--- title: 3D Geometry description: 3D geometry studies the properties, measurements, and relationships of points, lines, planes, and solids in three-dimensional space. Learners will understand how to calculate volumes, surface areas, and spatial coordinates for engineering, computer graphics, and physics applications. category: mathematics subcategory: geometry-and-trigonometry difficulty: beginner, intermediate, advanced url: /subject/3d-geometry --- # 3D Geometry 3D geometry studies the properties, measurements, and relationships of points, lines, planes, and solids in three-dimensional space. Learners will understand how to calculate volumes, surface areas, and spatial coordinates for engineering, computer graphics, and physics applications. ## Where to start Start with Paul's Online Math Notes - Calculus III, Paul Dawkins' free Lamar University notes with worked examples on 3D coordinates, vectors, lines, planes and quadric surfaces. If you only use one resource, make it Multivariable Calculus (MIT 18.02SC) by Denis Auroux, a full course with lecture videos and problems with solutions. Use the free GeoGebra 3D Calculator alongside to check your calculations visually. ## Available Resources 1 Videos • 1 Books • 3 Courses • 4 Websites ## Websites ### 1. GeoGebra 3D Calculator GeoGebra's free browser-based 3D graphing tool for plotting points, vectors, lines, planes, surfaces and solids and rotating them in space. Useful for checking hand calculations and building visual intuition for intersections, distances and cross-sections in three dimensions. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.geogebra.org/3d **Tags:** 3d-geometry, graphing-calculator, visualization, vectors, geogebra ### 2. Paul's Online Math Notes - Calculus III Paul Dawkins' free Calculus III notes from Lamar University, with worked examples on 3D coordinates, vectors, equations of lines and planes, quadric surfaces, partial derivatives and multiple integrals. Readers learn to set up and solve standard multivariable problems step by step. **Difficulty:** Beginner | **Price:** Free **Link:** https://tutorial.math.lamar.edu/classes/calciii/calciii.aspx **Tags:** calculus-iii, multivariable-calculus, 3d-geometry, vectors, lines-and-planes ### 3. geogebra.org GeoGebra.org is a free dynamic mathematics platform that combines geometry, algebra, calculus, and statistics through interactive applets. It provides tutorials, worksheets, and a large library of user-created resources and activities for exploring geometric concepts and beyond. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://geogebra.org **Tags:** websites, mathematics-statistics, mathematics ### 4. mathsisfun.com MathIsFun.com is a beginner-friendly math site that explains concepts with clear, step-by-step lessons and interactive activities. It covers topics from algebra and linear equations to geometry, fractions, data, and more, with practice problems, worksheets, and quizzes. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://mathsisfun.com **Tags:** websites, mathematics-statistics, algebra ## Courses ### 1. Vector Calculus Learn 3D geometry with Dr. Trefor Bazett's vector calculus course! Master multivariable calculus concepts & problem-solving. **Difficulty:** Advanced | **Price:** Free **Link:** https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa **Tags:** vector-calculus, multivariable-calculus, line-integrals, surface-integrals, vector-fields ### 2. Multivariable Calculus Master multivariable calculus! Explore functions of several variables, gradients, and more with this comprehensive course. **Difficulty:** Advanced | **Price:** Free **Link:** https://www.khanacademy.org/math/multivariable-calculus **Tags:** calculus, vector-calculus, partial-derivatives, vector-fields, video-lessons ### 3. Multivariable Calculus (MIT 18.02SC) **Author:** Denis Auroux Differential, integral and vector calculus in several variables: vectors and matrices, partial derivatives, optimization, double and triple integrals, line integrals, and the theorems of Green, Stokes and Gauss. Includes 106 lecture and recitation videos, notes, and problems and exams with solutions, built for independent study. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-02sc-multivariable-calculus-fall-2010/ **Tags:** multivariable-calculus, partial-derivatives, multiple-integrals, vector-calculus, line-integrals ## Videos ### 1. Vectors | Chapter 1, Essence of Linear Algebra **Author:** Grant Sanderson Opening chapter of Grant Sanderson's animated linear algebra series, contrasting the physics, computer science and mathematics views of vectors. Shows vectors as arrows and coordinate lists, and how addition and scalar multiplication work geometrically, laying intuition for linear combinations and transformations. **Difficulty:** Beginner | **Price:** Free **Link:** https://www.youtube.com/watch?v=fNk_zzaMoSs **Tags:** linear-algebra, vectors, vector-addition, visual-intuition ## Books ### 1. Solid Geometry **Author:** George Wentworth, David Eugene Smith A 1913 Wentworth-Smith textbook, reprinted by Forgotten Books, that develops solid geometry through definitions, theorems and proofs. It covers lines and planes in space, dihedral angles, polyhedrons, cylinders, cones and spheres, training readers to prove spatial results and compute areas and volumes. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/1333706030?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, geometry--trigonometry --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/3d-geometry