The Ancient Tradition of Geometric Problems [Paperback]

Wilbur Richard Knorr (Author)

Book Description

Publication Date: April 11, 2012

This highly regarded study focuses on attempts by Hippocrates, Archimedes, other ancient Greeks to solve three classical problems: cube duplication, angle trisection, and circle-quadrature. Topics include origins of the study of conics, introduction of special mechanical curves, use of sliding rulers and calculating procedures, and much more. 255 black-and-white illustrations. "Essential reading" — Mathematical Reviews. 1986 edition.

Product Details

• Paperback: 416 pages
• Publisher: Dover Publications (April 11, 2012)
• Language: English
• ISBN-10: 0486675327
• ISBN-13: 978-0486675329
• Product Dimensions: 9.4 x 6.1 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #381,643 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

3 of 4 people found the following review helpful:

4.0 out of 5 stars Scholarly, fragmented, but also of interest for non-experts, January 5, 2006

By 

Viktor Blasjo - See all my reviews
(REAL NAME)   

This review is from: The Ancient Tradition of Geometric Problems (Paperback)

This is a history of Greek mathematics from the point of view of problems and problem solving, not least the three classical problems: cube duplication, circle quadrature, angle trisection. Knorr argues that this restriction is not arbitrary: "One seems typically to assume that metamathematical concerns were the effective motivating force underlying efforts of geometers ... In general, I will find most convincing the 'internalist' position that technical research is directed toward the solution of problems arising from previous and current research efforts", mathematics thus being "on the whole autonomous in setting the directions of research". So the focus on problems is a way to understand the development of Greek mathematics by exposing the mindsets of the mathematicians. This aspect is naturally very interesting, and the mere presence of such perspectives sets this book apart from the bare bones histories of Heath et al. However, grand programs and pretty pots on the cover is not everything. Our fragmented knowledge of Greek mathematics does not allow Knorr's program to be carried out in a completely satisfactory manner; neither is the big picture one of Knorr's main concerns. Instead much of the book amounts to quite specialised scholarly analysis of sources and critique of other scholarly interpretations. In the end, one is not entirely convinced that Knorr has unveiled the key to understanding Greek mathematics. His criticism of other interpretative schemes is convincing but sometimes suspiciously convenient. So, for instance, Knorr rather enjoys arguing that philosophy never had a major influence on mathematics (thus supporting his point of view) while the more interesting and relevant questions of the influences of astronomy, mechanics and optics are largely silenced.