English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

An N-tiling of triangle ABC by triangle T is a way of writing ABC as a unionof N triangles congruent to T, overlapping only at their boundaries. Thetriangle T is the "tile". The tile may or may not be similar to ABC. In thispaper we study the case of isosceles (but not equilateral) ABC. We study threepossible forms of the tile: right-angled, or with one angle double another, orwith a 120 degree angle. In the case of a right-angled tile, we give a completecharacterization of the tilings, for N even, and prove that N must be even. Inthe latter two cases we prove the ratios of the sides of the tile are rational,and give a necessary condition for the existence of an N-tiling. For the casewhen the tile has one angle double another, we prove N cannot be prime or evensquarefree.

Tilings of an Isosceles Triangle