Triangulations of Ralph Heiner Buchholz

(a.k.a. SWE-Teufel, a.k.a. Rebecca's dad)

Update history
The good christian should beware of mathematicians, and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell.

--- St. Augustine (354-430 A.D.)


The following thumbnails provide links to excerpts from some of the papers below.

Ant antics
Aperiodic tiling
Dissolving salt
Elliptic Surface
Epitrochoidal mixer
Infinity Heresy
Kandelhardt paradox
Minimizing polygon
Missing Galilean
Newton meets Diophantus
On Triangles
Perfect pyramid
Perfect triangle
Quantum Locking
Robbins pentagons
Singular curves

Walking with Ants

√úber-cool sites

Bohemian Gravity String theory finally explained by Tim Blais.
Cornell Historical Mathematics Scanned English mathematics.
Dalek Relaxation Tape Your cares will melt away.
Dimensions Visualise the 4th dimension.
Gallica Scanned French mathematics.
Göttingerdigitalisierungszentrum Scanned German mathematics.
Harvard multimedia The inner life of a cell.
Hero's Pneumatics The pneumatics of Hero of Alexandria translated to english.
Hexaflexagons Very entertaining delivery by ViHart.
Number Theory Web Things of interest to number theorists.
Numberphile Recreational mathematics videos by Brady Haran.
Pi ist irrational German rap
Seventeen or bust Search for the smallest Sierpinski number.


Like most archaeological sites this site is ordered from most recent on top to the oldest layers on the bottom.

Date Title
Sep 2019
The status of D21 --- the search for a perfect triangle
presented at Colorado University (Boulder, CO).
Apr 2016
The status of D21 --- the search for a perfect triangle
presented at Capital Number Theory (ANU)
Jul 2014
The perfect cuboid is one step closer to non-existence (draft)
Jul 2010
Heron Triangles with three rational medians
co-author: Robert P. Stingley
Apr 2009
Cyclic pentagons with rational sides and area (draft)
co-author: Ezra A. Brown
Jul 2008
An edge minimization problem for regular polygons
co-author: Warwick de Launey
Apr 2006
On a geometric proposition, translated from the german,
Ueber einen geometrischen Satz by L. Fejes
Nov 2005
Cyclic rational area polygons, talk given at the Fall meeting of the MAA, Montgomery College, Germantown.
Mar 2005
Integrality in Algebraic Geometry, translated from the german,
Die Ganzzahligkeit in der Algebraischen Geometrie by Hermann Schubert
Aug 2004
Square-like triangles (draft)
Sep 2003
The Infinity Heresy (draft)
Feb 2003
Symmetries of triangles with two rational medians (submitted)
co-authors: Zoltan F. Bacskai, Randall L. Rathbun, Michael J. Smith
Jul 2001
Cyclic n-gons with rational area
co-author: James A. MacDougall
Jan 1999
When Newton met Diophantus : A study of rational-derived polynomials and their extension to quadratic fields
co-author: James A. MacDougall
Aug 1998
Heron Quadrilaterals with sides in arithmetic or geometric progressions
co-author: James A. MacDougall
Apr 1998
Pseudopowerful Numbers (draft)
Mar 1998
Heron Triangles and elliptic curves
co-author: Randall L. Rathbun
Jan 1997
An infinite set of Heron triangles with 2 rational medians
co-author: Randall L. Rathbun
Aug 1996
Volume of an N-dimensional Simplex (draft)
co-author: Michael J. Smith
Jun 1996
The square, the triangle and the hexagon
co-author: Warwick de Launey
Jun 1995
Triangles with 3 rational medians
Feb 1995
Rational-derived quartics
Jan 1995
An observation on Rolle's problem
Apr 1991
Perfect Pyramids
Jul 1990
Epitrochoidal Mixer
Nov 1989
On Triangles with rational altitudes, angle bisectors or medians
Jul 1986
Polygons with Integral Internal Angles
Nov 1985
Spiral Polygon Series
Jul 1985
Mayan Calendar
Apr 1985
Topology in Biology
Oct 1983
Gathematics: Mathematics in the Gas Industry
Nov 1981
Riemann Zeta Function


Date Title
Notebook 6 Mathematics wins---but physics makes a token appearance.
Notebook 5 The struggle continues.
Notebook 4 Mathematics, Physics and archaeology---a struggle for supremacy.
Notebook 3 Recreational mathematics emerges from the back of one little matchbox at ComSteel.
Notebook 2 The influence here is Martin Gardener's Mathematical Games as well as university maths.
Notebook 1 The one that started it all. Heavily influenced by the 1972 World Book Science Yearbook.


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... My current research interests.

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