Explain this
Proof: Interesting activities in conjecture and mathematical proof
How the publisher describes it:
“This book provides many accessible proofs and invites students to make their own conjectures and proofs. Starting with conversations about proof, the reader is provided with the expert methods, key examples and engaging challenges that lead to success. Easy entry points are provided for every type of proof, including geometric proof and induction.”
Review by Colin Foster
In brief:
Problems, puzzles and proofs are intermingled with explanation and advice, and the book avoids excessive formality, adopting a light, even humorous, tone throughout.
“Covers a vast array of mathematical areas”
Paul Brown has put together a very interesting collection of mathematical problems and proofs. In just over 100 pages, he manages to cover a vast array of mathematical areas, complete with full solutions and discussion at the back. There is also an associated website with some downloadable files. For me, the examples chosen were a mixture of the familiar and the unfamiliar.
There are standard proofs of such things as Pythagoras’ Theorem and the irrationality of the square root of 2, which mathematics teachers will be very familiar with, but I also enjoyed several that I don’t remember seeing before, including one showing that cubes are ‘roughly’ multiples of 9 and a neat way of summing the first n Fibonacci numbers. The book also contains several lovely proofs without words, including one I will definitely come back to, showing at a glance that the angle in a semicircle must be 90 degrees.
Problems, puzzles and proofs are intermingled with explanation and advice, and the book avoids excessive formality, adopting a light, even humorous, tone throughout. It is an engaging resource, with plenty to interest any young mathematician and much for any mathematics teacher to delve into. Enjoy!
Colin Foster • King Henry VIII School, Coventry, UK
Publisher: P B Perth
£17.95
