Geometry by Construction: Object Creation and Problem-solving in Euclidean and Non-Euclidean Geometries
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- Publisher : Universal Publishers (February 5, 2015)
- Language : English
- Paperback : 150 pages
- ISBN-10 : 1627340289
- ISBN-13 : 978-1627340281
- Item Weight : 8.8 ounces
- Dimensions : 6.69 x 0.32 x 9.61 inches
- Best Sellers Rank: #697,540 in Books (See Top 100 in Books)
- Customer Reviews:
Top reviews from the United States
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HOWEVER, investigating with constructions opens up all sorts of unforeseen ideas. All you have to do is find some Euclidean idea which fails in non-Euclidean geometry and see what version of that idea does hold in hyperbolic or elliptic. I have seen the author's research - new ideas every year.
I do embroidery and I embroidered a construction of the elliptic squaring the circle project. Very pretty. So there's that.
This book is great for college students of varying levels of geometric understanding. Each section provides an introduction, rules for each geometry, guidance on some need-to-know constructions, and proofs for those constructions. You'll definitely want to get out your compass and straight-edge to work along as you progress through the book. Geometry by Construction does an excellent job of engaging readers in constructions, and readers who actively participate with the text will see the biggest benefit.
If you're a geometry pro and already know a thing or two about hyperbolic and elliptic geometry, this book is still for you. Instead of learning the rules for the first time, it gives you a good opportunity to review those rules. And don't forget about trying out the homework/practice problems.
The questions McDaniel included in this book are not your average homework problems – you cannot go out and simply find the answers online. These problems are designed to challenge readers. They require you to recall the rules you've been learning (or reviewing) and to think creatively, taking that knowledge and what you are given in the problem and using that to arrive at the solution.
Besides containing challenging questions that compel readers to think more critically than required for your average geometry book, the other element that sets this book apart is the inclusion of recent discoveries in hyperbolic and elliptic geometry. Not “recent” as in “from 100 years ago,” which is certainly recent compared to how far back we know the history of Euclidean geometry goes, but rather “recent” as in “within the last 10 years.” With so much still to be discovered about hyperbolic and elliptic geometry, McDaniel works with a student each summer doing math research, and parts of the research of five students have been featured in Geometry by Construction.
Between the introductions to each geometry, engaging homework problems, and interesting inclusion of recent hyperbolic and elliptic discoveries, I would highly recommend introducing Geometry by Construction to your curriculum if you are a teacher or professor, and adding it to your collection if you are a geometry lover.
Secondary HS Teacher/Librarian
Robert Donius, St. Bonaventure University