The best geometry books

1 authors have picked their favorite books about geometry and why they recommend each book.

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The Projective Cast

By Robin Evans,

Book cover of The Projective Cast: Architecture and Its Three Geometries

Robin Evans was a versatile architectural historian and theorist who died too young. This highly original and unusual book, published after his death, is about the relationship of geometry to architecture, and how methods of drawing, including perspective and orthographic projection, can influence what is conceived and built. I admire the way in which Evans, unlike many architectural historians, is able to combine deep scholarship with a working practical understanding of how buildings are made, and how they are used in practice. There has been no other recent writer on architecture with so subtle a mind.


Who am I?

If I was asked to describe the central theme of my life's work in a phrase, it would be 'geometry in the arts'. I'm an architect originally, now a professor in London, and have always loved drawing and the art of perspective. In the 1990s I became fascinated with the idea that Johannes Vermeer used the camera obscura, an obsession that led to my book Vermeer's Camera. I'm now working on Canaletto's Camera. And I have ideas for yet another book, on perspective, to be called Points of View. I've chosen five books on these topics that I've found most thought-provoking and inspiring.


I wrote...

Vermeer's Camera: Uncovering the Truth Behind the Masterpieces

By Philip Steadman,

Book cover of Vermeer's Camera: Uncovering the Truth Behind the Masterpieces

What is my book about?

Over 100 years of speculation and controversy surround claims that the great seventeenth-century Dutch artist, Johannes Vermeer, used the camera obscura to create some of the most famous images in Western art. This intellectual detective story starts by exploring Vermeer's possible knowledge of contemporary optical science, and outlines the history of this early version of the photographic camera, which projected an image for artists to trace. By analysing the perspective of Vermeer's paintings, I have been able to reconstruct his studio and provide exciting new evidence to prove that Vermeer did indeed use the camera.

Euclid's Elements

By Dana Densmore (editor), Thomas L. Heath (translator),

Book cover of Euclid's Elements

This is the bestselling textbook of all time. Euclid’s Elements has been the model for correct thinking for thousands of years. The traditional year-long course on axiomatic reasoning about geometry was easily my favorite course in high school. In fact, I sort of assumed that I was slow in that I could not “see” the underlying axioms in other classes. I simply did not realize that the other high school subjects were not axiom-based. 

The story goes that as a young prairie lawyer, Abraham Lincoln carried around with him a tattered copy of the Elements so that he could learn how to think (even though he never really had much formal education). I hope this is true. Even more so, I want to believe that he developed his profound oratorial skill from the power behind Euclid.


Who am I?

I love mathematics and truly believe that “Functions Describe the World.” I'm deeply satisfied that I've spent my professional life discovering new mathematics and explaining known mathematics to others. I was an undergraduate at the University of Texas, Austin, got my PhD from Brown University, then spent three years as a G.C. Evans Instructor at Rice University, before moving to Williams, where I've been ever since. Besides writing All the Math You Missed (But Need to Know for Graduate School), I've also written Algebraic Geometry: A Problem Solving Approach (with a number of co-authors) and Electricity and Magnetism for Mathematicians: A Guided Path from Maxwell’s Equations to Yang-Mills, and a number of research articles.  


I wrote...

All the Math You Missed: (But Need to Know for Graduate School)

By Thomas A. Garrity,

Book cover of All the Math You Missed: (But Need to Know for Graduate School)

What is my book about?

People who are starting graduate school in mathematics are full of hopes and dreams to become great mathematicians. That is good. But most are suddenly confronted with the cold hard fact that they are expected to know a daunting breadth of mathematics, a breadth that few actually have or even could have had. This book is an attempt to help my younger future colleagues. 

Each of its twenty chapters covers a key part of the math needed for graduate school. All beginning graduate students know the math in some of the chapters. Hardly any are comfortable with the material in all of the chapters. This book will help them “get into the game,” concentrating on why the math in each chapter is important and pointing them to resources to learn more. 

Anno's Math Games III

By Mitsumasa Anno,

Book cover of Anno's Math Games III

I stumbled on this in a used bookstore. What a find! The old-school, kid-friendly illustrations lead swiftly from simple beginnings (“What happens when you stretch a painting?”) to the depths of undergraduate topology. I haven’t used this in the classroom yet, but honestly, I could imagine busting it out with anyone from first-graders to first-year PhD candidates.


Who am I?

Explaining math demands great visuals. I should know: I explain math for a living, and I cannot draw. Like, at all. The LA Times art director once compared my cartoons to the work of children and institutionalized patients. (He printed them anyway.) In the nerdier corners of the internet, I’m known as the “Math with Bad Drawings” guy, and as a purveyor of artless art, I’ve developed an eye for the good stuff: striking visuals that bring mathematical concepts to life. Here are five books that blow my stick figures out of the water. (But please buy my book anyway, if for no deeper reason than pity.)


I wrote...

Math Games with Bad Drawings: 75 1/4 Simple, Challenging, Go-Anywhere Games--And Why They Matter

By Ben Orlin,

Book cover of Math Games with Bad Drawings: 75 1/4 Simple, Challenging, Go-Anywhere Games--And Why They Matter

What is my book about?

It's the ultimate mathematical game chest: 70-plus games, playable with just paper, pens, and the occasional handful of coins. Drawing from Argentine puzzle magazines, Japanese schoolyards, Parisian universities, and everywhere in between, I hand-picked the games with three adjectives in mind: (1) fun, (2) thought-provoking, and (3) easy to play. Each takes a minute to learn and a lifetime to master. Better yet, each brings out the best in human thought, from cognitive psychology to quantum mechanics.

Teaching and Learning Algebra

By Doug French,

Book cover of Teaching and Learning Algebra

This may seem an odd choice, but as a maths popularizer I need to know all that I can about why some people find the main elements of the subject so difficult. I found Doug French's book exceptionally helpful in this respect, even though it is aimed principally at high school teachers. This is partly because he focuses throughout on the most important mathematical ideas and difficulties. Moreover, the scope is wider than the title suggests, for he also ventures imaginatively into both geometry and calculus.


Who am I?

I am an applied mathematician at Oxford University, and author of the bestseller 1089 and All That, which has now been translated into 13 languages. In 1992 I discovered a strange mathematical theorem – loosely related to the Indian Rope Trick - which eventually featured on BBC television. My books and public lectures are now aimed at bringing mainstream mathematics to the general public in new and exciting ways.


I wrote...

The Wonder Book of Geometry: A Mathematical Story

By David Acheson,

Book cover of The Wonder Book of Geometry: A Mathematical Story

What is my book about?

What is the quickest route to mathematics at its best? 

In this book, I try to show how geometry can provide the answer, by drawing on its rich history, quirky personalities, and practical applications. Throughout, I highlight elegant methods of deduction and the most surprising results, and claim that, in this way, anyone can begin to enjoy some of the wonders of mathematics within just half an hour of starting.

Translations from Drawing to Building and Other Essays

By Robin Evans,

Book cover of Translations from Drawing to Building and Other Essays

The book introduced Interior Design as an intellectual subject with a firm theoretical grounding that went beyond style and taste to influential and foundational concepts and promoted it as a serious field of study. It is a collection of accessible essays and so is easy to dip into. My favourite essay is "Figures, Doors and Passageways," which discusses the formation of contemporary systems of circulation, the development of the corridor, and the evolution of modern ideas of personal privacy.


Who am I?

For more than thirty years I have been discussing, formulating ideas, and writing about Architecture, Building Reuse, and Interiors. I lead the MA Architecture and Adaptive Reuse programme and direct graduate atelier Continuity in Architecture at the Manchester School of Architecture. I am currently the Visiting Professor at the University IUAV of Venice where I am conducting research on the sustainable adaptation of existing buildings with particular emphasis on the environmental concerns within the inherently fragile city of Venice.


I wrote...

Inside Information: The Defining Concepts of Interior Design

By Sally Stone,

Book cover of Inside Information: The Defining Concepts of Interior Design

What is my book about?

Inside Information is a chatty and well-informed conversation about the theoretical ideas that inform the interior. Written as a collection of 26 conversations, from Ante to Zeitgeist, Inside Information explores the rich diversity of areas that inform the subject, and ideas that underpin it. This thesaurus of interiors transcends the boundaries and genres that often define interiors, providing a comprehensive view of the concepts and vocabulary of interior design. It is a practical introduction for the professional, a set of provocation for the scholar, a ‘good read’ filled with anecdote and speculation for the amateur, and primer for the students.

The Dot and the Line

By Norton Juster,

Book cover of The Dot and the Line: A Romance in Lower Mathematics

Picking up this short picture book, I expected a dose of Phantom Toolbooth-esque wordplay. Not at all. This five-minute love story, about a line yearning for a dot, somehow enlarges into a meditation on geometric structure itself. From such a brief book, I didn’t expect new insights about how simple geometry underlies our most intricate thinking—but then again, that’s what delightful visuals will do for you.


Who am I?

Explaining math demands great visuals. I should know: I explain math for a living, and I cannot draw. Like, at all. The LA Times art director once compared my cartoons to the work of children and institutionalized patients. (He printed them anyway.) In the nerdier corners of the internet, I’m known as the “Math with Bad Drawings” guy, and as a purveyor of artless art, I’ve developed an eye for the good stuff: striking visuals that bring mathematical concepts to life. Here are five books that blow my stick figures out of the water. (But please buy my book anyway, if for no deeper reason than pity.)


I wrote...

Math Games with Bad Drawings: 75 1/4 Simple, Challenging, Go-Anywhere Games--And Why They Matter

By Ben Orlin,

Book cover of Math Games with Bad Drawings: 75 1/4 Simple, Challenging, Go-Anywhere Games--And Why They Matter

What is my book about?

It's the ultimate mathematical game chest: 70-plus games, playable with just paper, pens, and the occasional handful of coins. Drawing from Argentine puzzle magazines, Japanese schoolyards, Parisian universities, and everywhere in between, I hand-picked the games with three adjectives in mind: (1) fun, (2) thought-provoking, and (3) easy to play. Each takes a minute to learn and a lifetime to master. Better yet, each brings out the best in human thought, from cognitive psychology to quantum mechanics.

The Magic of Math

By Arthur Benjamin,

Book cover of The Magic of Math: Solving for X and Figuring Out Why

Have you ever been to a mathematics lecture where the speaker wore a tuxedo and baffled the audience with his mystifying knowledge of numbers? Well, I have and the speaker was Arthur Benjamin, who combined mathematics and magic. He even displayed this knowledge with Stephen Colbert on his earlier show The Colbert Report. It is our good fortune that he describes much of this mathematical wizardry in this fascinating book. 


Who am I?

I have enjoyed mathematics and writing since I’ve been a kid, not only enjoying doing research in mathematics but assisting others to appreciate and enjoy mathematics. Along the way, I’ve gained an interest in the history of mathematics and the mathematicians who created mathematics. Perhaps most important, my primary goal has been to show others how enjoyable mathematics can be. Mathematics has given me the marvelous opportunity to meet and work with other mathematicians who have a similar passion for mathematics.


I wrote...

Mathematical Proofs: A Transition to Advanced Mathematics

By Gary Chartrand, Albert Polimeni, Ping Zhang

Book cover of Mathematical Proofs: A Transition to Advanced Mathematics

What is my book about?

Why was this book written? This is the book its three authors wish we had when we were students. If you have encountered calculus already, then what lies beyond it? This is what this book is all about. What exactly does a mathematician do? Some mathematicians simply enjoy mathematics – others also create new mathematics. They look for or observe patterns that suggest something appears to be true. If they guess correctly, then they need to convince others why it’s true, beyond any doubt. This is where proofs enter.

For example, the famous mathematician Ron Graham felt that all numbers (positive integers) are interesting. Suppose not. Then there is a smallest number that’s not interesting – which makes this number interesting. That’s a proof! 

Riddles in Mathematics

By Eugene P. Northrop,

Book cover of Riddles in Mathematics: A Book of Paradoxes

I was given this book when I was about 15, and devoured it. It is an eclectic collection of mathematical paradoxes, fallacies, and curiosities so strange that they seem impossible. Mathematical magic tricks, a proof that all numbers are equal, a proof that all triangles are isosceles, a curve whose length is infinite but whose area is finite, a curve that crosses itself at every point, a curve that fills the interior of a square. Infinities that are bigger than other infinities. The Saint Petersburg Paradox in probability, a calculation that you should pay the bank an infinite amount of money to play one fair coin-tossing game. The smallest number that cannot be named in fewer than thirteen words (which I’ve just named in twelve words).


Who am I?

As a kid I read every popular math book I could lay my hands on. When I became a mathematician I wanted to do more than teaching and research. I wanted to tell everyone what a wonderful and vital subject math is. I started writing popular math books, and soon was up to my neck in radio, TV, news media, magazines... For 12 years I wrote the mathematical Recreations Column for Scientific American. I was only the second mathematician in 170 years to deliver the Royal Institution Christmas Lectures, on TV with a live tiger. The University changed my job description: half research, half ‘outreach’. I had my dream job.


I wrote...

Flatterland: Like Flatland Only More So

By Ian Stewart,

Book cover of Flatterland: Like Flatland Only More So

What is my book about?

Edwin Abbott Abbott’s 1884 Flatland, a classic of popularization, tells of a world of two dimensions inhabited by geometric figures. Really, it’s about the Fourth Dimension, much in vogue at the time. That’s mild compared to the inventions of today’s mathematicians and physicists.

Flatterland explores these mindboggling new ideas using Abbott’s scenario of imaginary worlds. Victoria Line, a thoroughly modern young woman in Flatland’s disintegrating male-dominated culture, explores these novel universes, guided by the Space Hopper. She encounters the doughmouse at the topologists’ tea party, puzzles over the five-sided squares of Platterland, argues with Superpaws the quantum cat, and grapples with relativity in the domain of the Hawk King. Like Flatland, the book is partly about imaginative and important math, and partly about social inequality.

Japanese Gardens

By Gunter Nitschke,

Book cover of Japanese Gardens

Focusing on how attitudes toward gardens and nature transformed over time, this book starts with the first gardens in Japan and ends with contemporary examples. The chronological approach emphasizes the transitions from one era and style to the next, while the author focuses in on the important influences and aspects of each. The wide range of ideas and examples draw the reader in and also provide ideas for further “digging in.”  


Who am I?

When I first saw an image of a Japanese garden, it was unlike anything I had seen before. I just knew I had to visit Japan to see the gardens and try to understand the culture that produced this artistry. I later had the opportunity to work for a small Japanese architecture firm in Tokyo. During those seven years, I explored gardens, landscapes, villages, and cities, trying to absorb as much of the culture as I could. Japanese gardens still fascinate me, and I love learning about contemporary designers and gardeners in Japan who are keeping the traditional spirit alive, while exploring what a garden can be in the present day.


I wrote...

Zen Garden Design: Mindful Spaces by Shunmyo Masuno - Japan's Leading Garden Designer

By Mira Locher,

Book cover of Zen Garden Design: Mindful Spaces by Shunmyo Masuno - Japan's Leading Garden Designer

What is my book about?

Zen Buddhist priest Shunmyo Masuno understands that today's busy world leaves little time or space for self-reflection, but that a garden—even in the most urban of spaces—can provide some respite. In his words, "The garden is a special spiritual place where the mind dwells." With this in mind, Masuno has designed scores of spectacular Japanese gardens and landscapes with the aim of helping people achieve a balanced life in the 21st century.

This book explores Masuno's design process and ideas, which are integral to his daily Zen training and teachings. It features 15 unique gardens and contemplative landscapes completed in six countries over as many years—all thoughtfully described and documented in full-color photos and drawings.

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