Equilateral triangles and continuous curves

Equilateral Triangles in Finite

Packing and Covering a Unit Equilateral Triangle with Equilateral Triangles

Packing and covering are elementary but very important in combinatorial geometry , they have great practical and theoretical significance. In this paper, we discuss a problem on packing and covering a unit equilateral triangle with smaller triangles which is originated from one of Erd˝ os' favorite problems.

Online Packing of Equilateral Triangles

We investigate the online triangle packing problem in which a sequence of equilateral triangles with different sizes appear in an online, sequential manner. The goal is to place these triangles into a minimum number of squares of unit size. We provide upper and lower bounds for the competitive ratio of online algorithms. In particular, we introduce an algorithm which achieves a competitive rati...

Counting All Equilateral Triangles In

We describe a procedure of counting all equilateral triangles in the three dimensional space whose coordinates are allowed only in the set {0, 1, ..., n}. This sequence is denoted here by ET (n) and it has the entry A102698 in “The On-Line Encyclopedia of Integer Sequences”. The procedure is implemented in Maple and its main idea is based on the results in [3]. Using this we calculated the valu...

Unilateral and equitransitive tilings by equilateral triangles

A tiling of the plane by polygons is unilateral if each edge of the tiling is a side of at most one polygon of the tiling. A tiling is equitransitive if for any two congruent tiles in the tiling, there exists a symmetry of the tiling mapping one to the other. It is known that a unilateral and equitransitive (UE) tiling can be made with any finite number of congruence classes of squares. This ar...