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Description
Introduction to Projective GeometryThis lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well motivated approach to projective geometry. Subsequent chapters explore Euclidean and non Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each
This lucid introductory text offers both an analytic and an axiomatic approach to plane projective geometry. The analytic treatment builds and expands upon students' familiarity with elementary plane analytic geometry and provides a well-motivated approach to projective geometry. Subsequent chapters explore Euclidean and non-Euclidean geometry as specializations of the projective plane, revealing the existence of an infinite number of geometries, each Euclidean in nature but characterized by a different set of distance- and angle-measurement formulas. Outstanding pedagogical features include worked-through examples, introductions and summaries for each topic, and numerous theorems, proofs, and exercises that reinforce each chapter's precepts. Two helpful indexes conclude the text, along with answers to all odd-numbered exercises. In addition to its value to undergraduate students of mathematics, computer science, and secondary mathematics education, this volume provides an excellent reference for computer science professionals.Binding Type: Paperback
Publisher: Dover Publications
Published: 12/09/2008
ISBN: 9780486468952
Pages: 556
Weight: 1.60lbs
Size: 9.10h x 6.10w x 1.20d
Review Citations: Scitech Book News 03/01/2009 pg. 40
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4.2 ★★★★★
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Product Reviews
★★★★★ 4
Dog loves them, but don't leave them unattended
Style: Small, Size: 5 Chews
My pug loves these. Be careful, they sometimes crumble into shards, so always be present. My dog has swallowed some and threw them back up.
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Reviewed in the United States on January 8, 2026
★★★★★ 5
Well made dog toy
Color: Blue
The snoops are great for our active labrador. He is a very aggressive chewer, and so far, has not destroyed a snoop yet. He has mulitples. They are a great size for filling with treats or kibble and they keep him engaged in the activity. He even likes to carry them when he does his zoomies sometimes. They are lightweight and sturdy, and the material is nice and flexible. Great toy / puzzle ball to have around for your pup!
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Reviewed in the United States on June 9, 2026
★★★★★ 5
Very durable
Color: Blue
I have never written a review but just have to say how much our Pitbull LOVES this toy. It is very sturdy very good since he is such an aggressive chewer. This is only the second product I have found that he can’t destroy in 5 minutes. It keeps him busy for a long time and plays with it long after the treats are gone which is good as too many treats and he would gain weight. Highly recommend it. He weighes 70 lbs and the largest one is the perfect size. Kibble doesn’t work as it empties out immediately. I use Beggin Strips cut to size just to fit in the hole—they will come out but not all at once and survive his chewing on the toy.
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Reviewed in the United States on March 8, 2026
★★★★★ 5
Great you made super well
Color: Blue Lil Snoop, Color: Blue Lil Snoop
This is such an awesome toy. It’s super durable strong bounces and a perfect size. We got the small. We got blue because our pup can see it. It allows for creativity and endless limits to what you can make for it to be a fun experience. It has a nice sized hole in the center which allows you to add treats and food. Pop it inward and it slightly if large enough prevents the treats from coming out super fast. The ball rolls bounces and they can grip it nicely.
It is easy to clean
The only thing I didn’t like was the way the plastic tabs were situated inside the toy as you just be careful you don’t allow it to drip inside and dog gets it. No noise just fun. Our 15lb Cavapoo loves it
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Reviewed in the United States on February 17, 2026
★★★★★ 4
FUN AND DONE!
Color: Orange
First, I looove that I could get this dog toy in my favorite color! The orange color also helps to locate it, if your doggo has rolled it somewhere you don't know.
This bowl toy is very durable, safe, and easy to pull open and fill. The only reason I don't give it 5 Stars is because the opening is so big, after it's closed, that unless you have pretty large pieces/treats in it, or jam-pack them in, they easily fall out, when my dog rolls the toy around.
What I do, is put a whole Greenie in the bowl and then add treats around it. She's thrilled to have a treat or two spill out, as she rolls the bowl around. But what really keeps her occupied is trying to get to the Greenie. This is where the durability plays such a key role! Our dog is a Pit-Terrier and an extremely aggressive chewer, but the fold in the bowl is so strong that even her attempts to chew through it or claw it out don't work. That said, I would still supervise your dog's play with this. I know, if she really wanted to, our dog could eventually chew through the strong material to get to the Greenie, but thank goodness it's too thick and too wedged in to be worth all that time. The awkward shape of the bowl also makes it hard for her to grip it in her mouth foe chewing.
For a dog's quick fun, amusement, and reward, this is a winner!!
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Reviewed in the United States on July 4, 2025
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