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	Helge von Koch
		Niels Fabian Helge von Koch (January 25, 1870 - March 11, 1924) 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.
		One of his results was a 1901 theorem proving that the Riemann hypothesis is equivalent to a strengthened form of the prime number theorem.
		He described the Koch curve in a 1906 paper entitled "Une méthode géométrique élémentaire pour l'étude de certaines questions de la théorie des courbes plane" [1].
	www.ebroadcast.com.au /lookup/encyclopedia/he/Helge_von_Koch.html (123 words)

	Helge von Koch Summary
		Von Koch, the son of a career soldier, was born in Stockholm, Sweden on January 25, 1870.
		Von Koch curves and snowflakes are also unusual in that they have infinite perimeters, but finite areas.
		Niels Fabian Helge von Koch (January 25, 1870 - March 11, 1924) was a Swedish mathematician, who gave his name to the famous fractal known as the Koch snowflake, which was one of the earliest fractal curves to have been described.
	www.bookrags.com /Helge_von_Koch (613 words)

	Koch biography
		The second of von Koch's papers was published in 1892, the year in which von Koch was awarded a doctorate for his thesis which contained the results of the two papers.
		In July 1911 von Koch succeeded Mittag-Leffler as professor of mathematics at Stockholm University.
		Von Koch is famous for the Koch curve which appears in his paper Une méthode géométrique élémentaire pour l'étude de certaines questions de la théorie des courbes plane published in 1906.
	www-history.mcs.st-andrews.ac.uk /Biographies/Koch.html (742 words)

	efg's Fractals And Chaos -- von Koch Curve Lab Report
		The purpose of this project is to show how to create a von Koch curve, including a von Koch snowflake.
		For the von Koch "snowflake," start with an equilateral triangle, and apply the "rule" above to each of the line segments.
		The von Koch curve has a self-similarity, Hausdorff dimension, D = log 4/ log 3 = 1.2619.
	www.efg2.com /Lab/FractalsAndChaos/vonKochCurve.htm (696 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		Niels Fabian Helge von Koch (January 25, 1870 - March 11, 1924) was a Swedish mathematician, who gave his name to the famous fractal known as the Koch snowflake, which was one of the earliest fractal curves to have been described.
		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.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Helge_von_Koch (173 words)

	kochcurve info window (Site not responding. Last check: 2007-10-13)
		The Koch curve is as difficult to understand as the Cantor set or the Serpinski tree.
		Actually Koch's motivation for finding this curve was to provide another example for the discovery made by the German mathematician Karl Weierstrass, who in 1872 had precipitated a minor crisis in mathematics.
		It therefore might come as a surprise that the area enclosed by the Koch curve is finite the proof of which we leave as an exercise for a motivated reader.
	ccl.northwestern.edu /cm/models/kochcurve/info.html (639 words)

	Problem Set 1
		Among the most famous line systems are the von Koch snowflake, first described by Helge von Koch in 1904, the Peano curve, the Hilbert curve, and the Cantor set.
		For the von Koch snowflake, the initiator is an equilateral triangle, and the generator consists of a line segment with the middle third removed and replaced by two sides of an equilateral triangle, as shown.
		In the case of the von Koch snowflake, after stage 0 we have an equilateral triangle, after stage 1 we have a six-pointed star, after stage 2 we have a six-pointed star with little bumps on each point, etc.
	www.cs.dartmouth.edu /~brd/Teaching/AI/Homeworks/ps1.html (1278 words)

	text4
		Koch discovered that by continuing the process endlessly on an increasingly smaller scale it became a continuous curve containing an infinite number of minute bends.
		The Koch curve is of infinite length yet finite space; it is more than a line with one dimension but less than a plane with two dimensions; it is an endless loop where lines never cross; and at any level of magnification a portion resembles the whole.
		Because the repetitions are identical, the Koch curve is a fractal that is self-similar under linear transformation.
	www.scientific-religious.com /text4.html (1262 words)

	Koch's Snowflake, Mandelbrot's Coastline, Alaska Science Forum
		In 1904, the Swedish mathematician Helge von Koch described an interesting curiosity.
		Koch had shown that a finite area can be enclosed by an infinite line.
		In the 1960s, Koch's snowflake resurfaced in the hands of another mathematician given to upsetting his colleagues.
	www.gi.alaska.edu /ScienceForum/ASF9/920.html (780 words)

	Koch Snowflake
		In 1904 the Swedish mathematician Helge von Koch proposed a method for constructing a "snowflake" curve.
		Like the Sierpinski curve, the Koch curve is a closed limit curve of infinite length that bounds a region of finite area.
		Thus the Koch snowflake is an infinitely long curve that encloses a finite area.
	home.comcast.net /~davebowser/fractals/koch.html (457 words)

	Kochbücher für Hobby- und Gourmetköche
		Und 21 der jungen Spitzenköche stellen in einem Kochbuch zwei neue Kreationen aus der Rubrik Gemüse, Kräuter and Salate“ vor — alle reden von der grünen Küche, hier wird ein Kocherlebnis daraus: wie bei Thymian-Kaninchen-Spieß mit Blattsalaten und Thymianöl.
		Jeder Koch ist dabei Pate eines Lebensmittels, das er in einer Warenkunde vorstellt und das die Grundlage seiner Rezepte ist: Nils Potthast kocht zum Beispiel mit Artischocken und Harald Schmitt mit Lauch.
		Wie bei einem Einkaufsbummel durch einen bunten und mit turbulentem Leben erfüllten Suk lässt sie sich von den einzelnen Zutaten inspirieren statt von fertigen Gerichten.
	www.kochmesser.de /buecher.html (3390 words)

	CS212 F98 Problem Set 1
		For the von Koch snowflake, the initiator is an equilateral triangle with sides oriented in a clockwise direction.
		The generator of the von Koch snowflake is a rule that says: for any (oriented) line segment, remove the middle third and replace it by two sides of an equilateral triangle.
		For the von Koch snowflake, the first figure would be the equilateral triangle, the second would be a six-pointed star, the third would be a six-pointed star with little bumps on each point, etc.
	www.cs.cornell.edu /html/cs212-fall98/psets/ps1/ps1.html (1717 words)

	CS212 S98 Problem Set 1
		For the von Koch snowflake, the initiator is an equilateral triangle.
		In the case of the von Koch snowflake, the zero'th figure would be an equilateral triangle, the first figure would be a a six-pointed star, the second figure would be a six-pointed star with little bumps on each point, etc.
		For instance, we should be able to use the square initiator with the original von Koch generator.
	www.cs.cornell.edu /courses/cs212/1998sp/psets/ps1.html (1561 words)

	Koch curve - ExampleProblems.com
		The Koch curve is a mathematical curve, and one of the earliest fractal curves to have been described.
		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.
		The area of the Koch snowflake is 8/5 that of the initial triangle, so an infinite perimeter encloses a finite area.
	www.exampleproblems.com /wiki/index.php?title=Koch_curve&printable=yes (459 words)

	Das Fest
		Und endlich wieder einmal konnte Marianne Nentwich vorführen, welch großartige Schauspielerin sie ist.
		Eine Reihe herausragender Schauspieler, von denen nicht jeder für sich spielt, die vielmehr gemeinsam ein starkes Ensemble bilden.
		Ein starker Stoff, von Regisseur Tiedemann minutiös ausdifferenziert vorgetragen, und dies in einem luxuriösen Ambiente (Bühne Etienne Pluss), das die aufkeimenden Verlogenheiten umso drastischer erscheinen lässt.
	www.josefstadt.org /Theater/Stuecke/Josefstadt/Das_Fest.html (932 words)

	biografia di Niels Fabian Helge von Koch - caos e oggetti frattali - Eliana Argenti e Tommaso Bientinesi
		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.
		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.
		Se si parte da un triangolo equilatero e si applica questo procedimento si ottiene il "fiocco di neve" di von Koch.
	www.webfract.it /FRATTALI/Koch.htm (269 words)

	von Koch curve (Site not responding. Last check: 2007-10-13)
		The von Koch curve is another famous example of a fractal.
		Swedish mathematician Helge von Koch proved that this curve is continuous but nowhere differentiable.
		The von Koch curve is the limit of the set Gk as k tends to infinity, in other words it's what we get if we keep on performing the recursive subdivision described ad infinitum.
	people.bath.ac.uk /dp235/vonkoch.html (321 words)

	The Koch Curve and Visual Resolution at nOnoscience
		The Koch Curve or the von Koch snowflake was discovered by Helge von Koch (1870-1924) in 1904.
		This is the “zeroth” iteration of the Koch curve.
		In the class it was explained that the koch curve is continuous ane “nowhere ” differentiable.
	www.nonoscience.info /2006/08/28/the-koch-curve-and-visual-resolution (1953 words)

	entrepreneurship.de
		Auf der Plattform wird das bereits erfolgreiche Konzept von nordostfussball.de auf alle dritten Liegen erweitert und weiterentwickelt.
		Startup heißt eine Initiative von gruenderinnenzeit.de, die im Wintersemester 2007 erstmalig an der Humboldt-Universität und der Alice Salomon Fachhochschule angeboten wird.
		Helge Löbler: SMILE-SelbstManagementInitiative Leipzig lernt gründen im Labor für Entrepreneurship
	www.labor.entrepreneurship.de /blog (1068 words)

	NetLogo Models Library: Koch Curve
		Helge von Koch was a Swedish mathematician who, in 1904, introduced what is now called the Koch curve.
		The Koch curve is as difficult to understand as the Cantor set or the Sierpinski tree.
		It therefore might come as a surprise that the area enclosed by the Koch curve is finite; the proof of this we leave as an exercise for the reader.
	ccl.northwestern.edu /netlogo/models/KochCurve (767 words)

	interest (Site not responding. Last check: 2007-10-13)
		One mathematician, Helge von Koch, captured this idea in a mathematical construction called the Koch curve.
		Keep on adding new triangles to the middle part of each side, and the result is a Koch curve.
		However, the inner area of the Koch curve remains less than the area of a circle drawn around the original triangle.
	home.comcast.net /~barrebarrett/interest.htm (1180 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		The genuine Von Koch curve, also called snowflake curve, is derived as the limit of a polygonal contour.
		At every step, as shown on the left, the middle third of every side of the polygone is replaced with two linear segments at angles 60° and 120°.
		Of course, the Von Koch curve does not look like a "natural" curve.
	www.freewebs.com /cabriology/vonkoch.htm (250 words)

	Reference.com/Encyclopedia/Helge
		Helge or Helgi is a Scandinavian name derived from Proto-Norse *Hailaga (dedicated to the gods).
		Helge is a given name, a variant of Helgi – an Old Norse name, and the origin of Oleg.
		Niels Fabian Helge von Koch – a Swedish mathematician
	www.reference.com /browse/wiki/Helgi (151 words)

	Lindenmayer Fractals - Generating Fractals - Examples
		It is named after Helge von Koch, who described it in 1904.
		This is a modification of the Koch snowflake, mentioned by Mandelbrot in 1982.
		Mandelbrot is responsible for a huge amount of work and research in the field of fractals, and in fact has an entire field of fractal types named after him.
	www.math.ubc.ca /~cass/courses/m308-03b/projects-03b/skinner/ex-generating.htm (759 words)

	Koch snowflake
		One of the most symmetric and easy to understand fractals; it is named after the Swedish mathematician Helge von Koch (1870-1924), who first described it in 1906.
		The Koch curve has infinite length because each iteration increases the length of a line segment one third, and the iterations go on forever.
		Variations on the flat Koch snowflake include the so-called exterior snowflake, the Koch antisnowflake, and the flowsnake curves.
	www.daviddarling.info /encyclopedia/K/Koch_snowflake.html (267 words)

	Creating Data Types
		In 1904, von Koch described the geometric construction, which we now refer to as the Koch curve.
		Von Koch proved that, in the limit, the Koch snowflake is a curve of infinite length, but it does not have a tangent at any point.
		A randomized Koch snowflake is generated exactly like the Koch snowflake, except that we flip a coin to generate the clockwise and counterclockwise direction at each step.
	www.cs.princeton.edu /introcs/32datatype (7062 words)

	EROSION CONTROL \| FEATURE ARTICLE - The Fractal Nature of Erosion
		Discovered by mathematician Helge von Koch in 1904, this snowflake is a prime example of the fractal geometry related to the problem of measuring Great Britain's coastline.
		After an infinite number of iterations, the von Koch snowflake is finished.
		The von Koch snowflake and Sierpinski triangle are certainly bizarre shapes, but it is easier to harness these figures with mathematics than it is with the random coastline of Great Britain.
	www.forester.net /ecm_0205_fractal.html (3248 words)

	Self-similarity
		One of the first works of Fractal Art was made in 1904 by a Swedish mathematician named Helge von Koch, and his piece was the so-called Koch Snow Flake.
		Koch's Snow Flake is sterile while with God's flakes, variety makes all the difference.
		Koch's tiniest triangles are identical to the big triangle, but way down the line this concoction proves to be an impossible structure.
	www.abarim-publications.com /SelfSimilarity.html (1017 words)

	Arlo Caine's Web Page / Mathematics / Limits with ... (Site not responding. Last check: 2007-10-13)
		Even in the bleak lanscape of a frozen tundra, patterns can be found at all scales, whether in the gentle curve of a wind swept serac or in the intricate crystalline structure of a snowflake.
		Niels Fabian Helge von Koch (1870-1924) was a swedish mathematician who first played with the figures we are discussing.
		In fact, this sequence of drawings does have a limit, in a technical sense, and that limit is called "von Koch's Curve." What's interesting, is that if you arrange 3 copies of the curve along the edges of an equilateral triangle, you get the figure at left.
	math.arizona.edu /~caine/chaos.html (1180 words)

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