College geometry students, professors interested in undergraduate research and secondary geometry teachers will find three rich environments in this textbook. The first chapter contains many of the standards of Euclidean college geometry. The second and third chapters introduce nonEuclidean models where some Euclidean rules hold and others do not. With emphases on constructions and proofs, the reader is encouraged to create the objects under investigation and verify the results with reasoning. Since both models of "bent" spaces exist in Euclidean geometry, the reader gains facility with Euclidean moves through the whole book, even while exploring nonEuclidean spaces. The book itself is meant to be unpacked, expanded and taken further, just like the problems it contains. Geometry by Construction challenges its readers to participate in the creation of mathematics. The questions span the spectrum from easy to newlypublished research and so are appropriate for a variety of students and teachers. From differentiation in a high school course through college classes and into summer research, any interested geometer will find compelling material. Teachers and professors might especially appreciate the way constructions provide openended questions which resist internet searches for solutions. College students should find the five refereed results from undergraduates like themselves encouraging. The active reader joins the mathematical tradition of a laboratory being a notebook plus a compass and ruler (or a dynamic geometry program on a computer.) New ideas await exploration and here are examples!
About Michael McDaniel
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Author  :  Michael McDaniel 
Publisher  :  Universal Publishers 
Data Published  :  05 February 2015 
ISBN  :  1627340289 
EAN  :  9781627340281 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  150 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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