21. Kosmologika - Vetenskapsmännen Huygens, Christiaan (16291695) Hörmander, Lars (1931- ) Israel, Werner (1931-) Kerr, Roy Patrick (1934- ) koch, helge von (1870-1924) Kovalevskaja, Sofia http://w1.371.telia.com/~u37103753/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. Helge Von Koch Captured This Idea In A Mathematical Construct: Slide 21 of 44. http://www.cquest.utoronto.ca/env/env200y/LECTURES/Lecture11/sld021.htm

23. Helge Von Koch Captured This Idea In A Mathematical Construct: Slide 9 of 53. http://www.cquest.utoronto.ca/env/jie222y/LECTURES/lecture6/sld009.htm

24. Efg's Fractals And Chaos -- Von Koch Curve Lab Report Neils Fabian helge von koch's Snowflake . ScreenvonkochSnowflake.JPG (37028 bytes), Swedishmathematician helge von koch introduced the koch curve in 1904. http://homepages.borland.com/efg2lab/FractalsAndChaos/vonKochCurve.htm

Fractals and Chaos von Koch Curve Lab Report Neils Fabian Helge von Koch's "Snowflake" Purpose The purpose of this project is to show how to create a von Koch curve, including a von Koch snowflake. Mathematical Background Swedish mathematician Helge von Koch introduced the "Koch curve" in 1904. Starting with a line segment, recursively replace the line segment as shown below: The single line segment in Step 0, is broken into four equal-length segments in Step 1. This same "rule" is applied an infinite number of times resulting in a figure with an infinite perimeter. Here are the next few steps: If the original line segment had length L, then after the first step each line segment has a length L/3. For the second step, each segment has a length L/3 , and so on. After the first step, the total length is 4L/3. After the second step, the total length is 4 L/3 , and after the k th step, the length is 4 k L/3 k . After each step the length of the curve grows by a factor of 4/3. When repeated an infinite number of times, the perimeter becomes infinite. For a more detailed explanation of the length computation, see [ , p. 107] or

25. Von Koch Curve koch Snowflake. Levy efgs Computer Lab Fractals and Chaos von koch CurveReport Biography of helge von koch (18701924) . http://www.apriljuju.com/philadelphia-museum-of-fine-art.htm

26. Www.time2bcool.at/Exiter18 - Virtualcard Von Helge Koch Translate this page helge koch. offline im chat . Nachricht an helge koch Um den Absender mitzuschicken,log' dich bitte ein oder führe in deinem Text den Absender an! http://www.time2bcool.at/ger/ccshow.asp?ccid=HCP4MK4UCHPT21O

27. Www.helgebreloer.de Translate this page Im Jahr 1996 wurde von helge Breloer eine fortlaufende Diskussionsveranstaltungeingeführt Methode koch am Runden Tisch GRUGA-PARK IN ESSEN In diesem Kreis http://www.helgebreloer.de/

Helge Breloer Helge Breloer 49733 Haren-Emmmeln Tel.: 05932-6490 Fax: 05932- 2174 E-mail: HelgeBreloer@t-online.de Helge Breloer, Methode Koch Baumwert- und Baumschadenberechnung Es werden folgende Themen behandelt: Rechtliche und methodische Grundlagen der Methode Koch Das Sachwertverfahren ZierH 2000 – ein Sachwertverfahren? Die einzelnen Wertermittlungsschritte nach der Methode Koch: Totalschaden: Wertminderungen, Abgrenzung von Total- und Teilschaden Teilschaden: Reststandzeit bzw. Behandlungsdauer, Funktionsverlust, Ersatzinvestition, Teilschaden in Relation zum Baumwert Praxis der Baumwert- und Baumschadenberechnung PC-Programme: Totalschaden und Teilschaden Beurteilung eines Baumes vor Ort Aufnahme der Daten durch die Teilnehmer Wertermittlung und Teilschadenberechnung durch die Teilnehmer Termine 3. April 2003 Verkehrssicherungspflicht Umfang und Grenzen der Haftung des Baumkontrolleurs vor Ort Art und Umfang der Baumkontrollen Wie oft muss kontrolliert werden? Lichtraumprofil Baumschutzsatzung und Nachbarrecht Ausnahmegenehmigungen und Befreiungen Kostenlast - mit und ohne Baumschutzsatzung?

28. Literartur Translate this page von Werner koch, 3. Auflage, bearbeitet von helge Breloer - Auszug - Verlag VersicherungswirtschafteV Karlsruhe 1997, ISBN 3-88487-634-1, 94 Seiten, 27 http://www.helgebreloer.de/literatur.htm

neu neu Die Buchreihe Zu Band 1, Was ist mein Baum wert? „Methode Koch", Thalacker Medien , Postfach 8364, 38133 Braunschweig, Tel. 0531-180040, Fax 0531-3800425 Werner Koch, 3. Auflage, bearbeitet von Helge Breloer - Auszug - Verlag Versicherungswirtschaft e.V. Karlsruhe 1997, ISBN 3-88487-634-1, 94 Seiten, 27 Tabellen, 3 Schaubilder, kart. Helge Breloer Die vom Bundesgerichtshof anerkannte Methode Koch im Vergleich zu anderen Methoden Stand 1988 SCHRIFTENREIHE TAXATIONSPRAXIS HEFT LP 21 Claus Mattheck/Helge Breloer Der Baumbruch in Mechanik und Rechtsprechung 2. Auflage 1994 Rombach Verlag Freiburg/Brsg. Helge Breloer 49733 Haren (Ems) Tel.: 05932-6490 Fax: 05932-2174 www.baeumeundrecht.de Kontakt: info@baeumeundrecht.de

29. Fractales : Courbes De Von Koch Et De Minkowski en flocon de neige (snowflake) et a été découverte par helge von koch. http://mariefrance.hellot.free.fr/mfh/Classique1.html

Fractales Classiques Fractales dites "self-similar" A l'origine de ce type de fractales est un , une courbe plus ou moins complexe et un initiateur, En pratique, on s'arrête après une dizaine d'itérations : certaines courbes dites "space filling", ont la propriété comme leur nom l'indique, de remplir très vite toute la surface, l'initié dira que leur dimension fractale est de 2 et pour d'autres, le résultat esthétique est obtenu très vite aprés 5 ou 6 itérations. dimension Courbe en flocon de neige C'est la courbe la plus connue; elle est appelée courbe en flocon de neige (snowflake) et a été découverte par Helge von Koch. L'initiateur est un triangle équilatéral. B. Mandelbrot en parle dans son livre "The Fractal Geometry of Nature". Courbe en flocon de neige Etape 1 Etape 2 Cette courbe est une variante de la courbe précédente, la courbe en flocon de neige. L'initiateur est un carré. Bien que le générateur semble prôche de ceux présentés sur ces pages, le résultat est bien différent. Ces courbes sont ramifiées, contrairement aux courbes qui ne se coupent jamais et sont dites "self-avoiding" ou "nonramified".Les 2 courbes présentées correspondent, l'une au motif , le générateur , tracé à l'intérieur du carré, et l'autre à l'extérieur du carré. B Mandelbrot consacre un chapitre : Ramification and Fractal Lattices à ce type de courbes.

30. Untitled Translate this page Niels Fabian helge von koch. Nato il 25 gennaio 1870 a Stoccolma,morto l'11 marzo 1924 a Stoccolma. Fu studente di Mittag-Leffler 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.

31. Flocon De Von Koch. Translate this page En 1904, helge von koch (1870-1924 - Suède) publie l'article « Sur une courbecontinue sans tangente, obtenue par une construction géométrique http://www.chez.com/algor/math/koch.htm

Flocon de von Koch. En 1904, Helge von Koch (1870-1924 - Suède) publie l'article : « Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire » qui décrit la ligne actuellement connue sous le nom de 'flocon de von Koch'. La méthode. Pour tracer cette courbe, il faut: Tracez un triangle équilatéral Remplacer le tiers central de chaque côté par une pointe dont la longueur de chaque côté égale aussi au tiers du côté Recommencer cette construction sur chaque côté des triangles ainsi formés. Un peu d'aide. Reprenons la construction de la première étape: Si on considère que les points a et b ont pour coordonnées (x a ,y a ) et (x b ,y b ), nous obtenons: le point c (fin du premier tiers de ab) a pour coordonnées: (x a +(x b -x a )/3, y a +(y b -y a le point d (fin du deuxième tiers de ab) a pour coordonnées: (x a +2*(x b -x a )/3, y a +2*(y b -y a le point e (sommet du triangle construit sur le tiers central de ab) a pour coordonnées: ((x c +x d )*cos 60°-(y d -y c )*sin 60°, (y c +y d )*cos 60°+(x d -x c )*sin 60°) Comment faire?

32. Koch Snowflake -- From MathWorld koch Snowflake, A fractal, also known as the koch island, which wasfirst described by helge von koch in 1904. It is built by starting http://mathworld.wolfram.com/KochSnowflake.html

Applied Mathematics Complex Systems Fractals Koch Snowflake A fractal , also known as the Koch island , which was first described by Helge von Koch in 1904. It is built by starting with an equilateral triangle , removing the inner third of each side, building another equilateral triangle at the location where the side was removed, and then repeating the process indefinitely. The Koch snowflake can be simply encoded as a Lindenmayer system with initial string "F-F-F" string rewriting rule Let be the number of sides, be the length of a single side, be the length of the perimeter , and the snowflake's area after the n th iteration. Further, denote the area of the initial n triangle , and the length of an initial n = side 1. Then The capacity dimension is then Now compute the area explicitly, so as Some beautiful tilings , a few examples of which are illustrated above, can be made with iterations toward Koch snowflakes. In addition, two sizes of Koch snowflakes in area ratio 1:3 tile the plane , as shown above (Mandelbrot). Another beautiful modification of the Koch snowflake involves inscribing the constituent triangles with filled-in triangles, possibly rotated at some angle. Some sample results are illustrated above for 3 and 4 iterations.

33. Von Koch's Snowflake Fractal By René called von koch's Snowflake. This figure was first constructed bythe mathematician helge von koch in 1904. The curve begins with http://cis.elizabethtowncc.com/Rene/VonKochSnowflakeHome.html

von Koch's Snowflake Fractal Curve by The interactive drawing below (a Java applet) shows the first level of a fractal curve called von Koch's Snowflake. This figure was first constructed by the mathematician Helge von Koch in 1904. The curve begins with an equilateral triangle, then each side of the triangle is subdivided into three equal parts, the middle segment is removed and replaced by two sides of an equilateral triangle. This process gives us the initial figure below. The actual curve is defined as the limit of the process outlined above as the number of iterations approaches infinity. In the figure below, the number of iterations is limited to six because the limitations of the display are reached at that level. That is, the curves obtained by iterating more than six times are practically indistinguishable from the one at level six on a computer display. In the applet below, you can choose a level and a color. The computer will then draw a fractal snowflake with as many iterations as you selected using the chosen color. Back to the beginning of Fractal Curves Updated: April 2000.

34. Die Fraktale Koch-Kurve Als Java-Applet Translate this page Insel). Nach helge von koch, schwed. Mathematiker, 1870-1924. html. (helgevon koch). Download koch_Kurve.zip (Applet und Code ca. 2 kb). http://www.jjam.de/Java/Applets/Fraktale/Koch_Kurve.html

JJAM Home Applets Fraktale: Juliamenge Juliamenge MA JuliaFinder Koch-Kurve ... L-System 2 Mathematik: Funktionsplotter Eratosthenes-Sieb Verschiedenes: Morsezeichen-Ticker Scripts Gäste 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 eMail

35. Stephen Wolfram: A New Kind Of Science -- Index T-z Goldbach's Conjecture, 911 von Kármán, Theodore (Hungary/Germany/USA, 18811963)and vortex streets, 998 von koch, NF helge (Sweden, 1870-1924) and nested http://www.wolframscience.com/nks/index/names/t-z.html?SearchIndex=t-z

36. Kalender Translate this page Niels Fabian helge von koch 54 Jahre, Mathematiker (22.09.2001) Inhaltsuchen oben *25 Jan 1870 Stockholm +11 Mrz 1924 Danderyd. http://www.info-kalender.de/kal/k000125.htm

S a m i n f o k a l e n d e r J a n Januar Februar April Mai ... (suchen) Marie-Paule Belle Inhalt suchen oben *25 Jan 1946 Dagmar Berghoff Inhalt suchen oben *25 Jan 1943 Berlin Roy Black Inhalt suchen oben *25 Jan 1943 +9 Okt 1991 Filme Robert Boyle Inhalt suchen oben *25 Jan 1627 +30 Dez 1691 London Robert Burns 37 Jahre, schott. Dichter Inhalt suchen oben *25 Jan 1759 +21 Jul 1796 Dumfries Anton Diel 61 Jahre, Bundestagsabge. (SPD) Inhalt suchen oben *25 Jan 1898 +6 Apr 1959 Bundestag Antonio Eanes Inhalt suchen oben *25 Jan 1935 Alcains John Arbuthnot Fisher Inhalt suchen oben *25 Jan 1841 +10 Jul 1920 London Petra Gerster Inhalt suchen oben *25 Jan 1955 Worms David Grossman Inhalt suchen oben *25 Jan 1954 Jerusalem Niels Fabian Helge von Koch Inhalt suchen oben *25 Jan 1870 +11 Mrz 1924 Danderyd Inhalt suchen oben *25 Jan 1958 Uerdingen Dean Jones Inhalt suchen oben *25 Jan 1936 Decatur Alabama. Alicia Keys Inhalt suchen oben *25 Jan 1981 New York NY. 60 Jahre, Bundestagsabge. (CDU) Inhalt suchen oben *25 Jan 1943 Essen Bundestag Witold Lutoslawski Inhalt suchen oben *25 Jan 1913 Warschau Tim Montgomery Inhalt suchen oben *25 Jan 1975 Gaffney South Carolina.

37. 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.

38. 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.

39. Capítulo 1 - Objetos Fractales. Autosemejanza Translate this page Este es el caso del matemático suizo helge von koch (1870-1924) “On a ContinuousCurve without Tangents Constructible from Elementary Geometry”. http://coco.ccu.uniovi.es/geofractal/capitulos/01/01-09.shtm

40. ORESME NKU Sept 1998 a most comfortable facility, to read the paper On a continuous curve without tangentsconstructible from elementary geometry by helge von koch (an English 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

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