Helge von Koch

Swedish mathematician

Helge von Koch

Niels Fabian Helge von Koch

Born| (1870-01-25)25 January 1870

Stockholm, Sweden

Died| 11 March 1924(1924-03-11) (aged 54)

Danderyd Municipality, Sweden

Nationality| Swedish
Alma mater| Stockholm University College, Uppsala University
Known for| Koch snowflake
Scientific career
Fields| Mathematician
Institutions| Royal Institute of Technology, Stockholm University College

Niels Fabian Helge von Koch (25 January 1870 – 11 March 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described.

He was born to Swedish nobility. His grandfather, Nils Samuel von Koch (1801–1881), was the Chancellor of Justice. His father, Richert Vogt von Koch (1838–1913) was a Lieutenant-Colonel in the Life Guards of Horse of the Swedish Army. He was enrolled at the newly created Stockholm University College in 1887 (studying under Gösta Mittag-Leffler), and at Uppsala University in 1888, where he also received his bachelor's degree (filosofie kandidat) since the non-governmental college in Stockholm had not yet received the rights to issue degrees. He received his PhD in Uppsala in 1892. He was appointed professor of mathematics at the Royal Institute of Technology in Stockholm in 1905, succeeding Ivar Bendixson, and became professor of pure mathematics at Stockholm University College in 1911.

Von Koch wrote several papers on number theory. One of his results was a 1901 theorem proving that the Riemann hypothesis implies what is now known to be the strongest possible form of the prime number theorem.[1]

He described the Koch curve in a 1904 paper entitled "On a continuous curve without tangents constructible from elementary geometry" (original French title: "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire").[2]

He was an invited speaker at the International Congress of Mathematicians in 1900 in Paris with talk Sur la distribution des nombres premiers[3] and in 1912 in Cambridge, England, with talk On regular and irregular solutions of some infinite systems of linear equations.[4]

## Notes[edit]

1. ^ von Koch, Niels Helge (1901), "Sur la distribution des nombres premiers", Acta Mathematica, 24: 159–182, doi:10.1007/BF02403071, S2CID 119914826
2. ^ von Koch, Helge (1904). "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire". Arkiv för Matematik (in French). 1: 681–704. JFM 35.0387.02.
3. ^ "Sur la distribution des nombres premiers". Congrès Int. Math., Paris 1900. ICM proceedings. University of Toronto Press. 1902. pp. 195–8. JFM 32.0205.01.
4. ^ "On regular and irregular solutions of some infinite systems of linear equations". Proc. 5. Intern. Math. Congr. ICM proceedings. Vol. 1\. University of Toronto Press. 1913. pp. 352–365. JFM 44.0402.01.

## References[edit]

* Marquis of Ruvigny and Raineval (1911). The Plantagenet Roll of the Blood Royal: Mortimer-Percy Volume). pp. 250–251.
* Edgar, Gerald, ed. (1993). Classics on Fractals. Addison-Wesley. ISBN 9780201587012. "contains an English translation of the paper 'On a continuous curve...'"

## External links[edit]

* Works by or about Helge von Koch at Internet Archive
* O'Connor, John J.; Robertson, Edmund F., "Helge von Koch", MacTutor History of Mathematics Archive, University of St Andrews
* Helge von Koch at the Mathematics Genealogy Project

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Fractals

Characteristics|

* Fractal dimensions
* Assouad
* Box-counting
* Higuchi
* Correlation
* Hausdorff
* Packing
* Topological
* Recursion
* Self-similarity

Iterated function
system|

* Barnsley fern
* Cantor set
* Koch snowflake
* Menger sponge
* Sierpinski carpet
* Sierpinski triangle
* Apollonian gasket
* Fibonacci word
* Space-filling curve
* Blancmange curve
* De Rham curve
* Minkowski
* Dragon curve
* Hilbert curve
* Koch curve
* Lévy C curve
* Moore curve
* Peano curve
* Sierpiński curve
* Z-order curve
* String
* T-square
* n-flake
* Vicsek fractal
* Hexaflake
* Gosper curve
* Pythagoras tree
* Weierstrass function

Strange attractor|

* Multifractal system

L-system|

* Fractal canopy
* Space-filling curve
* H tree

Escape-time
fractals|

* Burning Ship fractal
* Julia set
* Filled
* Newton fractal
* Douady rabbit
* Lyapunov fractal
* Mandelbrot set
* Misiurewicz point
* Multibrot set
* Newton fractal
* Tricorn
* Mandelbox
* Mandelbulb

Rendering techniques|

* Buddhabrot
* Orbit trap
* Pickover stalk

Random fractals|

* Brownian motion
* Brownian tree
* Brownian motor
* Fractal landscape
* Lévy flight
* Percolation theory
* Self-avoiding walk

People|

* Michael Barnsley
* Georg Cantor
* Bill Gosper
* Felix Hausdorff
* Desmond Paul Henry
* Gaston Julia
* Helge von Koch
* Paul Lévy
* Aleksandr Lyapunov
* Benoit Mandelbrot
* Hamid Naderi Yeganeh
* Lewis Fry Richardson
* Wacław Sierpiński

Other|

* "How Long Is the Coast of Britain?"
* Coastline paradox
* Fractal art
* List of fractals by Hausdorff dimension
* The Fractal Geometry of Nature (1982 book)
* The Beauty of Fractals (1986 book)
* Chaos: Making a New Science (1987 book)
* Kaleidoscope
* Chaos theory

Authority control databases

International|

* ISNI
* VIAF

National|

* France
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* Germany
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Academics|

* MathSciNet
* Mathematics Genealogy Project
* zbMATH

People|

* Deutsche Biographie

Other|

* IdRef

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