Mathematics

30-Second Maths: The 50 Most Mind-Expanding Theories in by Julian Baggini, Richard J. Brown, Antonia Macaro

By Julian Baggini, Richard J. Brown, Antonia Macaro

From Rubik's cubes to Godel's incompleteness theorem, every thing mathematical defined, with color illustrations, in part a minute. Maths is having fun with a resurgence in acceptance. So how are you going to keep away from being the one dinner visitor who has no suggestion who Fermat used to be, or what he proved? The extra you recognize approximately Maths, the fewer of a technology it turns into. 30 moment Maths takes the pinnacle 50 most tasty mathematical theories, and explains them to the overall reader in part a minute, utilizing not anything greater than pages, 2 hundred phrases and one photo. learn at your personal speed, and realize that maths could be extra attention-grabbing than you ever imagined.

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Extra info for 30-Second Maths: The 50 Most Mind-Expanding Theories in Mathematics, Each Explained in Half a Minute

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Presentamos tambi´en los algoritmos b´asicos del dise˜ no geom´etrico asistido por computadora (Computer Aided Geometric Design-CAGD) en t´erminos de esta relaci´on. El m´as importante de estos algoritmos es el de de Casteljau, el cual es muy u ´til tanto en implementaciones pr´ acticas como en el contexto te´orico. 1 Polinomios sim´ etricos A cada curva polin´omica b(u) de grado ≤ n se le puede asociar un u ´nico polinomio sim´ etrico b[u1 . . un ] con las siguientes tres propiedades: • b[u1 .

Por lo tanto, se puede calcular la derivada r−´esima en u calculando primero n − r pasos del algoritmo de de Casteljau, seguido por r diferencias y posteriormente multiplicando por el factor n · · · (n − r + 1)/(b − a)r . Entonces resulta: b(r) (u) = n · · · (n − r + 1) (b − a)r . 10 para una c´ ubica. 10: Los planos tangente y osculador en el esquema de de Casteljau. A lo largo del c´ alculo de los puntos ∆r bn−k para todo k, a trav´es de los pasos 0 del algoritmo de de Casteljau y de las diferencias hacia adelante se generan los puntos intermedios ∆k bij , i + j + k ≤ n.

5, 1], INTERSECTAR (b0 , . . , bm ; c′0 , . . , c′n ; ε) INTERSECTAR (b0 , . . , bm ; c′n , . . 8 3. T´ecnicas de B´ezier La propiedad de variaci´ on decreciente La subdivisi´on no es solamente una herramienta de utilidad pr´actica sino tambi´en es importante desde el punto de vista te´orico. A continuaci´on vemos como ´esta se puede emplear para demostrar la propiedad de la variaci´ on decreciente: El n´ umero de veces que un plano arbitrario H corta a una curva b(t); t ∈ [0, 1] es menor o igual que el n´ umero de veces que H corta al pol´ıgono de B´ezier de b(t).

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