Hyperbolic Functions: with Configuration Theorems and Equivalent and Equidecomposable Figures (Dover Science Books) | 
 enlarge | Authors: V. G. Shervatov, B. I. Argunov, L. A. Skornyakov, V. G. Boltyanskii
Publisher: Dover Publications
Category: Book
List Price: $10.95
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Rating:  1 reviews
Sales Rank: 1007915
Media: Paperback
Edition: Dover Ed
Pages: 176
Number Of Items: 1
Shipping Weight (lbs): 0.4
Dimensions (in): 8.3 x 5.4 x 0.3
ISBN: 0486458865
Dewey Decimal Number: 516.5
EAN: 9780486458861
Publication Date: March 15, 2007
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Product Description
This single-volume compilation of three books centers on Hyperbolic Functions, an introduction to the relationship between the hyperbolic sine, cosine, and tangent, and the geometric properties of the hyperbola. Configuration Theorems concerns theories on collinear points and concurrent lines, and Equivalent and Equidecomposable Figures examines the dissection and reassembly of polyhedrons. 1963 edition.
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| Customer Reviews:
Great on equidecomposable figures November 5, 2007
J. Bogaarts (Netherlands)
6 out of 6 found this review helpful
This is three booklets in one. It is a translation of a Russian book from the fifties that was meant for high school level students interested in mathematics.
The first booklet is about the hyperbolic functions sinh, cosh and tanh that are investigated first by studying a hyperbola by elementary methods and later on by using complex numbers. I don't think that many non mathematicians will enjoy hyperbolic functions and mathematicians will get their information from other texts.
The second booklet is about the Desargues and the Pappus Pascal theorems and related material. It is meant as an introduction to the theory of geometric configurations but does not go much beyond the two theorems mentioned. There is a chapter illustrating the relation between algebraic identities and configuration theorems but this only gives one example.
The last booklet is really great. It presents the theory of equidecomposable figures in two and three dimensions. Euclid defined the area of polygons in essence by cutting them up into triangles and then summing the areas of these triangles. An immediate consequence is the following theorem: If two polygons can be cut up into two sets of triangles in such a way that the two sets contain the same number of triangles and the triangles in the first set are congruent to the ones in the second set, then the polygons will have the same area. In this book the converse of this theorem is proven and it is also shown that in three dimensions the converse of the theorem will not work. It cointais also some nice material on computing volumes.
If you are interested in elementary geometry you should consider buying this book, even if it were only for the equidecomposable figures.
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