Universität Bielefeld
Fakultät für Mathematik

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Achim

2. Dan

Location:: 8°29'37.5"E 52° 2'20"N 147m
Timezone: Middle European (Summer) Time: UTC+2 == MEST: -- 1. Apr^* - 31. Oct⁺; UTC+1 == MET : -- 1. Nov^* - 31. Mar⁺; ^* precisely: last Sunday in previous month; ⁺ precisely: last Sunday in this month
Address:: Achim Flammenkamp
Fakultät für Mathematik
Universitätsstraße 25; Universität Bielefeld
Postfach 100131
33501 Bielefeld
Nordrhein-Westfalen
Germany
Europe
Email:: achim@uni-bielefeld.de
URL:: http://wwwhomes.uni-bielefeld.de/achim/
PGP-key ID:: DAB9090D; use finger achim@chagall.mathematik.uni-bielefeld.de for my public key book

Own Mathematical Works

Exploring NP-hard problems via branch & bound techniques on computers.

E.g. in 1981: Counting special 0-1-matrices: My first such, hundreds of CPU-hours consuming, project together with Torsten Sillke.

For people who care fir citations
Number Theory and Combinatoric
- Generation of primequads
- Waiting values of words in random sequences
- minimal addition chains
- no-three-in-line problem
- sociable groups -- aliquot sequences
- multiply perfect numbers
- Sprague-Grundy-Values of Grundy's Game
- and other ``Take-and-Break'' games
- highly composite numbers
- long periods in subtraction games
- Densest sphere packings in R³ (in german)
- and finally --- an abstract proof
  table of p_min(i) and v_min(i)
Analytic
- Do you remember Escher's map: z -> z^{½(1 + cos ß - i sin ß)}
- Area of the Mandelbrot-Set
- The analytic Tower-Function
- Quickestsort
Geometry
- diagonal intersections in regular n-gons
- Construction of extremal polyedra
- bijective pixel rotation in Euclidean plane
My Diplomarbeit
consists of three parts Additionsketten, Sociable Numbers, as a reprint of Math. Computation 56 (1991), p. 871-873 availible, and the No-Three-in-Line Problem as a reprint of Journal of Combin. Theory, Ser. A 60 (1992), p. 305-311 availible.
My Dissertation
of January 1997 has the topic Lange Perioden in Subtraktions-Spielen and is now availible as compressed PS-file (1.3MB). It is written in german and for a short overview look at my summarium.
Since July '97 a book of Achim Flammenkamp is availible with the title Lange Perioden in Subtraktions-Spielen (ISBN 3-932136-10-1). This is an enlarged study (more than 200 pages) of my dissertation thesis orderable from Hans-Jacobs-Verlag, Lage, Germany for 49,- DM. Have a look at the english translation of its abstract and the summarium.

Further Mathematical Interests

Hobbys

e^2PIi - 1 = 0

0 is the basic number of set theory
1 is the basic number of algebra
2 is the basic number of logic
e is the basic number of analysis
PI is the basic number of geometry
i is the basic number of complex analysis
What is ?
Conway's Game of Life
Go - Wei Qi - Baduk
There are about 4.63*10¹⁷⁰ Go positions on a 19×19 board.

W3 Informations

in german: ordentliche HTML-Beschreibung
in german: Die Goldenen Regeln für schlechtes HTML
WWW - Search
- AltaVista for word search
- Yahoo for subject search
- World Wide Web Worm
WWW FAQ
Falken's Web Tools
Anonymous FTP list

Miscellany

Infos to Sharp PC-E220
astronomy
collected Background Pictures with b/w-catalogue(106kB)
back to my old university
back to my department
other WWW-Server of mathematical departments in Germany
:-)
Numbers, numbers, numbers ...
The Geometry Junkyard
My private heap of links
Annoyed by junk, bulked email or spam?
Local People's Homepage
My really fast algorithm to generate primes via the Sieve of Eratosthenes and its C-source-code.
A C++ -package to handle finite nimber arithmetic.
Z80 CPU assembler & monitor for Linux
Open Important Problems in Science
- in Art: What is art and what is no art
- in Philosophy: Define Consciousness
- in Mathematics: Prove or disprove the Riemanean Conjecture
- in Computer Science: Prove or disprove NP=P
- in Physics: Develope a short concise theory of Quantengravitation
- in Chemistry: Synthesize a compound with given attributes or prove its nonexistence (e.g. Br0₄^- 1972)
- in Biology: Find the "correct" systematic of Organisms
Only for local access

Known Sociable groups

of order 1 (perfect numbers)
of order 2 (amicable numbers like (220,284) )
of order 4 (interesting)
of order >= 5 (rare)

Look at David Moews's Page or Jan M. Pedersen's Page for more information or at the progress in aliquot sequence computations.

Münzenprägen ist ein altes 2 Personenspiel, das seinen Ursprung in China hat. Man muß abwechselnd eine ganze Zahl > 1 ansagen. Dabei sind solche Zahlen ausgeschlossen, die sich als Summe bereits genannter Zahlen darstellen lassen. Verloren hat der Spieler, der keine Zahl mehr ansagen kann. Eine vorzügliche Darstellung findet sich in Winning Ways for Your Mathematical Plays, E.R.Berlekamp, J.H.Conway, R.K.Guy (1982) Deutsche Ausgabe: Gewinnen - Strategien für mathematische Spiele Band 3, Kapitel 5, S. 149, Vieweg, 1986. Siehe auch neuere Ergebnisse

Primequads or How I got in contact with computer science

As a fifteen year old boy, I found in school a foreign assembler program on dash cards which contained about 100 asm statments for an antic deskcalculator called MONROE, if I remember right. When I succeeded to decypher this code I recognized its sense: Generating the list of primequads. A primequad is a sequence of four successive primes with minimal distance. Because of divisibilty by 2,3,5 such a quad must be of the form 30n+11, 30n+13, 30n+17, 30n+19, except the first primequad 2,3,5,7. The list continues with n = 0,3,6,27,49,62,69,108,115 ... . Like the primetwin conjecture there is one for the frequency of primequads. See: An Introduction to the theory of numbers, G.H. Hardy and E.M. Wright, Oxford 1979, 5. Edition

Diese Arbeit über Wartewerte wurde von Torsten Sillke 1983 angeregt: Betrachte eine unendliche Folge von Buchstaben aus einem n-elementigen Alphabet A. Jeder Buchstabe soll unabhängig und mit Wahrscheinlichkeit 1/n in dieser Folge an Position i stehen. Lege nun ein festes Wort endlicher Länge an den Anfang dieser Folge und frage nach der durchschnittlichen Verschiebung längs der Folge bis das Wort zum ersten Mal auftritt. Dies bezeichnet den Wartewerte dieses Wortes. Der Autokorrelationsstring als Zahl zur Basis n interpretiert, ergibt genau diesen Wert. Nun stellt sich die Frage, welche Wartewerte/Autokorrelationsstrings für feste Länge k können überhaupt auftreten. Eine rekursive Charakterisierung dieser Werte macht keine Schwierigkeiten, wohl aber ihre genaue Anzahlbestimmung. Asymptotisch wächst ihre Anzahl wie e^{C ln² n} mit C = 1/ln(4). Eine gute Einführung ist: Periods in Strings, L.J. Guibas and A.M. Odlyzko, Journal of Combinatorial Theory, Serie A 30, p.19-42 (1981).

The number of intersection points of the diagonals of regular n-gons was calculated 1979-1980 by me. Surprisingly, this number is a polynom of fourth degree in n, n mod 2, n mod 6, n mod 30 and n mod 7*360. I must admit, that I found only the correct formulae, but didn't proof them. Shortly afterwards, I got knowledge of the existence of G. Bol's article in Nieuw Archief voor Wiskunde 18 (1936). About two years later I got acess of this paper and my interest on this topic was satisfied. Luckily, I discovered 1995 an article in the WEB with a exact discussion of this topic again. So I need not to write down the whole story again, but can point you to B. Poonen's and M. Rubinsteins's paper. Here you can fetch it as compressed PS-file with all the diagramms.

What's

that?
Based on an idea of Christian Zylka, FH-Erfurt, Peter Serocka and I constructed this interesting body 1994. It describes the balance of four fluids in communicating tubes, if two of them can be pairwise balanced.
Here are a few more VRML-objects.

Sorry, still to d ocument:

Computing the Area of the Mandelbrot Set. Have a look at What is known
Quickestsort or How to Select the Sort Key Optimal
Extremal Polyeder in R³
Bijective Rotation of Z²
The Analytic Approximation to the Exponential Iterated

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I hope you were pleased with visit no 27425 since June 1997.