneurl=%2Fmanuel%2Bsada#[/url][br][br][br]

Information