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Description
Convex SurfacesIn this self contained geometry text, the author describes the main results of convex surface theory, providing all definitions and precise theorems. The first half focuses on extrinsic geometry and applications of the Brunn Minkowski theory. The second part examines intrinsic geometry and the realization of intrinsic metrics. Starting with a brief overview of notations and terminology, the text proceeds to convex curves, the theorems of Meusnier and
In this self-contained geometry text, the author describes the main results of convex surface theory, providing all definitions and precise theorems. The first half focuses on extrinsic geometry and applications of the Brunn-Minkowski theory. The second part examines intrinsic geometry and the realization of intrinsic metrics.Starting with a brief overview of notations and terminology, the text proceeds to convex curves, the theorems of Meusnier and Euler, extrinsic Gauss curvature, and the influence of the curvature on the local shape of a surface. A chapter on the Brunn-Minkowski theory and its applications is followed by examinations of intrinsic metrics, the metrics of convex hypersurfaces, geodesics, angles, triangulations, and the Gauss-Bonnet theorem. The final chapter explores the rigidity of convex polyhedra, the realization of polyhedral metrics, Weyl's problem, local realization of metrics with non-negative curvature, open and closed surfaces, and smoothness of realizations.
Binding Type: Paperback
Publisher: Dover Publications
Published: 02/04/2008
ISBN: 9780486462431
Pages: 196
Weight: 0.47lbs
Size: 8.44h x 5.88w x 0.43d
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4.6 ★★★★★
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★★★★★ 5
Best ever dog toy
Color: Pink
This is such the clever toy and actually I think it makes my pup more clever too. The ball is tough enough to withstand excessive chewing. I really can’t say enough good things about this particular dog toy. This will keep my dogs attention for such a long period of time and you can truly just watch the wheels turning in his head as he figures out how to get the food out would buy again and I probably will just to have a back up.
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Reviewed in the United States on March 25, 2026
★★★★★ 5
Fun lil ball
Color: Pink
My 1.6 lb yorkie puppy loves to get her treats from here. She gets them in no time. Lol
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Reviewed in the United States on May 7, 2026
★★★★★ 5
Treat Puzzle Ball
Color: Pink
This seems very decently made, keeps puppy occupied, easy to use
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Reviewed in the United States on March 2, 2026
★★★★★ 4
Great for 22 pound mini schnauzer/mini greyhound mix
Color: Pink
I have a dog that is half miniature schnauzer and they love to sniff and snuffle. He is enjoying this ball. I put the little freeze dried liver cubes in it and he will play with it until he gets them all out, and maybe keep playing for a bit. I can't give it 5 stars because I don't know quite how I'm going to clean the inside of it. I can't speak for how well it cleans his teeth because he hasn't had it that long. It is sturdy. He's a 22 pound medium size dog and I'm confident he cannot chew it to the point of destroying it. He's barely made a scratch on it so it may break down over time but it's not something a small or medium dog should be able to chew through the first day. He's had it about 2 weeks and we use it every day and it's holding up very well. It's not interesting enough to him to play with it without treats in it but he rarely plays with a toy unless I'm actively playing with the other end of the toy or throwing it for him to chase (part Italian greyhound too so he does like chasing) but he will get excited when he sees this ball as he knows treats are going to be in it. This one is a good size for him and he can pick it up with his teeth. (This is the hot pink one with the blue ball inside) Definitely worth the price if I can figure out how to sufficiently clean inside of it. So far rinsing with warm water seems to keep it hygienic. It's silicone so everything pretty much slides out. I wouldn't put any moist treats in it though. It's quiet. No squeaker, but he has plenty of toys that squeak and we didn't get it for that. It definitely appeals to his sniffing and snuffling instincts.
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Reviewed in the United States on May 27, 2026
★★★★★ 5
nice
Color: Blue, Color: Blue
Smaller than I thought it would be. but it’s a good toy my Frenchie likes it
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Reviewed in the United States on December 25, 2025