6,425 research outputs found
Tilings of an Isosceles Triangle
An N-tiling of triangle ABC by triangle T is a way of writing ABC as a union
of N trianglescongruent to T, overlapping only at their boundaries. The
triangle T is the "tile". The tile may or may not be similar to ABC. In this
paper we study the case of isosceles (but not equilateral) ABC. We study three
possible forms of the tile: right-angled, or with one angle double another, or
with a 120 degree angle. In the case of a right-angled tile, we give a complete
characterization of the tilings, for N even, but leave open whether N can be
odd. In the 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 case when the tile has one angle double another, we prove N cannot be prime
or twice a prime.Comment: 34 pages, 18 figures. This version supplies corrections and
simplification
Review of: Only Connect: Discovery Pathways, Library Explorations and the Information Adventure
A novel concept for the world of publishing in this field, Only Connect has been produced primarily as an electronic book to incorporate multimedia resources. Initial viewing of the printed version proved somewhat disconcerting due to the lack of an index and the ‘chapter chooser’ which encourages a non-linear engagement with the book. However, after reading the introduction, this becomes completely logical as there is no sense of a clear progression between chapters. This book has been designed around a range of interpretations and experiences of information literacy (IL) from a number of perspectives. The chapter chooser recommends starting to read at any point and navigating in any order. In fact, the only theme that links these chapters is that of a form of information literacy
Amenities and the returns to human capital
A demonstration that regional differences in the returns to human capital do not necessarily imply structural differences in regional labor markets, but could be reflecting compensation for regional differences in amenities.Labor market ; Wages
Interurban comparisons of the quality of life
A methodology is developed for constructing quality-of-life comparisons for metropolitan areas in which the full bundle of an area's attributes is valued, rather than the typical method of focusing on individual characteristics.Cost and standard of living ; Regional economics
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