Rep-tiling for triangles

✍ Scribed by Stephen L. Snover; Charles Waiveris; John K. Williams

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 409 KB
• Volume: 91
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(91)90110-n

✦ Synopsis

In this paper we prove that one can only tile a triangle with tiles all congruent to each other and similar to the original triangle when k ', I* + k*, or 3k* tiles are used. The result is based on the geometry of packing and a result of I. Niven's on rational trigonometric values. In addition we describe how to tile most triangles.

1. Constructions

Construction of a k2-tiling. Take any triangle and divide each of its sides into k pieces of equal length. Then draw the line segments joining the corresponding points as in Fig. 1.