2004-12-16

    Los puentes de Leiden

    Lola, en un magnífico post sobre la teoría de grafos y los puentes de Königsberg, explica muy bien cómo Euler resolvió el problema siguiente:

    ¿Pueden recorrerse, en un sólo trayecto y sin pasar dos veces por el mismo puente, todos los puentes de la ciudad X?

    Obviamente, el problema original eran los 7 puentes de la ciudad de Kant (y, ahora me entero, también de Goldbach). Yo, que soy más complicado, os pongo la siguiente imagen:



    Es el mapa del antiguo Leyden, un poquito después de que nos echaran de aquí a base de malas artes con el agua (rompieron los diques e inundaron los campos en los que el ejército tenía montado el asedio). No digo el número de puentes, entre otras cosas, porque no los he contado, pero planteo el desafío: ¿alguien podría decirme si es posible hacer un recorrido turístico por los puentes de Leiden sin aburrir al personal pasando dos veces sobre el mismo?

    Para los que no distingan los puentes bien, este otro mapa de Leiden tiene más resolución.

Referencias (TrackBacks)

URL de trackback de esta historia http://evolucionarios.blogalia.com//trackbacks/24394

Comentarios

1
De: Lola Fecha: 2004-12-16 10:06

Alguien que sepa html... que me diga cómo poner una figurita al lado de la otra y no una debajo de otra... ejem...



2
De: Cluje Fecha: 2004-12-16 10:34

Me imagino a Kant perdido en sus reflexiones, realizando todos los posibles recorridos por los siete puentes, y de este modo demostrando sin saberlo el primer problema de la Topo.

Por otra parte, si alguien busca Koenigsberg en el mapa y no la encuentra, su nombre actual es Kaliningrado.



3
De: Anónima Fecha: 2004-12-16 11:03

Según la wikipedia, Köningberg es también la ciudad natal de ¡Goldbach!.

Y entiendo lo que dice Euler, pero prefiero ni imaginarme como debe ser la demostración :o



4
De: Tiza Fecha: 2004-12-16 11:13

Alguien que sabe html te dice que tienes que insertar una tablita...no se como es tu editor en el blog. Me ha encantado tu post de hoy lola...muy bueno.



5
De: Nfer Fecha: 2004-12-16 11:28

Muy bueno, Tiza, es cierto.
Es más hasta me animaré a tomar lápiz y papel a ver qué me sale. Eso luego que entre BM, que algo dirás, ¡¡¡anda di algo BM!!!
En el de ayer dejé una pequeña aclaración (¿o confusión?) sobre la escatológica derivación del tema...no teman por mí, Argentina es el paraíso de los psicólogos :-))



6
De: BioMaxi Fecha: 2004-12-16 11:36

O sin poner tablas, estas líneas deberían servir:

Texto por arriba

< img src="http://descartes.cnice.mecd.es/taller_de_matematicas/rompecabezas/casita.gif" align="middle" border="0" >< img src="http://descartes.cnice.mecd.es/taller_de_matematicas/rompecabezas/sobre.gif" align="middle" border="0" >

Texto por abajo

(El espacio delante o detrás de cada tienes que quitarlo)



< td >
< img src="http://descartes.cnice.mecd.es/taller_de_matematicas/rompecabezas/casita.gif" >< /td >< td >< img src="http://descartes.cnice.mecd.es/taller_de_matematicas/rompecabezas/sobre.gif" >< /td >< /tr >< /table >

Lo mismo que antes, quitando los espacios que sobran.

7
De: BioMaxi Fecha: 2004-12-16 11:42

Aunque la verdad es que las tablas son muy cómodas:

< table >



8
De: BioMaxi Fecha: 2004-12-16 11:44

anda que gracia, se sale del comentario. Se me habrá olvidado poner algún espacio....

Empieza < table >< tr > y sigue con lo que hay fuera del cuerpo del comentario...

Cuando lo tengas, borra mis comentarios, que queda fatal :)



9
De: Lola Fecha: 2004-12-16 11:47

joe... vengo de la (pesadísima) charla que me he tragado... y me encuentro hasta comentarios fuera de los cuadrados de los comentarios... Es que a mi se me saca del LaTeX y...

Voy a intentarlo :)



10
De: Lola Fecha: 2004-12-16 11:50

Pueeeees.... no me va... bueno, da igual, ya aprenderé...



11
De: BioMaxi Fecha: 2004-12-16 11:54

Pues voy a coger el mapa de Leiden (el antiguo, que queda más bonito) y a hacerle el grafo, hale. A vosotros no os podré plantear el reto de cruzar toooodos los puentes porque sabeis el truco, pero me da que estas Navidades se lo voy a poner difícil a la family...
... aunque conociéndoles, pasarán del tema XD



12
De: Alberto Fecha: 2004-12-16 12:01

A Konigsberg la llamo la ciudad ubicua, porque aparece cuando menos te lo esperas. No sólo los puentes o Kant. Fundada por los caballeros teutónicos (significa montaña del rey), puerto hanseático, capital de la Prusia Oriental, enclave Alemán rodeado por Polonia tras la primera guerra mundial, causa inmediata de la segunda, actualmente encalve ruso entre Lituania y Polonia con el nombre de Kaliningrado... Y también en el nombre de:

Heywood(y) Allen Stewart Konigsberg



13
De: BioMaxi Fecha: 2004-12-16 12:17

Lola y demás interesados:

he colgado en mi blog un mapa del viejo Leiden, por si os animais a encontrar la solución equivalente...
http://evolucionarios.blogalia.com/historias/24394

He pensado que, aunque sepais el truco, os va a tener entretenidos un buen rato, contando puntos y lineas ;-)



14
De: Zifra Fecha: 2004-12-16 13:13

Esto es lo mío: Teoría de Grafos...y lo difícil del Teorema de Euler es el "si". El "solo si" es bastante fácil de probar.

Es decir, lo difícil es probar que para TODOS los grafos con 0 ó 2 vértices de grado impar existe un recorrido/circuito euleriano.



15
De: Lola Fecha: 2004-12-16 14:17

Pues si... cierto. De hecho, es un teorema con mucha lógica... como que uno va diciendo al leer la demostración "pues... claro"...



16
De: Nfer Fecha: 2004-12-16 16:03

y si y solo si, os lo dejo toito pa ustedes.
Zifra, adelante con los faroles, y ¡¡¡gracias por hacerme doblar de risa con ese link de la masturbación!!!!!.



17
De: Carlos Fecha: 2004-12-16 19:51

Anónima , el teorema es bastante sencillo, cualquiera con muy poco conocimiento de base y unas cuantas definiciones básicas de teoría de grafos podría entenderlo.



18
De: Nfer Fecha: 2004-12-16 20:57

Averr: el teorema es sencillo. O sea que lo primero que tengo que entender es el teorema...luego los puentes, sean de Konigsberg, de Leiden o de Madison, ¿da igual?



19
De: Dem Fecha: 2004-12-16 21:01

Biomaxi acaba de poner en evidencia una técnica de Blogalia injection (aprendices de hacker busquen SQL Injection en google) ;)

(No creo que en este caso vaya a ser un problema gordo de seguridad, pero el administrador quizás debería echarle un ojo a las posibles complicaciones).



20
De: Nfer Fecha: 2004-12-16 21:53

Carlos, a lo que vi, el teorema es sencillo, ejem,... Gracias. Cero o dos, o te quedas de un lado si eres honesto...

En cuanto a lo de los puentes, temo que es como mi calle: Me contaron que un niño quería cruzar y le pregunta a una ancianita que ve en el otro lado "señora, ¿cómo hago para cruzar?" y la ancianita le dice "pues niño, no sé, yo nací de este lado..."



21
De: Miguelito Fecha: 2004-12-16 23:17

Que interesante....aunque no sé si podre retener el teorema mucho tiempo...ya sabes....mi kedadez...pero gracias por este buen rato. Buen viaje, amiga.

Un besazo



22
De: Mitch Fecha: 2004-12-17 17:22

Fijate que yo nunca habia estudiado teoria combinatoria de grafos hasta que fui a EEUU, donde resulta que dan unos cursos de doctorado que en España podrían darse perfectamente en primer ciclo de licenciatura... pero no se dan. Es el tipo de teoria que una vez has estudiado te parece todo tan fácil e inmediato, pero si no la has visto no se te ocurren los métodos a usar. Aún recuerdo cuando volví a Zaragoza teniendo que recurrir a mi libro de teoría de grafos de Florida (de un nivel patético) junto con mi director de tesis, la definición de matroide.

Por cierto, el si y solo si es una de esas cosas que te parecen triviales después de haber visto algo de teoría de grafos, aunque no recuerdes ni un sólo teorema.



23
De: Xac Fecha: 2004-12-17 21:33

Bueno, si aplicamos un poco de pensamiento lateral ... ale hop!. Ya está. Dudo que a Euler se le ocurriera plegar el papel.



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