Review of The Pythagorean Theorem by Eli Maor, 02 Aug 2008
This is an excellent book on the history of the Pythagorean Theorem. I learnt a great deal of history of mathematics in relation to Pythagorasfs Theorem. This book is suitable to any student who has basic knowledge of calculus but the layperson will also find it interesting.
The book starts with the assertion that the Babylonians knew Pythagorasfs Theorem 1000 years before Pythagoras but it was the Greeks who proved the result.
There are a number of gems in the book which are not that well known in the mathematics community:
Hypotenuse is derived from the Greek words hypo meaning eunderf or edownf and teinen meaning eto stretchf. Maor points out the reason for this is that the hypotenuse of a right triangle in Euclidfs Elements was always on the bottom. (I did not know this).
There are over 400 proofs of Pythagorasfs Theorem.
It was the French lawyer eFrancois Vietef who first converted verbal algebra into symbolic algebra.
Many more of these gems crop up throughout the book.
Maor does give a number of different proofs of Pythagorasfs Theorem.
More importantly the author does not shy away from producing mathematical expressions and symbols in a popular book like this. Here are a few examples:
1. Every even perfect number is of the form 2^(n-1)*(2^n-1).
2. Vietefs Identity product which expresses 2/Î in terms of ã2.
3. Shows how the area of one arch of the cycloid is 3 times the area of the circle generating it.
4. Gives an excellent brief description of Hilbert Spaces and non Euclidean geometry.
5. Explains why Pythagorasfs Theorem is not valid in non-Euclidean geometry.
There are many more fantastic mathematical examples. The more serious mathematics is left for the appendices.
Additionally Maor has provided an excellent general history of mathematics such as:
The first woman mathematician was Hypatia (370 to 415).
The University of Gottingen was world renown for mathematics up until the Second World War.
How Edmund Landau (1877 to 1938) shunned all references to geometry. Maor points out that Landau wrote a 372 page book eDifferential and Integral Calculusf and it does not contain a single illustration.
How Euler discovered differential geometry but its modern form is due to Riemann and Gauss.
There are also non-mathematical examples of history in the book such as the first European University was Bologna founded in 1088 and why the Christians burned the Library of Alexandria.
You will learn a lot from this book because it has been thoroughly researched and shows the different fields where Pythagorasfs Theorem is used.
The author has also made excellent use of illustrations so the layperson can understand without learning all the details.
Maor has an exceptional method of writing very technical mathematics in a seamlessly way.

Review of The Pythagorean Theorem by Eli Maor, 02 Aug 2008
This is an excellent book on the history of the Pythagorean Theorem. I learnt a great deal of history of mathematics in relation to Pythagorasfs Theorem. This book is suitable to any student who has basic knowledge of calculus but the layperson will also find it interesting.
The book starts with the assertion that the Babylonians knew Pythagorasfs Theorem 1000 years before Pythagoras but it was the Greeks who proved the result.
There are a number of gems in the book which are not that well known in the mathematics community:
Hypotenuse is derived from the Greek words hypo meaning eunderf or edownf and teinen meaning eto stretchf. Maor points out the reason for this is that the hypotenuse of a right triangle in Euclidfs Elements was always on the bottom. (I did not know this).
There are over 400 proofs of Pythagorasfs Theorem.
It was the French lawyer eFrancois Vietef who first converted verbal algebra into symbolic algebra.
Many more of these gems crop up throughout the book.
Maor does give a number of different proofs of Pythagorasfs Theorem.
More importantly the author does not shy away from producing mathematical expressions and symbols in a popular book like this. Here are a few examples:
1. Every even perfect number is of the form 2^(n-1)*(2^n-1).
2. Vietefs Identity product which expresses 2/Î in terms of ã2.
3. Shows how the area of one arch of the cycloid is 3 times the area of the circle generating it.
4. Gives an excellent brief description of Hilbert Spaces and non Euclidean geometry.
5. Explains why Pythagorasfs Theorem is not valid in non-Euclidean geometry.
There are many more fantastic mathematical examples. The more serious mathematics is left for the appendices.
Additionally Maor has provided an excellent general history of mathematics such as:
The first woman mathematician was Hypatia (370 to 415).
The University of Gottingen was world renown for mathematics up until the Second World War.
How Edmund Landau (1877 to 1938) shunned all references to geometry. Maor points out that Landau wrote a 372 page book eDifferential and Integral Calculusf and it does not contain a single illustration.
How Euler discovered differential geometry but its modern form is due to Riemann and Gauss.
There are also non-mathematical examples of history in the book such as the first European University was Bologna founded in 1088 and why the Christians burned the Library of Alexandria.
You will learn a lot from this book because it has been thoroughly researched and shows the different fields where Pythagorasfs Theorem is used.
The author has also made excellent use of illustrations so the layperson can understand without learning all the details.
Maor has an exceptional method of writing very technical mathematics in a seamlessly way.


A joy, and not just for mathematicians, 08 Feb 2008
This book is amazing. It takes a very boring and dry subject and makes it accesible and interesting, without ever once 'dumbing down'. This is NOT trigonometry for dummies. This is Trigonometric Delights, and it lives up to its title.

Ranging through historic approaches to trigonometry, coupled with sections on areas that obviously delighted the author when he discovered them, the book never loses the reader, which is an amazing achievement.

If I had to think of who would buy this book, then I would say:
any parent of a child (13-18) finding maths hard/boring/impenetrable
any university student
all maths teachers (especially the part about the unit circle)
anyone who liked Simon Singh's Fermats Last Theorem, but would have
liked to see more of the subject matter and less of the story

Basically, if you are interested enough to be reading a review of this book then you should buy it. You will not be disappointed. If you are not reading reviews about this book, don't buy it.


Very good if expensive!, 18 Oct 2001
The book starts with angles and chords and a description of Plimpton 322. These chapters are good enough but the book seems to get better with each chapter. As a mathematics teacher, I found some of the chapters fantastic and others good, if a little heavy. The chapter "Two theorems from Geometry" states a few things I didn't previously know and made me think a lot!
The book is a little expensive, but like "e: The Story of a Number", the book is well written, interesting and most of all shows beauty in mathematics.
The appendix with a list of trigonometric formulae (not the basic ones you will already know) is wonderful.
If you like trig, get it, if not, you will when you read it!

Review of The Pythagorean Theorem by Eli Maor, 02 Aug 2008
This is an excellent book on the history of the Pythagorean Theorem. I learnt a great deal of history of mathematics in relation to Pythagorasfs Theorem. This book is suitable to any student who has basic knowledge of calculus but the layperson will also find it interesting.
The book starts with the assertion that the Babylonians knew Pythagorasfs Theorem 1000 years before Pythagoras but it was the Greeks who proved the result.
There are a number of gems in the book which are not that well known in the mathematics community:
Hypotenuse is derived from the Greek words hypo meaning eunderf or edownf and teinen meaning eto stretchf. Maor points out the reason for this is that the hypotenuse of a right triangle in Euclidfs Elements was always on the bottom. (I did not know this).
There are over 400 proofs of Pythagorasfs Theorem.
It was the French lawyer eFrancois Vietef who first converted verbal algebra into symbolic algebra.
Many more of these gems crop up throughout the book.
Maor does give a number of different proofs of Pythagorasfs Theorem.
More importantly the author does not shy away from producing mathematical expressions and symbols in a popular book like this. Here are a few examples:
1. Every even perfect number is of the form 2^(n-1)*(2^n-1).
2. Vietefs Identity product which expresses 2/Î in terms of ã2.
3. Shows how the area of one arch of the cycloid is 3 times the area of the circle generating it.
4. Gives an excellent brief description of Hilbert Spaces and non Euclidean geometry.
5. Explains why Pythagorasfs Theorem is not valid in non-Euclidean geometry.
There are many more fantastic mathematical examples. The more serious mathematics is left for the appendices.
Additionally Maor has provided an excellent general history of mathematics such as:
The first woman mathematician was Hypatia (370 to 415).
The University of Gottingen was world renown for mathematics up until the Second World War.
How Edmund Landau (1877 to 1938) shunned all references to geometry. Maor points out that Landau wrote a 372 page book eDifferential and Integral Calculusf and it does not contain a single illustration.
How Euler discovered differential geometry but its modern form is due to Riemann and Gauss.
There are also non-mathematical examples of history in the book such as the first European University was Bologna founded in 1088 and why the Christians burned the Library of Alexandria.
You will learn a lot from this book because it has been thoroughly researched and shows the different fields where Pythagorasfs Theorem is used.
The author has also made excellent use of illustrations so the layperson can understand without learning all the details.
Maor has an exceptional method of writing very technical mathematics in a seamlessly way.


A joy, and not just for mathematicians, 08 Feb 2008
This book is amazing. It takes a very boring and dry subject and makes it accesible and interesting, without ever once 'dumbing down'. This is NOT trigonometry for dummies. This is Trigonometric Delights, and it lives up to its title.

Ranging through historic approaches to trigonometry, coupled with sections on areas that obviously delighted the author when he discovered them, the book never loses the reader, which is an amazing achievement.

If I had to think of who would buy this book, then I would say:
any parent of a child (13-18) finding maths hard/boring/impenetrable
any university student
all maths teachers (especially the part about the unit circle)
anyone who liked Simon Singh's Fermats Last Theorem, but would have
liked to see more of the subject matter and less of the story

Basically, if you are interested enough to be reading a review of this book then you should buy it. You will not be disappointed. If you are not reading reviews about this book, don't buy it.


Very good if expensive!, 18 Oct 2001
The book starts with angles and chords and a description of Plimpton 322. These chapters are good enough but the book seems to get better with each chapter. As a mathematics teacher, I found some of the chapters fantastic and others good, if a little heavy. The chapter "Two theorems from Geometry" states a few things I didn't previously know and made me think a lot!
The book is a little expensive, but like "e: The Story of a Number", the book is well written, interesting and most of all shows beauty in mathematics.
The appendix with a list of trigonometric formulae (not the basic ones you will already know) is wonderful.
If you like trig, get it, if not, you will when you read it!

An excellent book, but NOT for a beginner., 01 Jul 2007
Although the book is supposedly addressed to those who "did little or no geometry", I wouldn't start with this book as a beginner. Silvester teaches at King's College, London (I was a student there), and expects his students to have a firm grasp of A-levels maths. You better be comfortable with trig identities, vectors (dot products), function notation and terminology (bijective, etc), basic linear algebra, and basic abstract algebra (groups). Good books to cover the basics are:
1)trig id and vectors (Bostock and Chandler - A Level maths)
2)functions (any basic book on Analysis like that of Binmore)
3)Abstract algebra (Teach yourself mathematical groups by Tony Barnard)
4)Linear Algebra (Howard Anton's Linear Algebra)

Silvester's book is quite compact, so you do need to work through it line by line, and he does provide answers to all the exercises, so that's a huge plus in my book. The book is quite comprehensive for one that "introduces" geometry as a first year university course.

Geometry for beginners??:-s, 04 Jul 2005
With this kind of book, the price is a bit of a rip off. Its actually very compacted, but still, for £25 its a bit much.

I was only meant to buy this book for the sake of my University course, and although it did help a little, I found the wording confusing and also I would never see how a person who had no knowledge of Geometry or mathematics would understand the book. It suggests that anyone could read this book, but I beg to differ.

Good points about this book: Good diagrams and good explanations for them. However the proofs are a bit wordy, and you tend to find that there are too many words on piece of paper and that they are trying to save as many trees as possible.

Ok, but could be better.

Review of The Pythagorean Theorem by Eli Maor, 02 Aug 2008
This is an excellent book on the history of the Pythagorean Theorem. I learnt a great deal of history of mathematics in relation to Pythagorasfs Theorem. This book is suitable to any student who has basic knowledge of calculus but the layperson will also find it interesting.
The book starts with the assertion that the Babylonians knew Pythagorasfs Theorem 1000 years before Pythagoras but it was the Greeks who proved the result.
There are a number of gems in the book which are not that well known in the mathematics community:
Hypotenuse is derived from the Greek words hypo meaning eunderf or edownf and teinen meaning eto stretchf. Maor points out the reason for this is that the hypotenuse of a right triangle in Euclidfs Elements was always on the bottom. (I did not know this).
There are over 400 proofs of Pythagorasfs Theorem.
It was the French lawyer eFrancois Vietef who first converted verbal algebra into symbolic algebra.
Many more of these gems crop up throughout the book.
Maor does give a number of different proofs of Pythagorasfs Theorem.
More importantly the author does not shy away from producing mathematical expressions and symbols in a popular book like this. Here are a few examples:
1. Every even perfect number is of the form 2^(n-1)*(2^n-1).
2. Vietefs Identity product which expresses 2/Î in terms of ã2.
3. Shows how the area of one arch of the cycloid is 3 times the area of the circle generating it.
4. Gives an excellent brief description of Hilbert Spaces and non Euclidean geometry.
5. Explains why Pythagorasfs Theorem is not valid in non-Euclidean geometry.
There are many more fantastic mathematical examples. The more serious mathematics is left for the appendices.
Additionally Maor has provided an excellent general history of mathematics such as:
The first woman mathematician was Hypatia (370 to 415).
The University of Gottingen was world renown for mathematics up until the Second World War.
How Edmund Landau (1877 to 1938) shunned all references to geometry. Maor points out that Landau wrote a 372 page book eDifferential and Integral Calculusf and it does not contain a single illustration.
How Euler discovered differential geometry but its modern form is due to Riemann and Gauss.
There are also non-mathematical examples of history in the book such as the first European University was Bologna founded in 1088 and why the Christians burned the Library of Alexandria.
You will learn a lot from this book because it has been thoroughly researched and shows the different fields where Pythagorasfs Theorem is used.
The author has also made excellent use of illustrations so the layperson can understand without learning all the details.
Maor has an exceptional method of writing very technical mathematics in a seamlessly way.


A joy, and not just for mathematicians, 08 Feb 2008
This book is amazing. It takes a very boring and dry subject and makes it accesible and interesting, without ever once 'dumbing down'. This is NOT trigonometry for dummies. This is Trigonometric Delights, and it lives up to its title.

Ranging through historic approaches to trigonometry, coupled with sections on areas that obviously delighted the author when he discovered them, the book never loses the reader, which is an amazing achievement.

If I had to think of who would buy this book, then I would say:
any parent of a child (13-18) finding maths hard/boring/impenetrable
any university student
all maths teachers (especially the part about the unit circle)
anyone who liked Simon Singh's Fermats Last Theorem, but would have
liked to see more of the subject matter and less of the story

Basically, if you are interested enough to be reading a review of this book then you should buy it. You will not be disappointed. If you are not reading reviews about this book, don't buy it.


Very good if expensive!, 18 Oct 2001
The book starts with angles and chords and a description of Plimpton 322. These chapters are good enough but the book seems to get better with each chapter. As a mathematics teacher, I found some of the chapters fantastic and others good, if a little heavy. The chapter "Two theorems from Geometry" states a few things I didn't previously know and made me think a lot!
The book is a little expensive, but like "e: The Story of a Number", the book is well written, interesting and most of all shows beauty in mathematics.
The appendix with a list of trigonometric formulae (not the basic ones you will already know) is wonderful.
If you like trig, get it, if not, you will when you read it!

An excellent book, but NOT for a beginner., 01 Jul 2007
Although the book is supposedly addressed to those who "did little or no geometry", I wouldn't start with this book as a beginner. Silvester teaches at King's College, London (I was a student there), and expects his students to have a firm grasp of A-levels maths. You better be comfortable with trig identities, vectors (dot products), function notation and terminology (bijective, etc), basic linear algebra, and basic abstract algebra (groups). Good books to cover the basics are:
1)trig id and vectors (Bostock and Chandler - A Level maths)
2)functions (any basic book on Analysis like that of Binmore)
3)Abstract algebra (Teach yourself mathematical groups by Tony Barnard)
4)Linear Algebra (Howard Anton's Linear Algebra)

Silvester's book is quite compact, so you do need to work through it line by line, and he does provide answers to all the exercises, so that's a huge plus in my book. The book is quite comprehensive for one that "introduces" geometry as a first year university course.

Geometry for beginners??:-s, 04 Jul 2005
With this kind of book, the price is a bit of a rip off. Its actually very compacted, but still, for £25 its a bit much.

I was only meant to buy this book for the sake of my University course, and although it did help a little, I found the wording confusing and also I would never see how a person who had no knowledge of Geometry or mathematics would understand the book. It suggests that anyone could read this book, but I beg to differ.

Good points about this book: Good diagrams and good explanations for them. However the proofs are a bit wordy, and you tend to find that there are too many words on piece of paper and that they are trying to save as many trees as possible.

Ok, but could be better.

A worthy book, 19 Jul 2001
An excellent book that covers a wide ground (see table of contents). I mainly bought it for Trigonometry but the Algebra section proved useful to know beforehand. what I really liked was the step by step instructions to find solutions, so many examples are given then they will say 'now do problem 39'. You do it and get it right and feel happy about it.

I needed to get better at trigonometric functions in order to do calculus and linear algebra. I also feel the book was geard towards that, the author has written a precalculus book also. The book was also fun to go through and has given me enormous confidence. Although the book is huge (at 1000 pages) it wasn't difficult at all.