Geometric Inequalities (New Mathematical Library) 1st Edition by Nicholas D. Kazarinoff (PDF)

Description

Simply stated problems about maximum and minimum lengths and areas invite the student to participate

User’s Reviews

Editorial Reviews: About the Author Nicholas D. Kazarinoff received his Ph.D in mathematics in 1954 from the University of Wisconsin, and went on to Associate Professor of Mathematics at the University of Michigan.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Perfect books for intro to geometric inequalities.

⭐I know. No one likes geometry. You have to take it in high school. And there are all these proofs to do. It’s no fun.But there are some interesting questions in geometry. And one of the most interesting ones is the Isoperimetric Theorem.Here it is.Of all plane figures with a given perimeter, the circle has the greatest area.This theorem was known well over two thousand years ago. And in the nineteenth century, Jacob Steiner almost proved it. He proved that if there is a figure which has a greater area than any other figure with the same perimeter, then it must be a circle. And this book shows how. I think Steiner’s proof should be shown to students in any honors geometry course.Unfortunately, Steiner only proved that if there was an answer, it had to be the circle. He never proved that there was an answer. And when this was pointed out to him, he thought this was not a serious objection.And yes, Karl Weierstrass did spot the error in Steiner’s proof, and he found a way to prove that there is an answer to the problem, finally solving a problem that had plagued mathematicians for so many centuries.If you are going to take a class in honors geometry in high school, and if my review hasn’t talked you out of doing so, get this book. You’ll enjoy it.

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