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         Koch Helge Von:     more detail
  1. Instruments and Measurements: Chemical Analysis, Electric Quantities, Nucleonics and Process Control: v. 2 by Helge Von Koch, Gregory Ljungberg, 1961-12
  2. Mathématicien Suédois: Ivar Fredholm, Albert Victor Bäcklund, Waloddi Weibull, Gösta Mittag-Leffler, Helge Von Koch, Johan Håstad (French Edition)
  3. Instruments and Measurements: Chemical Analysis, Electric Quantities, Nucleonics and Process Control, Vol. 2 (Proceedings Fifth International Instruments & Measurements Conference, Sep 1960, Stockholm, Sweden) by Helge; Ljungberg, Gregory; Reio, Vera (editors) von Koch, 1961-01-01
  4. Föreläsningar Öfver Teorin För Transformationsgrupper (Swedish Edition) by Helge Von Koch, 2010-01-09
  5. Instruments and Measurements: Chemical Analysis, Electric Quantities, Nucleonics and Process Control, Vol. 1 (Proceedings Fifth International Instruments & Measurements Conference, Sep 1960, Stockholm, Sweden) by Helge; Ljungberg, Gregory; Reio, Vera (editors) von Koch, 1961-01-01
  6. Instruments & Measurements 2vol by Helge Von Koch, 1961

21. Kosmologika - Vetenskapsmännen
Translate this page Huygens, Christiaan (1629-1695) Hörmander, Lars (1931- ) Israel, Werner (1931-) Kerr, Roy Patrick (1934- ) koch, helge von (1870-1924) Kovalevskaja, Sofia
http://www.kosmologika.net/Scientists/
På Kosmologikas sidor återfinns på många ställen länkar till kortare biografier över olika vetenskapsmän som har deltagit i utvecklandet av dessa spännande teorier. På denna sida finns länkar till alla dessa biografier samlade på ett enda ställe. Personerna är dels listade i både bokstavs- och födelsedagsordning men även efter nobelprisår (för de personer som har fått nobelpriset) samt i betydelsefullhetsordning för vetenskapen. Dessutom har jag nyligen lagt till Brucemedaljörer som är den högsta utmärkelsen inom astronomin, nobelpriset undantaget, samt Fields medalj som är matematikens nobelpris och som dessutom bara delas ut en gång vart fjärde år samt slutligen wolfpriset som är ett israeliskt pris som rankas steget under Nobelpriset men som ofta är åtminstone ett decennium snabbare med utnämningarna. Alfabetisk ordning Ahlfors, Lars (1907- )
Alembert, Jean le Ronde d' (1717-1783)

Alfvén, Hannes Olof Gösta (1908-1995)

Alpher, Ralph A. (1921- )
...
Zwicky, Fritz (1898-1974)

Födelsedagsordning Fermat, Pierre de (1601-1665)

22. Niels Fabian Helge Von Koch

http://alpha01.dm.unito.it/personalpages/cerruti/Az1/koch.html
Niels Fabian Helge von Koch Nato il 25 gennaio 1870 a Stoccolma, morto l'11 marzo 1924 a Stoccolma.
Fu studente di Mittag-Leffler e gli succedette nel 1911 all'Università di Stoccolma. E' famoso per la curva di Koch, costruita dividendo una linea in tre parti uguali e sostituendo il segmento intermedio con gli altri due lati del triangolo equilatero costruito su di esso. Questa costruzione si ripete su ognuno dei segmenti (ora 4) e così all'infinito. Si ottiene una curva continua di lunghezza infinita e non derivabile in alcun punto.
I principali risultati di Koch riguardano i sistemi di infinite equazioni lineari in infinite incognite.

23. A Curva De Koch
Translate this page A curva de koch foi apresentada pelo matemático sueco helge von koch,em 1904, construindo-aa partir de um segmento de recta. Construção
http://www.educ.fc.ul.pt/icm/icm99/icm14/koch.htm
Floco de Neve e Curva de von Koch A curva de Koch foi apresentada pelo matemático sueco Helge von Koch, em 1904, construindo-a a partir de um segmento de recta. Construção da Curva de von Koch:
  • Divide-se esse segmento em três partes iguais. Substitui-se o segmento médio por dois segmentos iguais, de modo a que, o segmento e médio e os dois novos segmentos formem um triângulo equilátero. Obteve-se uma linha poligonal com quatro segmentos de comprimento igual. Posteriormente, repetem-se os passos para cada um dos segmentos obtidos.
  • Obtém-se assim, no limite de iterações, uma curva que pode ser considerada como um modelo simplificado de uma costa, no entanto, quando comparada com a última, esta curva tem uma irregularidade demasiado sistemática. Tal como uma costa, a curva de von Koch tem um comprimento infinito. Esta curva deu origem a um outro fractal, conhecido como floco de neve ou ilha de von Koch (modelo rudimentar da costa de uma ilha e muito semelhante a um floco de neve). Este último modelo é construído partindo de um triângulo equilátero.

    24. Flocon de von Koch
    Translate this page Niels Fabian helge von koch est né le 25 janvier 1870 à Stockholmen Suède et mort le 11 mars 1924 dans cette même ville. La
    http://www.aromath.net/Page.php?IDP=423&IDD=0

    25. Snowflake Curve
    adding more and more, smaller and smaller triangles at each stage, is called thekoch s SNOWFLAKE CURVE, named after Niels Fabian helge von koch (Sweden, 1870
    http://scidiv.bcc.ctc.edu/Math/Snowflake.html
    The Snowflake Curve
    1. Start with an equilateral triangle whose sides have length 1. 2. On the middle third of each of the three sides, build an equilateral triangle with sides of length 1/3. Erase the base of each of the three new triangles. 3. On the middle third of each of the twelve sides, build an equilateral triangle with sides of length 1/9. Erase the base of each of the twelve new triangles. 4. Repeat the process with this 48-sided figure. See the likeness to a crystal of snow emerge?
    At the right, figure 4 is magnified by a power of two.
    The "limit curve" defined by repeating this process an infinite number of times, adding more and more, smaller and smaller triangles at each stage, is called the Koch's SNOWFLAKE CURVE , named after Niels Fabian Helge von Koch (Sweden, 1870-1924).
    The snowflake curve has some interesting properties that may seem paradoxical.
  • The snowflake curve is connected in the sense that it does not have any breaks or gaps in it. But it's not smooth (jagged, even), because it has an infinite number of sharp corners in it that are packed together more closely than pebbles on a beach.
  • n - 1 units are added at the nth step, so the length of the snowflake is larger than 3 + 1 + 1 + 1 + 1 + 1 + ....... = infinity.
  • 26. Manfred Boergens - Briefmarke Des Monats Januar 2004
    von Niels Fabian helge von koch (1870 - 1924).
    http://www.fh-friedberg.de/users/boergens/marken/briefmarke_04_01.htm
    Briefmarke des Monats Liste aller Briefmarken
    vorige Marke
    zur Leitseite
    Briefmarke des Monats Januar 2004
    Schweden 2000
    Fraktale "Schneeflocke" von Niels Fabian Helge von Koch (1870 - 1924) Im Jahre 1904, also vor 100 Jahren, konstruierte der Stockholmer Mathematikprofessor Helge von Koch fraktalen Kurve
    Konstruktion der Koch'schen Schneeflocke
    Die Koch'sche Schneeflocke ist eine fraktale Kurve
    haben. Dann ist die n -te Iteration ein Polygon mit n Seiten
    n
    Umfang n
    n a a . Das Ausgangsdreieck ( . Bei der i -ten Iteration kommen i-1 i . In der i i-1 i i-1 i n (endliche geometrische Reihe) noch n n n n
    Fraktale Dimension Fraktalen Gebilden kann man eine fraktale Dimension D zuordnen. Die Koch'sche Schneeflocke hat die Dimension D log log c r c und r D log c log r Sierpinski-Dreieck Waclaw Sierpinski c und r r . So ergibt sich D log log n -ten Iterationsschritt in r n c r , also D n -ten Iterationsschritt in r c r , also D n -ten Iterationsschritt in r c r und D
    entstanden. L L Sei nun s L(s) s L(1) L(s) L aufzufassen, zudem mit der Vorstellung, dass lim L(s) L s L(s) s gegen Unendlich.

    27. The Koch Curve
    © Copyright 2002, Jim Loy. Above left we see the first four orders of the kochcurve (drawn using Fractint and Paint Shop Pro), discovered by helge von koch.
    http://www.jimloy.com/fractals/koch.htm
    Return to my Mathematics pages
    Go to my home page
    The Koch Curve
    Above left we see the first four orders of the Koch curve (drawn using Fractint and Paint Shop Pro ), discovered by Helge von Koch. Sometimes, a straight line segment is called the first order. And then the four images above left are the next four orders. You can probably see how each order is built from the previous one. Above right we see the third order Koch island (or snowflake), made up of three Koch curves. Below, is the fifth order Koch curve, magnified four times. The sixth order Koch curve (below) looks much like the fifth order, except that each tiny point is indistinct. It's hard to tell what is going on. Actually it is made up of many tinier points. But the resolution of the graphic image is inadequate to show points that small. The actual Koch curve (and island) is the limit of infinitely many orders. It looks like the picture below, again with inadequate resolution. You may have noticed that the Koch curve is very self-similar (see Fractals and Self-Similarity ). Various parts of it (the infinite order version) are identical to larger and smaller parts. So, each point that you see in the fifth order curve becomes a very convoluted portion of the curve in higher orders.

    28. Helge Von Koch
    Article on helge von koch from WorldHistory.com, licensed from Wikipedia,the free encyclopedia. Return to Article Index helge von koch.
    http://www.worldhistory.com/wiki/H/Helge-von-Koch.htm
    World History (home) Encyclopedia Index Localities Companies Surnames ... This Week in History
    Helge von Koch
    Niels Fabian Helge von Koch January 25 March 11 ) was a Swedish mathematician, who gave his name to the famous fractal known as the Koch curve , which was one of the earliest fractal curves to have been described. He was born into a family of Swedish nobility . His grandfather, Nils Samuel von Koch (1801-1881), was the Attorney-General ("Justitiekansler") of Sweden. His father, Richert Vogt von Koch (1838-1913) was a Lieutenant-Colonel in the Royal Horse Guards of Sweden. von Koch wrote several papers on number theory . One of his results was a theorem proving that the Riemann hypothesis is equivalent to a strengthened form of the prime number theorem He described the Koch curve in a paper entitled "Une méthode géométrique élémentaire pour l'étude de certaines questions de la théorie des courbes plane" [1].
    Reference
    • The Plantagenet Roll of the Blood Royal (Mortimer-Percy Volume) by the Marquis of Ruvigny and Raineval (1911), pages 250 - 251
    External link

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    29. Collection De Nombres, Courbes Fractales Ou Pseudo-fratales
    Translate this page point. § Une partie quelconque de la courbe est semblable à la courbeentière. helge von koch (1870-1924). Pour être précis § La
    http://membres.lycos.fr/villemingerard/Suite/FracCour.htm
    NOMBRES - Curiosités, théorie et usages Accueil Dictionnaire Rubriques Index ... M'écrire Édition du: RUBRIQUE: FRACTALES Introduction Index des objets fractals Complexes Propriétés ... Suites Sommaire de cette page COURBE DE KOCH - FLOCON DE NEIGE Autres courbes Courbe de Peano Courbe de Hilbert Courbe du dragon Pages voisines Symétries Points Paradoxes Géométrie ... Chaîne d'Or Bienvenue aux lecteurs de Tangente – BP 10214 – 95106 Argenteuil - cedex COURBES FRACTALES
    • Courbes continues sans dérivée – dérivable nulle part Courbes de dimension différente de 1 - comprise entre 1 et 2
    Monstre mathématique!
    Voir Introduction aux fractales COURBE DE KOCH - FLOCON DE NEIGE Flocon de neige ou courbe de Koch (1904) Deux principes de construction Une figure initiale: un triangle équilatéral
    Une règle de transformation
    Sur le tiers central de chaque segment Poser un triangle équilatéral, et Effacer la base
    Répétez cette opération sur la figure obtenue
    Et, ceci, autant de fois que vous le voulez
    Cette courbe converge uniformément vers une courbe continue sans point double elle n'admet de tangente en aucun point Une partie quelconque de la courbe est semblable à la courbe entière Helge von Koch Pour être précis: La courbe de von Koch correspond à la transformation d'un côté du triangle équilatéral Le flocon de neige est la figure obtenue en utilisant trois courbes de von Koch le long des côtés d'un triangle équilatéral Théorie Courbe de Koch ou flocon de neige Courbe de longueur infinie et d'aire

    30. Euclide ( 3e Siècle Avant Jésus-Christ)
    Translate this page dans la nature. 1904 Publication de la courbe de von koch par lemathématicien suédois helge von koch. 1915 Publication du
    http://membres.lycos.fr/fractales001/histoire.html
    • Euclide
    • ( 3e siècle avant Jésus-Christ)
      Ce mathématicien grec a rassemblé l'essentiel de la géométrie connue à son temps et a développé le principe de dimension entière de l'espace (première, deuxième, troisième).
      Cette géométrie, trop régulière, ne donne pas de bons modèles de la réalité. En effet, un arbre peut-il vraiment être décrit par des rectangles?
      Cliquer ici pour revenir où vous étiez

    • JULIA Gaston Maurice

    • français, 1893-1978
      Né en Algérie en 1893, il fut envoyé au front français durant la première Guerre Mondiale, où il fut blessé et perdit son nez (il devra porter un masque). C'est lors de longs séjours dans les hôpitaux que ce jeune mathématicien ébauchera ses premiers travauxsur un sujet "pointu" relatifs aux fonctions complexes en prolongement de ceux commencés par Fatou :
      Mémoire sur l'itération des fonctions rationnelles, publié en 1918.
      Les ensembles de Julia ainsi découverts sont très "curieux" :
      ils ont un aspect fractal et seront la source des travaux de Benoît Mandelbrot des années 1970 où l'apport de l'outil informatique permit la visualisation de ces ensembles étonnants remettant en cause le concept usuel de courbe.
      A l'âge de 25 ans, il publie un ouvrage, "Mémoire sur l'itération des fonctions", qui fut honoré du Grand Prix de l'Académie des sciences.

    31. Il Fiocco Di Neve Di Koch
    Translate this page Variazione tematica. Mutazioni geometriche nella metafonia,il fiocco di neve el’isola di helge von koch.
    http://www.nicolaschepis.it/fiocco_di_neve_di_koch.htm
    V ariazione tematica Mutazioni geometriche nella metafonia, il fiocco di neve e l’isola di Helge Von Koch Metafonia Ipotesi e Verità di Nicolò Schepis Un rumore offre un’immensa profusione d’armoniche, che rende complesso un sistema, una dimensione del caos dal quale non possiamo prevedere gli effetti. Quante parti mancanti d’infiniti anelli ci sono sconosciuti? Se visualizzassimo nella nostra scena visiva uno sfondo turbolento di una nuvola, avvalendoci di un ingranditore che ci permettesse di poter osservare il fenomeno con risoluzioni diverse, ci accorgeremmo via, via, attraversando le protuberanze infinitesimali d’incontrare ramificazioni infinite, filamenti che si biforcano in grovigli sempre più complessi; afferma Penrose: “ a un ingrandimento maggiore, il piccolo risulta simile all’intero mondo Siamo d’innanzi ad una nuova geometria, Il matematico Helge Von Koch diede origine a figurazioni autosomiglianti, l’esempio più coinvolgente è il “ fiocco di neve ” o “ l’isola di Koch ”. Presumendo un’infinita reciprocità di figure autosomiglianti si rivela un paradosso affascinante della geometria frattale e cioè che il perimetro che si ottiene è illimitato al contrario della sua aria che è finita. Una linea illimitata circoscrive un’area finita.

    32. Koch Curve
    hode g?m?rique entaire pour l ?ude de certaines questions de la th?riedes courbes plane by the Swedish mathematician helge von koch 1. The
    http://www.fact-index.com/k/ko/koch_curve.html
    Main Page See live article Alphabetical index
    Koch curve
    The Koch curve is a mathematical curve , and one of the earliest fractal curves to have been described. It appeared in a paper entitled "Une méthode géométrique élémentaire pour l'étude de certaines questions de la théorie des courbes plane" by the Swedish mathematician Helge von Koch [1]. The better known Koch snowflake (or Koch star ) is the same as the curve, except it starts with an equilateral triangle (instead of a line segment ). Eric Haines has developed the sphereflake fractal , a three- dimensional version of the snowflake One can imagine that it was created by starting with a line segment, then recursively altering each line segment as follows:
  • divide the line segment into three segments of equal length. draw an equilateral triangle that has the middle segment from step one as its base. remove the line segment that is the base of the triangle from step 2.
  • After doing this once the result should be a shape similar to a cross section of a witch's hat. The Koch curve is the limit approached as the above steps are followed over and over again.

    33. Encyclopedia4U - Helge Von Koch - Encyclopedia Article
    helge von koch. This article is licensed under the GNU Free DocumentationLicense. It uses material from the Wikipedia article helge von koch .
    http://www.encyclopedia4u.com/h/helge-von-koch.html
    ENCYCLOPEDIA U com Lists of articles by category ...
    Encyclopedia Home Page
    SEARCH :
    Helge von Koch
    Niels Fabian Helge von Koch January 25 March 11 ) was a Swedish mathematician , who gave his name to the famous fractal known as the Koch curve , which was one of the earliest fractal curves to have been described. von Koch wrote several papers on number theory . One of his results was a theorem proving that the Riemann hypothesis is equivalent to a strengthened form of the prime number theorem He described the Koch curve in a paper entitled "Une méthode géométrique élémentaire pour l'étude de certaines questions de la théorie des courbes plane" [1].
    External links
    [1] A biography page of Niels Fabian Helge von Koch from the MacTutor History of Mathematics archive at the University of St Andrews http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Koch.html
    Content on this web site is provided for informational purposes only. We accept no responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. We encourage you to verify any critical information with the relevant authorities.
    Privacy
    This article is licensed under the GNU Free Documentation License . It uses material from the Wikipedia article " Helge von Koch

    34. Matematici E Filosofi
    helge von koch nacque a Stoccolma il 25 gennaio 1870; figlio di RichertVogt von koch, militare di carriera, e di Agathe Henriette Wrede, helge von
    http://www.itis-molinari.mi.it/documents/Tesina_Mate/matematici.html
    Placidus Johann Nepomuk, meglio noto come Bernhard Bolzano nacque il 5 ottobre 1781, a Praga e vi morì il 18 dicembre 1848. Bolzano fu un grande filosofo, matematico e teologo, diede un contributo significativo alla matematica e alla teoria del sapere. Bolzano entrò nella facoltà di filosofia dell’università di Praga nel 1796, studiando filosofia e matematica. Nell’autunno del 1800 iniziò gli studi teologici. Nel 1804 conseguì il dottorato in geometria e, in seguito, fu ordinato sacerdote . Sempre nel 1804 gli fu assegnata la cattedra di filosofia e religione all’università di Praga. Nel 1819, Bolzano fu sospeso dai suoi incarichi con l’accusa di essere eretico . Nel 1816 pubblicò Der Binomische Lehrsatz e nel 1817 Ein Analytischer Bewais. Egli si pose un problema profondo: la necessità di perfezionare e arricchire il concetto di numero. Bolzano pubblicò Wissenschaftslehre, sulla teoria del sapere. Il suo lavoro sui paradossi fu uno studio dell’infinito che fu pubblicato nel 1851. Diede un esempio di corrispondenza biunivoca tra elementi di un insieme infinito e gli elementi di un suo sotto-insieme proprio.
    Georg Cantor nacque a San Pietroburgo nel 1845 e morì nel 1918 ad Halle. Egli espose la teoria dei numeri irrazionali

    35. Koch
    Niels Fabian helge von koch. Born 25 Jan 1870 in Stockholm, SwedenDied 11 March 1924 in Stockholm, Sweden. Show birthplace location.
    http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Kch.htm
    Niels Fabian Helge von Koch
    Born: 25 Jan 1870 in Stockholm, Sweden
    Died: 11 March 1924 in Stockholm, Sweden
    Show birthplace location Previous (Chronologically) Next Biographies Index
    Previous
    (Alphabetically) Next Welcome page Helge Koch was a student of Mittag-Leffler and succeeded him in 1911 at Stockholm University. He is famous for the Koch curve. This is constructed by dividing a line into three equal parts and replacing the middle segment by the other two sides of an equilateral triangle constructed on the middle segment. Repeat on each of the (now 4) segments. Repeat indefinitely. It gives a continuous curve which is of infinite length and nowhere differentiable. Koch's principal results were on infinitely many linear equations in infinitely many unknowns. References (2 books/articles) References elsewhere in this archive: A poster of this mathematician is available Show me von Koch's curve Previous (Chronologically) Next Biographies Index
    Previous
    (Alphabetically) Next Welcome page
    History Topics Index
    Famous curves index ... Search Suggestions JOC/EFR December 1996 The URL of this page is:
    http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Koch.html

    36. Fractals: Von Koch Curve
    The von koch curves, named from the swedish mathematician helge von koch who originallydevised them in 1904, are perhaps the most beautiful fractal curves.
    http://users.swing.be/TGMSoft/curvevonkoch.htm
    DisplayHeader( "Geometric Fractals", "The Von Koch Curve", 0, "main_fractals.htm", "Back to Fractals Main Page"); Content Introduction Construction Properties Variations Author Biography All pictures from WinCrv Introduction The Von Koch curves, named from the swedish mathematician Helge Von Koch who originally devised them in 1904, are perhaps the most beautiful fractal curves. These curves are amongst the most important objects used by Benoit Mandelbrot for his pioneering work on fractals.
    More than any other, the Von Koch curves allows numerous variations and have inspired many artists that produced amazing pieces of art.
    Construction The construction of the curve is fairly simple.
    A straight line is first divided into three equal segments. The middle segment is removed and replaced by two segments having the same length to generate an equilateral triangle. Applying such a 4-sides generator to a straight line leads to this:
    This process is then repeated for the 4 segments generated at the first iteration, leading to the following drawing in the second iteration of the building process:
    The third iteration already gives a nice picture:
    Increasing the iteration number provides more detailed drawings. However, above 8 iterations, the length of the segments becomes so small ( in fact, close to a single pixel) that further iterations are useless, only increasing the time of curve drawing.

    37. El Conjunto De Koch
    Translate this page Definidas por helge von koch en 1904, estas curvas se forman a partir de un segmento,por la sustitución de su tercio central por dos segmentos de longitud
    http://platea.pntic.mec.es/~mzapata/tutor_ma/fractal/koch1.htm
    Práctica 2.-
    CURVAS POLIGONALES DE KOCH.
    Definidas por Helge von Koch en 1904, estas curvas se forman a partir de un segmento, por la sustitución de su tercio central por dos segmentos de longitud tambien un tercio, pero formando ángulos de 60º. Proceso que se repite recursivamente en cada segmento de las figuras que progresivamente se van obteniendo. Por tanto la poligonal de nivel 1 es un segmento: Para NIVEL=1
    Para NIVEL=2
    Para NIVEL=3
    Para NIVEL=4
    Para NIVEL=5
    Para NIVEL=6
    ACTIVIDAD A REALIZAR Elaborar los procedimientos LOGO para representar la Poligonal de Koch para un nivel n y una longitud dados.

    38. Koch
    Close Window. Tomorrow is Niels Fabian helge von koch s Birthday! We thank you foryour snowflakes. Happy Birthday koch. Born January 25 in Stockholm, Sweden.
    http://curvebank.calstatela.edu/birthdayindex/jan/jan24koch/jan25koch.htm
    Close Window Tomorrow is Niels Fabian Helge von Koch's Birthday! We thank you for your snowflakes. Happy Birthday Koch Born: January 25
    in Stockholm, Sweden Died: March 11, 1924
    near Stockholm, Sweden

    39. Koch Doodles
    all. It was invented by a Swedish mathematician called helge von koch(18701924) and is usually called the koch snowflake. To see
    http://www.geocities.com/aladgyma/articles/scimaths/koch.htm
    Koch Doodles
    One of the most famous fractals was invented long before the concept of a fractal was well-understood, or even understood at all. It was invented by a Swedish mathematician called Helge von Koch (1870-1924) and is usually called the Koch snowflake. To see how to construct it, take a line, divide it into thirds, and erect a triangle on the middle third. Next, take the four new lines and do the same to each of them. Et cetera ad infinitum. Play with these images to follow the process: Stage And if the line one begins with is one side of triangle, and the other two sides are treated in the same way, you get the Koch snowflake. Though it doesn’t end there, of course. One can use squares or rectangles instead of triangles, or both, and one can vary where one erects them and how high one erects them. The possibilities are endless, but you can get some flavor of them from the following: Image Stage Return to Subject Index Return to General Index Return to Maths Index

    40. FRACTALES - "Matemática De Belleza Infinita" => INTRODUCCIÓN Al Concepto Fract
    Translate this page Ahora bien. helge von koch no dejó a descubierto todos los misterios(o utilidades) de su isla. Antes de continuar, preferiría
    http://www.geocities.com/capecanaveral/cockpit/5889/koch2.html
    LAS CURVAS DE KOCH: Lagos, Islas y otros En la búsqueda de nuevos fractales, puede hacerse una comparación (y al mismo tiempo complementar esta búsqueda) al analizar los distintos tipos de curvas de Koch existentes (como la ya conocida Isla Tríada de Koch). El estudio para la generación de estos cuerpos está enfocado a la medición de longitudes de diversos acervos naturales, si así puede llamárseles. Por eso, no debe parecer extraño encontrar definiciones que incluyan a lagos o cabos (y otros). La primera vez que vi estos conceptos me parecieron muy peculiares e incluso crei que se trataba de una broma o un juego de doble sentido (aún tengo mis dudas). Primero que nada, trateremos aspectos ya conocidos del Triángulo de Koch (o copo K o Isla Tríada, como guste) y profundizaremos más en su construcción, para poder sumergirnos en los mentados derivados de esta formación. Como sabrá, la Isla Tríada de Koch se genera a partir de un GENERADOR, que en este caso es un triángulo equilátero. Al colocar otro "invertido" sobre los tercios medios de sus lados, se forma la conocida "Estrella de David". Sobre cada uno de los seis triángulos nuevos se repite lo mismo, infinitas veces. El resultado es nuestro conocido copo K. Si bien es cierto que en la formación de este fractal existen puntos que nunca dejan de desplazarse, tarde o temprano llegan a un límite (o mucho mejor dicho, tienden a un límite) que termina por definir la costa que rodea nuestra isla.

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