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The Wonder Book of Geometry: A Mathematical Story
How can we be sure that Pythagoras's theorem is really true ? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet?
David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.
David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.
288 pages, Hardcover
Published January 2, 2021
95 people are currently reading
515 people want to read
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Displaying 1 - 19 of 19 reviews
December 18, 2020
If ever you wanted a paradox, this book provides it in a remarkable way. Geometry, with its grinding pyramid of step-by-step proofs was my least favourite aspect of maths at school - I much preferred the puzzle-solving aspects of algebra, for example. David Acheson has failed to convince me that I was should really have loved it... however, this is by far the most approachable book on geometry I've ever read, and I wish it had been around in my day.
It's a textbook the way a textbook should be. There is context, from ancient Egyptian rope stretchers to those who have given the parallel postulate a good working over (including an oddity from Lewis Carroll). One of the worst things about the way I was taught geometry is that there was no consideration of applications, just those wretched theorems. Here, plenty of the geometry is introduced through a potential application. There's also some good historical background, including a regular view on Euclid from different points in history. Acheson has achieved something genuinely brilliant.
The only reason I can't get more excited about it is that is still, under cover of this beautiful facade, a textbook. It still spends far too long telling me about the details of, say, the midpoint theorem that I really don't care about. Although many aspects of it could fit within popular mathematics, this is not a popular maths book. However, if you need to learn the basics of geometry for whatever reason (there must be several reasons, surely) then this blows every known textbook on the topic out of the water. You may not get all the detail of all the theorems, but what's far more important is that you get an understanding of what is going on.
The Wonder Book of Geometry does what it does wonderfully. Acheson has done a remarkable job. But I'm afraid geometry still wasn't for me. I wasn't converted to be a fan of the subject - but I am of the book.
It's a textbook the way a textbook should be. There is context, from ancient Egyptian rope stretchers to those who have given the parallel postulate a good working over (including an oddity from Lewis Carroll). One of the worst things about the way I was taught geometry is that there was no consideration of applications, just those wretched theorems. Here, plenty of the geometry is introduced through a potential application. There's also some good historical background, including a regular view on Euclid from different points in history. Acheson has achieved something genuinely brilliant.
The only reason I can't get more excited about it is that is still, under cover of this beautiful facade, a textbook. It still spends far too long telling me about the details of, say, the midpoint theorem that I really don't care about. Although many aspects of it could fit within popular mathematics, this is not a popular maths book. However, if you need to learn the basics of geometry for whatever reason (there must be several reasons, surely) then this blows every known textbook on the topic out of the water. You may not get all the detail of all the theorems, but what's far more important is that you get an understanding of what is going on.
The Wonder Book of Geometry does what it does wonderfully. Acheson has done a remarkable job. But I'm afraid geometry still wasn't for me. I wasn't converted to be a fan of the subject - but I am of the book.
January 9, 2021
An excellent recreational maths book on geometry. Mainly the triangle and circle constructions often covered in senior school maths classes, but it covers other areas too. I can’t really add much to the review by another popular science writer on GR, which originally inspired me to have a look at this book.
https://www.goodreads.com/review/show...
If, in one of the circles of Hell, I was forced to teach geometry then this is the book I’d use as a textbook! It’s written to be accessible to those interested in recreational science and maths, with some humour and anecdotes alongside the more formal geometry. More involved proofs are hidden away at the back of the book for those wanting more depth. The serious side is interspersed with light distractions - for example, a short chapter describing regular articles on geometrical proofs in the 18th century Ladies Almanac, the cover of which praised the ‘fair sex’ for their wit as well as their beauty!
As with the afore mentioned reviewer I also disliked the formal geometrical proofs at school involving circles and triangles, aping Euclid, which is a shame as this book shows that if it’s taught properly there are lots of fascinating ‘coincidences’ in the relationships between angles and lines in such geometrical constructions.
I’ve found these interesting geometrical relationships of virtually no use in an engineering career - these things are sorted out in structural engineering by clever CAD software, or rarely one looks up relevant reference books! But where there is, potentially, everyday practical use the author highlights it to bring the concept to life.
If you enjoy recreational maths then this is the geometry book for you.
https://www.goodreads.com/review/show...
If, in one of the circles of Hell, I was forced to teach geometry then this is the book I’d use as a textbook! It’s written to be accessible to those interested in recreational science and maths, with some humour and anecdotes alongside the more formal geometry. More involved proofs are hidden away at the back of the book for those wanting more depth. The serious side is interspersed with light distractions - for example, a short chapter describing regular articles on geometrical proofs in the 18th century Ladies Almanac, the cover of which praised the ‘fair sex’ for their wit as well as their beauty!
As with the afore mentioned reviewer I also disliked the formal geometrical proofs at school involving circles and triangles, aping Euclid, which is a shame as this book shows that if it’s taught properly there are lots of fascinating ‘coincidences’ in the relationships between angles and lines in such geometrical constructions.
I’ve found these interesting geometrical relationships of virtually no use in an engineering career - these things are sorted out in structural engineering by clever CAD software, or rarely one looks up relevant reference books! But where there is, potentially, everyday practical use the author highlights it to bring the concept to life.
If you enjoy recreational maths then this is the geometry book for you.
January 3, 2024
Der erste Friedensvertrag nach dem Schulabschluss wurde mit der Mathematik unterzeichnet ,obwohl ich die Hälfte nicht mitgekriegt habe.
July 22, 2025
Lovely layout and sampling of curiosities but explanations much too shorthand.
January 21, 2021
The chapters in this book are short. I have to reread many parts of the book to fully understand it, but that is only because I never learned geometry in high school. I enjoyed learning the practical applications of geometry. I will try to teach myself geometry with other books. The most valuable subjects to me are angles and area.
Angles are valuable to learn because they can help to enjoy food and art. I learned that I can use geometry to evenly cut a pizza for my friends. I just have to learn how to cut a slide of pizza into a 45 degree angle. I like to go to museums to see paintings. I also like to look at beautiful scenic views of nature like the Grand Canyon and Niagara Falls. I am motivated to learn how to position my wheelchair to get the best widest view of these beautiful sights. Acheson makes a reference on how to accomplish this by drawing a horizontal line and a circle at eye level, but the process is more complicated for me because I am sitting down.
Learning about area is a valuable because I plan to replace the carpet in my house in the near future. I also want to install carpet into various parts in a new apartment or house in my later years. I learned from an example in this book that I can cover ground with carpet at various points and a maintain a curve at another point. This example helps me to understand to place carpet only in areas where I walk and exercise. I hope to use my geometric knowledge of area to design a bathroom that is large enough and safe for my wheelchair. I will strive to learn more about geometry and apply it to my life.
Angles are valuable to learn because they can help to enjoy food and art. I learned that I can use geometry to evenly cut a pizza for my friends. I just have to learn how to cut a slide of pizza into a 45 degree angle. I like to go to museums to see paintings. I also like to look at beautiful scenic views of nature like the Grand Canyon and Niagara Falls. I am motivated to learn how to position my wheelchair to get the best widest view of these beautiful sights. Acheson makes a reference on how to accomplish this by drawing a horizontal line and a circle at eye level, but the process is more complicated for me because I am sitting down.
Learning about area is a valuable because I plan to replace the carpet in my house in the near future. I also want to install carpet into various parts in a new apartment or house in my later years. I learned from an example in this book that I can cover ground with carpet at various points and a maintain a curve at another point. This example helps me to understand to place carpet only in areas where I walk and exercise. I hope to use my geometric knowledge of area to design a bathroom that is large enough and safe for my wheelchair. I will strive to learn more about geometry and apply it to my life.
June 21, 2025
For English learning purpose(?
October 12, 2022
Though still halfway from finishing this book, I still need to give it the highest rating for reminding me of how unbelievable (and beautiful) geometry is.
It is not a math book but a history book showing how the great minds of Ancient Greece (Thales, Pythagoras) come up with unbelievable theorems.
I give it 5 stars for showing the different proofs of the Pythagoras's theorems (a^2 + b^2 = c^2). I agree that the Euclid's proof is so creative and amazing.
Math is boring? I think we just lack imagination.
It is not a math book but a history book showing how the great minds of Ancient Greece (Thales, Pythagoras) come up with unbelievable theorems.
I give it 5 stars for showing the different proofs of the Pythagoras's theorems (a^2 + b^2 = c^2). I agree that the Euclid's proof is so creative and amazing.
Math is boring? I think we just lack imagination.
January 17, 2022
Geometry is fun. Geometry is the study of geometrical shapes. This helps us to understand the internal structure of subtle patterns and shapes. Geometry teaches us how a problem can be solved in different ways. It is the foundation of some other mathematical branches. Our Human Civilization has a very old and rich history of practising Geometry. Some great mathematicians have dedicated their lives to studying and contributing to Geometry. Their books and contributions have inspired many people from the next generations to invent or discover new items. This book has lots of interesting theorems, statements and brilliant proofs from Euclidean Geometry. This is a small but great book to inspire anyone to study Geometry.
July 23, 2021
This book is ideal for anyone who wants to find the fun in geometry.
I have a rather unique perspective on this book. As a prospective maths undergraduate student, I wanted a book that could make me think while satiating my thirst for interesting and cool mathematics. As other reviewers have said, geometry was not my cup of tea before reading this book. In fact, I wouldn't have considered reading a book on geometry had it not been recommended to me. That said, I enjoyed this book much more than I could have expected.
Acheson manages to make proving the basic, and rather tedious, theorems of euclidean geometry increadibly easy to follow and satisfying when he then takes these ideas further. I usually struggle to follow complicated geometrical proofs, but here every idea is accompanied by a useful and clear diagram and I found it really easy to dip in and out of this book without ever feeling lost. I enjoyed how some of the more complex proofs were given in the notes in order to make the base text more accessible.
This is a book that I wish I had when I was 13/14 as it would have given me a much better understanding of the point of geometry, as well as of many theorems which definitely would have been useful when I went on to do further mechanics at A-level. This is a book where it's great to have a pencil and paper at your side to sketch shapes and follow along with the arguments yourself.
Acheson done a great job as well at preparing me for ideas that I will doubtlessly face at university, like spherical geometry and rigourous proofs from axioms. I also particularly appreciated the sprinkling of relevant history, opinions, and perspectives throughout the book. Never before have I been so interested in geometry.
If anyone is looking for a gift for a teenage child interested in maths and who may want to take maths to university level, this book is perfect.
I have a rather unique perspective on this book. As a prospective maths undergraduate student, I wanted a book that could make me think while satiating my thirst for interesting and cool mathematics. As other reviewers have said, geometry was not my cup of tea before reading this book. In fact, I wouldn't have considered reading a book on geometry had it not been recommended to me. That said, I enjoyed this book much more than I could have expected.
Acheson manages to make proving the basic, and rather tedious, theorems of euclidean geometry increadibly easy to follow and satisfying when he then takes these ideas further. I usually struggle to follow complicated geometrical proofs, but here every idea is accompanied by a useful and clear diagram and I found it really easy to dip in and out of this book without ever feeling lost. I enjoyed how some of the more complex proofs were given in the notes in order to make the base text more accessible.
This is a book that I wish I had when I was 13/14 as it would have given me a much better understanding of the point of geometry, as well as of many theorems which definitely would have been useful when I went on to do further mechanics at A-level. This is a book where it's great to have a pencil and paper at your side to sketch shapes and follow along with the arguments yourself.
Acheson done a great job as well at preparing me for ideas that I will doubtlessly face at university, like spherical geometry and rigourous proofs from axioms. I also particularly appreciated the sprinkling of relevant history, opinions, and perspectives throughout the book. Never before have I been so interested in geometry.
If anyone is looking for a gift for a teenage child interested in maths and who may want to take maths to university level, this book is perfect.
March 31, 2023
There are many reasons to study geometry. The most important reason, and one this book does a superb job conveying, is that this shit is dope as fuck! The subtext is "30 minutes or less to fall in love with geometry all over again" and the book succeeds so wildly that I struggle to recall another book on any other topic that hit its mark so accurately.
Thales' theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle. Did you get that? If yes, then this is the book for you. Yeah, there's "applications", but that's not why we're here. We're here for Thales theorem. And across 32 chapters we keep coming back to it over and over and over again. At first it's surprising, then it's confusing, then it's just straight up delightful whenever the theory shows up out of nowhere.
Do you know who Thomas Simpson? Of course not, no one's heard of him before, and that's fine! The author was sufficiently enthralled by Simpson's meanderings to make him a main character.
My absolute favorite part of this book is asking "what the fuck", putting the book down, walking away, picking it back up again and suddenly getting it. This is the feeling I'm chasing whenever I pick up a math book. It's why I'm into math in the first place.
I cannot recommend this book enough.
Thales' theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ABC is a right angle. Did you get that? If yes, then this is the book for you. Yeah, there's "applications", but that's not why we're here. We're here for Thales theorem. And across 32 chapters we keep coming back to it over and over and over again. At first it's surprising, then it's confusing, then it's just straight up delightful whenever the theory shows up out of nowhere.
Do you know who Thomas Simpson? Of course not, no one's heard of him before, and that's fine! The author was sufficiently enthralled by Simpson's meanderings to make him a main character.
My absolute favorite part of this book is asking "what the fuck", putting the book down, walking away, picking it back up again and suddenly getting it. This is the feeling I'm chasing whenever I pick up a math book. It's why I'm into math in the first place.
I cannot recommend this book enough.
April 14, 2025
A fantastic teaching of Geometry!
Like most publicly schooled Americans, I have an aversion to mathematics beyond addition and subtraction. Books like this completely change my perspective on the higher and more complex mathematics. The explanation and presentation are interesting and engaging.
I particularly enjoyed the history given of the specific geometric discovery. The concepts are presented following the who and how and why of their discovery.
Additionally, alongside the mathematicians that invented the formulas; like Galileo, Newton, and Pythagoras, the author uses examples like; a story from Sherlock Holmes, and an historical example from WW2, where planes utilized Geometry in a unique way to bomb dams.
I know they say do not judge a book by its cover, but the author and/or publishers still gave it fun cover art, as well as populating the pages with many entertaining simple Illustrations, historic pictures, and comics.
⚠️ Parental Warnings ⚠️
None
Like most publicly schooled Americans, I have an aversion to mathematics beyond addition and subtraction. Books like this completely change my perspective on the higher and more complex mathematics. The explanation and presentation are interesting and engaging.
I particularly enjoyed the history given of the specific geometric discovery. The concepts are presented following the who and how and why of their discovery.
Additionally, alongside the mathematicians that invented the formulas; like Galileo, Newton, and Pythagoras, the author uses examples like; a story from Sherlock Holmes, and an historical example from WW2, where planes utilized Geometry in a unique way to bomb dams.
I know they say do not judge a book by its cover, but the author and/or publishers still gave it fun cover art, as well as populating the pages with many entertaining simple Illustrations, historic pictures, and comics.
⚠️ Parental Warnings ⚠️
None
August 1, 2021
Fabulous book.
It brought back some fabulous memories of my school days - 1972 in particular - when I discovered that I loved maths.
I enjoy reading “popular” maths books just for fun, but they can be a bit hit & miss, especially when the information gets too technical (for me anyway). The author got that balance perfect.
I also really enjoyed the snippets of history and the marvellous mathematicians of the past, and a few who weren’t quite so on top of the maths too!
I also loved the humour dotted throughout. My favourite was his mention of the website with 16000 special points in triangles - “we will exercise rather more restraint…”!
It brought back some fabulous memories of my school days - 1972 in particular - when I discovered that I loved maths.
I enjoy reading “popular” maths books just for fun, but they can be a bit hit & miss, especially when the information gets too technical (for me anyway). The author got that balance perfect.
I also really enjoyed the snippets of history and the marvellous mathematicians of the past, and a few who weren’t quite so on top of the maths too!
I also loved the humour dotted throughout. My favourite was his mention of the website with 16000 special points in triangles - “we will exercise rather more restraint…”!
August 21, 2021
It's a great book if you want to explore more fun stuff about Geometry, but essentially not for beginners. Of course, you have to have a background. The author introduces a lot of theorems, paradox and whatnot, but only introduces them. The explanations were a bit short and unclear to fully understand that's why I have to Google it to fully comprehend them. The book is more like a summary of fun geometry knowledge, so if you want that, go ahead and read it! I thought it was like Milo Beckman's 'Math Without Numbers' kind of structure/writing, but it's my fault though for my own expectations lol. Anyway, I enjoyed it nonetheless.
August 22, 2022
I loved this book. I've wanted a book that went through compass and ruler proofs in a not too academic way for ages. Euclid and school books are just too dry.
If you liked this Geometry Snacks by Ed Southall and Pantaloni Vincent are puzzles based on some of the same theorems.
If you liked this Geometry Snacks by Ed Southall and Pantaloni Vincent are puzzles based on some of the same theorems.
April 27, 2023
A good book. No one feels bored once reading. I think there are two ways to read this book. 1. Read like a story, enjoy the proof, and continue reading. 2. Take a copy and pencil and proof by writing. That will be more enjoyable but take a long time.
December 28, 2021
Could be an inspiring book for kids, not really for adults though.
January 23, 2024
I'd be lying if I said that last chapter didn't make me tear up a little. Fantastic journey through some of the awesome aspects of geometry. Looking forward to his other books.
April 9, 2025
An excellent mix of history, facts and geometry. Really enjoyed it so although it doesn't have the emotion that I usually demand for a 4 star book, it gets that fourth star.
June 16, 2021
Uno sguardo non molto classico alla geometria euclidea
La geometria euclidea per vari secoli - nemmeno troppi, in realtà: diciamo dal 1700 al 1950? - è stata considerata il simbolo di come si dovrebbe fare matematica. Premesso che secondo me il rigore è sempre d'obbligo, ho il sospetto che sbatterlo in faccia ai ragazzi in questo modo sia controproducente. Ecco perché questo libro è il benvenuto. Acheson non ha nessuna voglia di dimostrare tutto in perfetto ordine e con il minimo numero di assunzioni possibile; tanto per dire, parte dal teorema di Talete, che è stato la sua epifania geometrica e che non è tra le primissime proposizioni euclidee. Racconta poi di testi storici di geometria con approcci assolutamente antieuclidei, di teoremi che non si studiano a scuola come quello di Miquel o quello dei sette cerchi, dà dimostrazioni non standard del fatto che le tre altezze di un triangolo passano per uno stesso punto... Insomma un modo fresco per dare un nuovo sguardo a un campo plurimillenario.
La geometria euclidea per vari secoli - nemmeno troppi, in realtà: diciamo dal 1700 al 1950? - è stata considerata il simbolo di come si dovrebbe fare matematica. Premesso che secondo me il rigore è sempre d'obbligo, ho il sospetto che sbatterlo in faccia ai ragazzi in questo modo sia controproducente. Ecco perché questo libro è il benvenuto. Acheson non ha nessuna voglia di dimostrare tutto in perfetto ordine e con il minimo numero di assunzioni possibile; tanto per dire, parte dal teorema di Talete, che è stato la sua epifania geometrica e che non è tra le primissime proposizioni euclidee. Racconta poi di testi storici di geometria con approcci assolutamente antieuclidei, di teoremi che non si studiano a scuola come quello di Miquel o quello dei sette cerchi, dà dimostrazioni non standard del fatto che le tre altezze di un triangolo passano per uno stesso punto... Insomma un modo fresco per dare un nuovo sguardo a un campo plurimillenario.
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