5 papers
Tiling a triangle into a prime number of congruent triangles
Michael Beeson
We show that, apart from a few known exceptions, if a triangle is cut into congruent triangles, then is not a prime number. The exceptions are cutting an isosceles triangle…
Finite sets, mappings, cardinals, and arithmetic in intuitionistic New Foundations
Michael Beeson
NF set theory using intuitionistic logic is called iNF. We develop the theories of finite sets and their power sets and mappings, finite cardinals and their ordering, cardinal expo…
Solution of ErdÅs Problem 633
Michael Beeson, Miklos Laczkovich, Yan X. Zhang
We classify triangles that can be tiled only into a square number of congruent triangles, settling ErdÅs Problem 633.
Tilings of an Isosceles Triangle
Michael Beeson
An N-tiling of triangle ABC by triangle T is a way of writing ABC as a union of N triangles congruent to T, overlapping only at their boundaries. The triangle T is the "tile". The…
Rationality of certain triangle tilings
Michael Beeson, Yan X Zhang
We consider tilings of a triangle by congruent copies of a triangle that has one angle equal to , has non-commensurable angles (that is, not all angles are rationa…