21. De Kromme Van Helge Von Koch (1904) De Kromme van helge von koch (1904). Een lijnstuk wordt in drie gelijkestukken verdeeld. Het middelste stuk wordt weggelaten en http://home.planet.nl/~philip.van.egmond/wiskunde/koch1-n.htm

De Kromme van Helge von Koch (1904) Een lijnstuk wordt in drie gelijke stukken verdeeld. Het middelste stuk wordt weggelaten en er worden twee even grote lijnstukken toegevoegd. Zo ontstaat de tekening hieronder. In het midden is een gelijkzijdige driehoek ontstaan, waarvan de basis ontbreekt. Dan krijg je de tekening, hieronder. Na nog een keer hetzelfde principe toepassen, krijg je: Ik heb dat 100 keer gedaan en dan krijg je het volgende plaatje: Veronderstel dat de lengte van het eerste lijnstuk 1 dm (=10 cm)is. Dan wordt de lengte van elk van de lijnstukken in de tweede tekening 1/3 dm. De totale lengte van die 4 lijnstukken 4*1/3= 4/3 dm. In de derde tekening zijn er al 16 lijnstukken getekend. Elke keer wordt zo'n lijnstukje 3 keer zo klein, maar je krijgt wel 4 keer zoveel lijnstukken. De totale lengte wordt dus elke keer 4/3 keer zo groot. De totale lengte van de 16 lijnstukken is dus (4/3) ~ 1,78 dm.

22. TPE Fractales : Biographie De Von Koch Translate this page Waclaw Sierpinski. helge von koch. Michael Barnsley. E-mail. Biographie de von koch.Niels Fabian helge von koch est né le 25 janvier 1870 à Stockholm en Suède. http://irchat.free.fr/tpefractales/vkbio.php

@import url("style.css"); BOURDEAUDUCQ Sébastien / RIQUET Jean Charles TPE Fractales Vous êtes ici : Version imprimable Sommaire Page d'accueil et introduction I - Présentation Définition d'une fractale Le flocon de Von Koch Le triangle de Sierpinski L'ensemble de Mandelbrot Autres fractales basées sur les complexes La dimension fractale II - Les fractales dans la nature 1. Etude d'objets fractals naturels La côte de Bretagne Chez les végétaux : Le chou-fleur Le chou romanesco Les fougères Dans le corps humain : L'intestin grêle Les poumons Le réseau coronarien 2. La modélisation des fractales naturelles Les L-systèmes IFS Conclusion Divers Biographies des personnes célèbres ayant étudié les fractales Benoît Mandelbrot Gastion Julia Waclaw Sierpinski Helge Von Koch Michael Barnsley Annexes Bibliographie Le TPE Nous contacter Livre d'or E-mail Biographie de Von Koch Niels Fabian Helge Von Koch est né le 25 janvier 1870 à Stockholm en Suède. Il est célèbre par la courbe qui porte son nom , dont l'étude a été publiée en 1904. Il est mort le 11 mars 1924 à Stockholm en Suède, sa ville natale.

23. Helge Von Koch - Encyclopedia Article About Helge Von Koch. Free Access, No Regi von koch curve encyclopedia article about von koch curve. Free géométrique élémentaire pour l étude de certaines questions de la théoriedes courbes plane by the Swedish mathematician helge von koch Niels Fabian http://encyclopedia.thefreedictionary.com/Helge von Koch

Dictionaries: General Computing Medical Legal Encyclopedia Helge von Koch Word: Word Starts with Ends with Definition Niels Fabian Helge von Koch January 25 January 25 is the 25th day of the year in the Gregorian Calendar. There are 340 days remaining (341 in leap years). Events 1327 - Edward III becomes King of England. 1494 - Alfonso II becomes King of Naples. 1533 - Henry VIII of England marries his second wife Anne Boleyn. 1554 - Foundation of São Paulo city, Brazil. 1791 - The British Parliament splits the old province of Quebec into Upper and Lower Canada. Click the link for more information. Centuries: 18th century - 19th century - 20th century Decades: 1820s 1830s 1840s 1850s 1860s - Years: 1865 1866 1867 1868 1869 - Events Franco-Prussian War January 6 - The inauguration of the Musikverein (Vienna). January 10 - John D. Rockefeller incorporates Standard Oil Click the link for more information. March 11 March 11 is the 70th day of the year in the Gregorian Calendar (71st in Leap years). There are 295 days remaining. Events 1513 - Leo X is elected pope.

24. Helge Von Koch Födelseland Sverige Födelseår 1870 Död år 1924. helge von kochföddes i Sverige år 1870. Var helge von koch dog år 1924. Tillbaka http://www.kosmologika.net/Scientists/Koch.html

Födelseland: Sverige Födelseår: 1870 Död år: 1924 Helge von Koch föddes i Sverige år 1870. Var student till Gösta Mittag-Leffler (1846-1927) och disputerade redan vid 22 års ålder med en avhandling som kombinerade teorin för differentialekvationer med analytiska koefficienter med teorin för oändliga determinanter. Han är känd främst för Kochkurvan inom fraktalteorin. Han blev professor vid KTH år 1905 och efterträdde Gösta Mittag-Leffler som professor vid Stockholms högskola år 1911 men var sjuk ofta vilket ledde till att Marcel Riesz övertog hans tjänst. Helge von Koch dog år 1924.

25. 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)

26. Die Fraktale Koch-Kurve Als Java-Applet Translate this page Die koch-Kurve (auch Schneeflockenkurve oder kochsche Insel). Nach helge von koch,schwed. Mathematiker, 1870-1924. Niels Fabian helge von koch. (helge von koch). 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

27. 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.

28. 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.

29. Lexikon - Koch-Kurve Definition Erklärung Bedeutung Translate this page Artikel auf Englisch koch curve. Die koch-Kurve ist eine vom schwedischenMathematiker helge von koch erstmals 1904 vorgestellte Kurve. http://www.net-lexikon.de/Koch-Kurve.html

Suche: Info Mitglied werden A B ... Impressum Beta 0.71 powered by: akademie.de Wikipedia PHP PostgreSQL ... englischen Lexikon Google News zum Stichwort Koch-Kurve Definition, Bedeutung, Erkl¤rung im Lexikon Artikel auf Englisch: Koch curve Die Koch-Kurve ist eine vom schwedischen Mathematik er Helge von Koch erstmals vorgestellte Kurve . Es handelt sich bei ihr um eines der ersten formal beschriebenen fraktalen Objekte. Die Koch-Kurve ist auch als Kochsche Schneeflocke bekannt; letztere entsteht aus geeigneter Kombination dreier Koch-Kurven. Inhaltsverzeichnis 1 Konstruktion 2 Eigenschaften 3 Erstver¶ffentlichungen 4 Weblinks Konstruktion Man kann die Kurve anschaulich mittels eines iterativen Prozesses konstruieren. Zu Anfang ist ein Linienst¼ck der L¤nge "1" gegeben. Die Iteration besteht nun darin, dass alle Linienst¼cke der Kurve in drei gleichlange St¼cke unterteilt werden, auf dem jeweils mittleren St¼ck ein gleichseitiges Dreieck errichtet wird, und die Basis dieses Dreiecks (also das urspr¼ngiche Drittelst¼ck) entfernt wird. Diese Iteration wird nun unendlich oft wiederholt. Als Endergebnis entsteht die Koch-Kurve.

30. 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

31. 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.

32. 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

33. WisFaq! van von koch. Bij onze praktische opdracht voor wiskunde hebben we twee formulesgekregen. Een voor de omtrek van de fractal (de sneeuwvlok van helge van koch http://www.wisfaq.nl/showrecord3.asp?id=6344

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. 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 Helge von Koch in the news 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 A biography page of Niels Fabian Helge von Koch from the MacTutor History of Mathematics archive at the University of St Andrews Sponsored Links Harry Potter and the Prisoner of Azkaban unabridged on CD DVD New Releases ... to Ancestry.com!

36. 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.

37. 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

38. 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

39. 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.

40. 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.

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