Unsolved Problems in Geometry (Problem Books in Mathematics / Unsolved Problems in Intuitive Mathematics) [Hardcover]

Hallard T. Croft (Author), Kenneth J. Falconer (Author), Richard K. Guy (Author)

Book Description

ISBN-10: 0387975063 | ISBN-13: 978-0387975061 | Publication Date: May 28, 1991 | Edition: Corrected

Mathematicians and non-mathematicians alike have long been fascinated by geometrical problems, particularly those that are intuitive in the sense of being easy to state, perhaps with the aid of a simple diagram. Each section in the book describes a problem or a group of related problems. Usually the problems are capable of generalization of variation in many directions. The book can be appreciated at many levels and is intended for everyone from amateurs to research mathematicians.

Product Details

• Hardcover: 235 pages
• Publisher: Springer; Corrected edition (May 28, 1991)
• Language: English
• ISBN-10: 0387975063
• ISBN-13: 978-0387975061
• Product Dimensions: 9.3 x 6.3 x 0.7 inches
• Shipping Weight: 14.1 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,000,920 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

11 of 13 people found the following review helpful:

5.0 out of 5 stars A wide expanse of problems in geometry, August 1, 2000

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Unsolved Problems in Geometry (Problem Books in Mathematics / Unsolved Problems in Intuitive Mathematics) (Hardcover)

After the counting numbers, geometry is the oldest branch of mathematics and no doubt the first one that required abstract thinking. Even so, there is always a certain "concreteness" about it in the sense that diagrams can almost always be constructed. The range of problems that fall under the geometric umbrella is extremely wide and some even have practical uses.
This book is a testament to the wide range of problems that are geometric in nature. One of my favorites is known as the "worm problem." To be more precise, the question is, "find the convex set of least area where any continuous curve of length one can be placed in it." This type of problem has ramifications in optimal packings, where a single type of container needs to be constructed for all possible ways an object can fold. Other problems such as tiling and dissection; packing and covering and combinatorial geometry are also covered.
However, the best part of the book may be the extensive references. Every problem is followed by a list of references, so if you wish to take a crack at it, you will have little difficulty in locating the work done to the date of publication.
This is one of those books that always seems to beckon me when it lies on my bookshelf. Every once in awhile I pull it off and browse through it, admiring the skill and breadth of mathematicians in their pursuit of truth. It should be in every academic library.

Published in Journal of Recreational Mathematics, reprinted with permission