The 10 Best Geometry Textbooks
Special Honors
edX Introduction to Geometry If you're looking to take a self-paced class on your own time, consider this interactive course from online learning platform edX. You'll learn how to measure angles, prove and apply properties of triangles, quadrilaterals, and other polygons, calculate the volumes and surface areas of three-dimensional solids, and more. You can choose your path within each lesson and jump between lessons to review earlier material. The course covers a standard curriculum in high school geometry, and common core alignment is indicated where applicable. edx.org
Dragonbox Elements Intended for children aged 9 to 12, Dragonbox Elements is an interactive, fun game that secretly teaches geometry concepts to kids and gives them a head start in school. There are over 100 puzzles that youngsters can solve to gain a deep understanding of the logic of the subject. Charming characters and a thoughtful storyline help maintain interest while players build confidence. This app takes its cues from Euclid's "Elements" and enables users to master essential axioms and theorems after a short time. dragonbox.com
Editor's Notes
July 23, 2020:
Since we already had tried-and-tested, comprehensive high school texts like McDougal Littell Geometry and Glencoe Geometry Student Edition on board, we felt we could part ways with Holt Geometry. We added another challenging volume to balance out our selection, which features titles for struggling students, introductory texts, and more rigorous options. That volume is Geometry for Enjoyment and Challenge.
Like "Geometry" by Ray C. Jurgensen, Geometry for Enjoyment places a heavy emphasis on proof-based instruction and is sadly out of print. Normally we wouldn't recommend a book that won't be updated again, but this one has been sought after by high-performing schools and veteran teachers and tutors in the decades since its publication. Because Geometry is a branch of math that remains relatively free of revolutionary leaps forward, we felt this is a category where books with varying publishing dates can still be beneficial.
To give disinterested students another option outside of Painless Geometry, we brought on Must Know High School Geometry. Unlike many other titles in this category, Must Know is a recently written edition that boasts modern language and learning aids, including a flashcard app. This one only covers the most fundamental basics, though, so it can't replace a traditional textbook completely.
By the way, if you're teaching yourself at home you might want to consider picking up a geometry set to ensure you have everything you need to get started once your book arrives.
June 27, 2019:
Choosing the best geometry book for you is a highly individual choice that depends on your level of expertise, learning style, tastes, and intended application (are you learning for personal enjoyment, high school, university, tutoring, etc). There is no one size fits all, and so this list has textbooks for multiple ages and proficiency levels. We also made sure to include shorter options (Barron's Painless) for those who require review and the budget-conscious.
With that in mind, we prioritized our selections based on their usefulness, how well they arrange and elucidate the subject matter, if they use pedagogy, and writing styles that are approachable and not bogged down in pedantry. Our number one selection, Elementary Geometry for College Students, passed all these tests with flying colors.
This most recent update also saw the newest editions of the Painless Geometry series and Elementary Geometry for College Students, as well as the removal of Fundamental Concepts and Applications, which we felt wasn't comprehensive enough.
High schoolers who require comprehensive texts will find what they need in Holt Geometry, Glencoe Geometry Student Edition, or McDougal Littell Geometry, while those at the college level would do well with Geometry Revisited, Elementary Geometry for College Students, and "Geometry" by Ray C. Jurgensen. Despite being published decades ago, Introduction to Geometry is a solid choice if you're a hands-on learner who appreciates a challenge. Kinetic types should also consider Seeing, Doing, Understanding.
A Brief History Of Geometry
However, the history of the science goes back thousands of years, and it's actually pretty interesting!
You'd be forgiven for thinking that geometry was something invented by diabolical teachers with the specific intention of punishing you. However, the history of the science goes back thousands of years, and it's actually pretty interesting! Wait, come back — we're serious!
The ancient Egyptians were the first to use something resembling geometry around 3,000 B.C.E. They needed a way to quickly and easily survey land for agriculture, chart the course of the stars, and oh yeah — build a couple of pretty sweet pyramids.
The next great mathematical advancement would come from the famed Greek mathematician Euclid in about 300 B.C.E. He pioneered the method of making a series of small, intuitive statements, and then deducing a larger axiom from their sum. It was such a breakthrough that an entire branch of the science is named after him.
It would take nearly two millennia before the next big leap forward would come, but when it did, it came from France. The renowned philosopher Rene Descartes (of "I think, therefore I am" fame) figured out a way to use coordinates to illustrate proofs. His method incorporated algebra, and opened the door for the discovery of calculus.
Still, Euclidean geometry was the undisputed champ of the mathematical world until the early 19th century, when several mathematicians, including Carl Friedrich Gauss, altered Euclid's postulate involving parallel lines. Their discovery (which they cleverly named — wait for it — non-Euclidean geometry) led to the discovery of hyperbolic and elliptic geometry.
While there hasn't been a seismic shift in the field since the 1800s, advancements in geometry are still constantly being made. It's amazing to think that such an ancient field could still be ripe for discovery, but it's a testament to how rich and varied the math truly is.
Just think — if some numbers whiz makes a new discovery soon, you might have an entirely new type of math you'll be forced to learn!
Finding The Right Geometry Textbook For You
For many students, finding the right textbook is easy: simply take the one your teacher gives you.
If you're lucky enough to have some say in the matter, though — like if you're home-schooling or just wanting to learn about the fascinating world of mathematics — then you'll have to wade through the sea of available textbooks to try to find one that's right for you.
Ultimately, this is a personal decision, as each person will benefit from a different style of text.
Ultimately, this is a personal decision, as each person will benefit from a different style of text. You should ask yourself what teaching style serves you best, and then try to find a book that mimics that style effectively. Do you learn better from pictures and charts, or would you prefer to just mainline the numbers and hard data? Do you need extremely thorough explanations, or do you like it better when the author moves along briskly?
Some books even try to incorporate humor, which can be pretty hit-or-miss (there's a reason they don't have "Math Teacher Night" at The Comedy Store). Still, a writer with a light touch can take some of the drudgery out of learning the material, which could be all you need to keep plugging along.
Regardless of which style you end up preferring, it's important that any book you buy gives you plenty of opportunity to practice your skills. Look for one that has plenty of exercises — and detailed explanations of the answers, in case you get one wrong. Some come with CDs or online components, which can be very helpful when studying for a test, especially if the publisher updates the information frequently.
Finding the right level of difficulty is important, as well. After all, there's a lot to learn in geometry, and if you jump into the deep end with a book that assumes knowledge you don't have, you're going to have a bad time. That said, you still want to challenge yourself, so don't default to the easiest book out there.
At the end of the day, though, you're going to get out of your studies what you put into them, regardless of which book you end up choosing. Find one you're comfortable with, because chances are you'll be spending a lot of time with it.
Tips To Make Learning Easier
While geometry is far from easy, that doesn't mean that learning it has to be some Herculean effort. With a few basic strategies in place, you can make mastering the material quick, easy, and maybe even fun.
One of the first things you need to realize is that learning geometry will be virtually impossible if you don't understand the terminology.
One of the first things you need to realize is that learning geometry will be virtually impossible if you don't understand the terminology. If your book came with a glossary, read through it before you get too deep into the subject, and pay attention when vocabulary words come up in the text. If you don't know what a vertex is, for example, then good luck getting very far.
There are plenty of theorems and properties you'll need to know, so making flashcards is a smart idea early on. The sooner you can reflexively identify and understand each one, the quicker you'll be able to advance through the material. This is especially true for Euclid's postulates, so get intimately acquainted with those.
Make sure you have a quality compass, protractor, and ruler as well. These will help you quickly measure shapes and angles, especially if you can find options that are transparent.
However, there are no real shortcuts to success. You'll have to put the time and effort in, so block out a set schedule each week for studying the material. Luckily, the more time you put into it, the easier it will become, so you should be a geometry samurai in no time.