**CharlesAshbacher**

"A set of complex problems in real analysis are solved in detail"

A book by H. G. Eggleston

< read all 1 reviews-
Jun 23, 2010

- by CharlesAshbacher
- posted in Cafe Libri: Reviewing Books & More

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The following definition of convexity is used in this book.
+3

A subset X of R2 or R3 is convex if whenever x and y are in X the segment connecting them is also in X.

Using this definition, a series of problems are presented and solved. Organized by chapter, they are

Chapter 1) Problems in which convexity is used either by analogy or for subsidiary arguments

*) The intersection of connected open sets

*) Approximations to homomorphisms of R2 onto itself

*) On the projection of a plane set of finite linear measure

Chapter 2) Problems which can be reduced to problems on convex sets

*) Covering a three-dimensional set with sets of smaller diameter

Chapter 3) Problems on convex sets

*) Approximation to plane convex sets

*) Geometrical properties for which triangles are the extremal convex curves

Chapter 4) Problems concerned with the structure of subclasses of the class of convex sets

*) The asymmetry of curves of constant width

*) Sets of constant width contained in a set of given minimal width

*) Extremal properties of triangles circumscribing plane convex sets

*) On the closest packing by equilateral triangles

Each of the problems is dealt with in detail with theorems followed by proofs. A remark summarizing the problem occurs after every problem is resolved. In terms of difficulty, some real analysis background is necessary to understand the work.

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Charlie Ashbacher is a compulsive reader and writer about many subjects. His prime areas of expertise are in mathematics and computers where he has taught every course in the mathematics and computer … **more**

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CharlesAshbacher

This text for advanced undergraduates and graduate students examines problems concerning convex sets in real Euclidean spaces of 2 or 3 dimensions. It illustrates the different ways in which convexity can enter into the formulation as the solution to different problems in these spaces. 1957 edition.

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