41. The Koch Curve Above left we see the first four orders of the koch curve (drawn using Fractintand 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.

42. ORESME NKU Sept 1998 tangents constructible from elementary geometry by helge von koch (an The question of what von koch meant by a continuous uniform function arose. http://www.nku.edu/~curtin/oresme_sep_98.html

Please Email comments or suggestions to: curtin@nku.edu or to: otero@xavier.xu.edu ORESME Home Page Dan Curtin's Home Page

43. The ORESME Home PageVon Koch Section 4 The 1906 reference is helge von koch, Une méthode géométrique élémentaire pourl étude de certaines questiones de la théorie des courbes planes, Acta http://www.nku.edu/~curtin/grenouille.html

Von Koch Section IV. Please Email comments or suggestions to: curtin@nku.edu You may view the four pages of the 1906 paper that do not appear in the 1904 version. Acta Mathematica (1906), 145-174. You have Vardi's translation of pp. 145-170. Page 171 Page 172 Page 173 Page 174 ... Dan Curtin's Home Page

44. The Von Koch Curve This curve was constructed by the swedish mathematician helge von koch (1870 1924) as an example of a continuous curve in the plane without a tangent at http://www.nada.kth.se/~berg/vonkoch.html

The von Koch Curve A line is divided into three equal parts, on the middle third an equilateral triangle is drawn whose base is removed. If you as starting line choose the sides of an equilateral triangle, in the limit you get the von Koch snowflake curve. This curve was constructed by the swedish mathematician Helge von Koch (1870 - 1924) as an example of a continuous curve in the plane without a tangent at every point. The same curve is also an example of a nowhere differentiable continuous function.

45. Koch Snowflake One of the most symmetric and easy to understand fractals; it is named after theSwedish mathematician helge von koch (18701924), who first described it in http://www.daviddarling.info/encyclopedia/K/Koch_snowflake.html

Return to The Worlds of David Darling INDEX LATEST NEWS ARCHIVE ... Z entire Web this site Koch snowflake One of the most symmetric and easy to understand fractals exterior snowflake , the Koch antisnowflake , and the flowsnake curves ALL MATHEMATICS ENTRIES BACK TO TOP var site="s13space1234"

46. Von Koch Curve Neils Fabian helge vonkoch (18701924) curve first appear in his paper Une méthode géométrique......Draws nth iteration of von koch curve. http://members.lycos.co.uk/ququqa2/fractals/Koch.html

von Koch curve Instructions: Draws n th iteration of von Koch curve. Description: Neils Fabian Helge von Koch (1870-1924) curve first appear in his paper Une méthode géométrique élémentaire pour l'étude de certaines questions de la théorie des courbes plane published in 1906. This curve is constructed by dividing a line segment 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. You can observe process of creation of Koch curve by setting up the first step and incrementing number of steps using " " button. If one starts with an equilateral triangle and applies the construction, one gets the von Koch snowflake (sometimes called the von Koch star) as the limit of the construction. Others von Koch curves: Von Koch curve for a square Von Koch curve for triangles Random von Koch curve Contents ... Back to main page

47. Perfect & Pathological Math Biography Georg Cantor, helge von koch, Waclaw Sierpinski, David Hilbert.Week Three · Definitions of dimension · Topological dimension versus fractal http://www.moscholars.org/curriculum/Perfect and Pathological Mathematics.htm

Teachers Perfect and Pathological Mathematics I. Course description Quick! When is a coffee cup equivalent to a donut? Is it possible for a shape to have infinite surface area and finite area? How do you know? In this class, we will meet the fringe elements of the world of mathematics: we'll encounter well-behaved and mathematically beautiful ideas and theorems, and we'll spend a lot of time with the misbehaving miscreants that have stymied long-held mathematical assumptions. We'll not only study the functions, curves and ideas that have reassured and rocked the world of math; we'll also study the means by which a theorem, proposition or lemma becomes mathematically valid. In addition, we'll explore the lives of the movers and shakers of the history of math and develop some ideas about the evolving nature of mathematics. Was it invented or discovered? What are the most pressing mathematical questions of our time? II. Instructor's educational preparation and current employment III. Rationale for inclusion in a program for gifted students

48. Koch Curve g©om©trique ©l©mentaire by the Swedish mathematician helge von koch.The better known koch snowflake (or koch star) is the same as the curve, http://www.algebra.com/algebra/about/history/Koch-curve.wikipedia

Koch curve Regular View Dictionary View (all words explained) Algebra Help my dictionary with pronunciation , wikipedia etc Wikimedia needs your help in the final days of its fund drive. See our fundraising page The Red Cross and other charities also need your help. Koch curve The first four iterations of the Koch snowflake. The Koch curve. Contents Description Implementation External link See also Description The Koch curve is a mathematical curve , and one of the earliest fractal curves to have been described. It appeared in a paper entitled "Sur une courbe continue sans tangente, obtenue par une construction g©om©trique ©l©mentaire" by the Swedish mathematician Helge von Koch . 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.

49. EROSION CONTROL | FEATURE ARTICLE - The Fractal Nature Of Erosion Discovered by mathematician helge von koch in 1904, this snowflake is a primeexample of the fractal geometry related to the problem of measuring Great http://www.forester.net/ecm_0205_fractal.html

An abstract mathematical concept might eventually help create erosion-prediction models. By John M. Fuhrmann fractal predict erosion as well. It is time for this groundbreaking research to graduate from the laboratory to the field. The recent findings open a warehouse of mathematical tools to the erosion community. Fractal mathematics fills volumes of dusty books, and the critical discovery by Yonathan Shapir, Ph.D., and his colleagues pierces the membrane between physical erosion and years of complicated mathematical theory. The future of erosion research promises to be an exciting one as the Rochester laboratories pass the baton to geologists, engineers, and landscape architects. Fractals, Fractals Everywhere

50. 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 da Curva de von 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.

51. Helge Von Koch von koch, militare di carriera, e di Agathe Henriette Wrede, helge von koch http://www.matmatprof.it/filosofia_e_dintorni/matematici/helge_von_koch.htm

INDEX CERCA NEL SITO FORUM Luogo di discussione Filosofica MAILING LIST CHAT vota www.matmatprof.it nella categoria Cultura NEWS Libri su Nietzsche Sito su Nietzsche Pubblicazioni Leopardi filosofo GUIDA RAPIDA Scienza Medicina Salute Filosofia ... Letteratura APPROFONDIMENTI Biblioteca Biografie Il Pensiero Donne filosofe ... Filosofi matematici MINI CHAT /n nickname SITI PARTNER Portale di filosofia www.filosofico.net www.socrate.tk Festival della Filosofia ... Filosofia Politica IPSE DIXIT Helge von Koch Nacque a Stoccolma il 25 gennaio 1870; figlio di Richert Vogt von Koch, militare di carriera, e di Agathe Henriette Wrede, Helge Von Koch frequentò una buona scuola superiore di Stoccolma, completando i suoi studi nel 1887, quindi si inscrisse all'Università di Stoccolma. Pubblicò numerosi lavori di matematica, riguardanti i sistemi lineari e le equazioni differenziali, per i quali fu molto apprezzato, e, infine, nel 1911, divenne professore di matematica all'Università di Stoccolma. Von Koch è famoso per la curva che porta il suo nome e che apparve nel suo lavoro Une méthode géométrique élémentaire pour l'étude de certaines questions de la théorie des courbes planes , pubblicato nel 1906. Morì sempre a Danderyd, presso Stoccolma l'11 Marzo 1924.

52. DIMENSIONS OF THE FRACTALS Find a dimension of the snowflake curve (of helge von koch). You will draw itwith plotting simplifed expression koch_CURVE(2,-2,2,2,n), where n can be http://rc.fmf.uni-lj.si/matija/logarithm/worksheets/fractal.htm

DIMENSIONS OF THE FRACTALS Between the late 1950s and early 1970s Benoit Mandelbrot evolved a new type of mathematics, capable of describing and analysing the structured irregularity of the natural world, and coined a name for the new geometric forms: fractals . Fractals are forms with detailed structure on every scale of magnification. The simplest fractals are self-similar. Small pieces of them are identical to the whole. We are going to see only some very simple examples. Some pictures: The dimension of the fractal is very interesting. We are used to the idea, that a line is one-dimensional, a plane two-dimensional, a solid three-dimensional. But in the world of fractals, dimension aquires a broader meaning, and need not be a whole number. We are going to study the dimensions of the fractals on the example of Sierpinski gasket. This is obtained by repeatedly deleting the middle quarter of a triangle, removing smaller and smaller pieces, forever. The Sierpinski gasket can be thought of as being composed of three identical gaskets, each

53. Helge Von Koch - Wikipedia, Den Fria Encyklopedin helge von koch hörde till en adlig familj och var sonson till helge von kochutmärkte sig genom en till såväl innehåll som omfång betydande matematisk http://sv.wikipedia.org/wiki/Helge_von_Koch

Wikimedia:Wikimedia beh¶ver din hj¤lp f¶r att samla in 200 000 dollar. Titta p¥ insamlingssidan f¶r mer information. Helge von Koch Fr¥n Wikipedia, den fria encyklopedin. Niels Fabian Helge von Koch Niels Fabian Helge von Koch , f¶dd 25 januari i Stockholm , d¶d 11 mars i Danderyd strax norr om Stockholm, d¤r han ¤ven bodde st¶rre delen av sitt liv, svensk matematiker som ¤r mest k¤nd f¶r att ha givit sitt namn till en av de f¶rsta fraktalerna Koch-kurvan Inneh¥ll Familj Karri¤r Produktion Se ¤ven ... redigera Familj Helge von Koch h¶rde till en adlig familj och var sonson till justitiekanslern Nils Samuel von Koch (1801-1881) och son till ¶verstel¶jtnanten i Livgardet till h¤st Richert Vogt von Koch (1838-1913), som ¤ven var romanf¶rfattare. Han hade tv¥ syskon som utm¤rkte sig p¥ skilda omr¥den, komposit¶ren Sigurd von Koch och socialpolitikern Gerard Halfred (G.H.) von Koch redigera Karri¤r Efter studentexamen vid H¶gre reall¤roverket i Stockholm 1887, skrevs von Koch samma ¥r in som student vid Stockholms h¶gskola och f¶ljande ¥r (1888) vid Uppsala universitet . Han var l¤rjunge till G¶sta Mittag-Leffler i Stockholm, men d¥ Stockholms h¶gskola ¤nnu inte hade examensr¤tt, avlade han sin

54. MathBlues.com > Featured Articles > Dazzling Fractals One of the mathematicians he researched was helge von koch. In 1904, almost 50years earlier, koch had a brush with fractals. koch constructed an odd figure http://www.mathblues.com/mainpages/sampleissue/articles/1/

SAT Tips Poll Math Doodles Contests ... Sample Issue Clouds are not spheres, mountains are not cones, coastlines are not circles and bark is not smooth, nor does lightning travel in a straight line. - Benoit Mandelbrot I n nature, irregularity rules! Look around you and notice that natural forms don't have much respect for the naïve shapes of Euclidean geometry (squares, circles, triangles, spheres, cones, etc...). Straight lines and smooth curves, which are the key features of Euclidean geometry, are only rough approximations for describing irregular shapes. The irregularity in natural systems is a sign of their incredible complexity. How do you understand this complexity? In the 1970s, Yale professor Benoit Mandelbrot searched for a new geometry to describe irregularity. Mandelbrot's search led him to shapes that he named fractals. He coined the word fractal from the Latin fractua , which means irregular. He found that fractals offer a useful and more realistic representation, or model, of natural systems. Inspired by the work of several mathematicians before him, Mandelbrot channeled his creative genius into developing the new geometry.

55. Forschungsbericht Translate this page Karch helge, in den Forschungsschwerpunkten (und Projekten auf Basis der koch Gunter Fritz, in den Drittmittelprojekten. Vergleich von Effekten einer http://www.zv.uni-wuerzburg.de/forschungsbericht/FOBE-akt/prd-K.htm

Personenindex Schlagwortindex Startseite: Forschungsbericht Personenindex K Kackstätter Uwe in den Drittmittelprojekten: Bodenphysikalische, geochemische und tonmineralogische Untersuchungen an ausgewählten nordbayerischen Tonlagerstätten (BayForrest-Projekt F-22(F)) Diffusionsverhalten organischer und anorganischer Modellsubstanzen in ausgewählten geologischen Einheiten (BayForrest-Projekt F-22(2F) Kacprzak Sylwia in den Forschungsschwerpunkten (und Projekten auf Basis der Grundausstattung): Die rasante Entwicklung quantenchemischer Methoden erlaubt zunehmend komplexere Anwendungenin prakti... Kagerhuber Ulrike in den Forschungsschwerpunkten (und Projekten auf Basis der Grundausstattung): Apoptose in Maus-Fibroblasten... in den Drittmittelprojekten: Apoptose in Maus-Fibroblasten Kahle Erhart in den Forschungsschwerpunkten (und Projekten auf Basis der Grundausstattung): Forschungsschwerpunkte1. Editionen medizinischer Standardwerke der Spätantike, des Mittelalters und... Kaiser Dorkas in den Forschungsschwerpunkten (und Projekten auf Basis der Grundausstattung): BIOTA West Africa in den Drittmittelprojekten: Arthropoden als Ökosystem Ingenieure: Der Einfluß von Ameisen und Termiten auf Bodeneigenschaften und Vegetation Kaiser Udo in den Drittmittelprojekten: Verbundübergreifende Reanalysen zu Prädiktoren des Patientenschulungserfolges und Entwicklung von allgemeinen Empfehlungen zur Evaluation von Patientenschulungen (Projekt QF) Verbundübergreifende Reanalysen zu Prädiktoren des Patientenschulungserfolges und Entwicklung von allgemeinen Empfehlungen zur Evaluation von Patientenschulungen (Projekt QF) Kaiser Werner

56. Die Fraktale Koch-Kurve Als Java-Applet Translate this page Eigentlich wollte helge von koch 1904 nur eine Kurve beschreiben, die, obwohlsie fast überall stetig ist, an keiner Stelle eine Tangente besitzt, http://www.jjam.de/Java/Applets/Fraktale/Koch_Kurve.html

JJAM Home Applets Tetraeder ... Kugel 2 Fraktale: Juliamenge Juliamenge MA Julia-Generator Koch-Kurve ... Lindenmayer-System 2 Mathematik: Funktionsplotter Eratosthenes-Sieb Miller-Rabin-Test Verschiedenes: Morsezeichen-Ticker Analoguhr Scripts Kontakt - Applets : Fraktale : Koch-Kurve - Die fraktale Koch-Kurve als Java-Applet. Mehr Zacken mit linkem Mausklick - Weniger mit rechtem Mausklick. [Die fraktale Koch-Kurve als Java-Applet mit Quellcode zum Download. Das Applet der Koch-Kurve lässt sich allerdings nur mit aktiviertem Java betrachten !] Die Koch-Kurve (auch Schneeflockenkurve oder kochsche Insel). Nach Helge von Koch, schwed. Mathematiker, 1870-1924 KochKurve.java (Helge von Koch) Download Koch_Kurve.zip (Applet und Code ca. 2 kb) Impressum Datenschutz Nutzung eMail

57. De.wikipedia.org/wiki/Helge_von_Koch helge von koch Wikipedia - Translate this page helge von koch Figlio di Richert Vogt von koch, militare di carriera, e AgatheHenriette Wrede. Frequenta una buona scuola superiore e finisce i suoi http://de.wikipedia.org/wiki/Helge_von_Koch

58. Adelborgska Klippsamling -Kända Döda Personer: K von koch, helge, Professor, Avliden von koch, RGH, Redaktör, 40årsdag von koch,Carl, Överste, Avliden von koch, RV, Överstelöjtnant, Avliden http://www.genealogi.net/sf_arkiv/listor/adelborg/adelb_reg_k.htm

Adelborgska klippsamlingen "Kända döda" En användbar samling tidningsurklipp hos GF är Otto Adelborgs samling som sträcker sig mellan 1907 och 1978. Den har den lite missvisande ryggtiteln "Kända döda" men alla klippen handlar inte om avlidna, och många personer är inte särskilt kända heller. Otto Adelborgs urval är högst personligt. Personregister finns på data och i utskrift. Här kan Du ta fram listor över personer i Adelborgs klippsamling: K Kafle, E.S., Kapten, Avliden Kafle, E.S., Kapten Bohusläns reg, Avliden Kajerdt, John, Major, Avliden Kalén, Magnus, Läroverksadjunkt, Avliden Kallenberg, Frithiof, Hovrättsråd, Avliden Kallenberg, Ernst, Professor, Avliden Kalling, Sven, Greve, Bergsingenjör, Avliden Kalling, Bo, Greve, Professor, Avliden Kalling, Axel, Greve, Disponent, Avliden Kalling, Gustaf, Greve, Konstnär, Avliden Kalling, Göran, Greve, Advokat, Avliden Kallstenius, Gottfrid S.N., Professor, Avliden

59. INDEX OF NAMES von koch, NF helge (Sweden, 18701924) and nested curves, 934 von Neumann,John (Hungary/USA, 1903-1957) and CAs, 876, 879, 928 and computers, 1108 http://www.wolframscience.com/nksonline/index/names/t-z.html?SearchIndex=Turing,

60. STEFAN STENUDD - KAOS - Nyordning För Oordningen - - - - - Fraktaler av koch. helge von koch (18701924) doktorerade i Uppsala 1892, arbetadesom docent vid Stockholms Högskola till 1905, sedan som professor på http://www.stenudd.se/myter/kaos.htm

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