Minkowski Curve in Acheron 2.0
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(since Jan 2010)
Construction Back to Top
As almost all fractals curves, the construction of the Minkowski curve is
based on a recursive procedure.
The length of the Minkowski curve increases at each iteration. On each iteration, the length of the segments is divided by four and the number of segments is multiplied by eight, hence the total curve length is multiplied by 2 with each iteration.
Obviously, the length of the curve tends to infinity as the iteration number increases.
All Variations described are available using Acheron 2.0
Born: 22 June 1864 in Alexotas, Russian Empire (now Kaunas, Lithuania)
Died: 12 Jan 1909 in Gottingen, Germany
Hermann Minkowski studied at the Universities of Berlin and Konigsberg. He received his doctorate in 1885 from Konigsberg. He taught at several universities, Bonn, Konigsberg and Zurich. In Zurich, Einstein was a student in several of the courses he gave.
Minkowski accepted a chair in 1902 at the University of Gottingen, where he stayed for the rest of his life. At Gottingen he learnt mathematical physics from Hilbert and his associates.
By 1907 Minkowski realised that the work of Lorentz and Einstein could be best understood in a non-educlidean space. He considered space and time, which were formerly thought to be independent, to be coupled together in a four-dimensional 'space-time continuum'. This space-time continuum provided a framework for all later mathematical work in relativity.
Minkowski was mainly interested in pure mathematics and spent much of his time investigating quadratic forms and continued fractions. His most original achievement, however, was his 'geometry of numbers'.
At the young age of 44, Minkowski died suddenly from a ruptured appendix.
School of Mathematics and Statistics - University of StAndrews, Scotland