Though often kept separate in more formal academic settings, both math and art are integrally related in reality. Each discipline supports and plays an integral role in understanding and appreciating the other. So whether you’re here to start your investigation of the interdisciplinary connections, or to integrate these two fields to enhance student engagement in and understanding of math, we’ve found a wealth of resources to guide you along the way.
Below, you’ll find a variety of websites to help you understand the relationship between art and math, incorporate these connections into your own learning and teaching (no matter your level of mathematical understanding or artistic ability), and just explore some really cool math art on the web.
General Math Art Resources
- The Bridges Organization for Art and Mathematics hosts a yearly conference showcasing the connections between art and mathematics. Its focus on integrating the two fields and producing resources to support others in this mission makes this site a must-visit for those serious about interdisciplinary work in art and math.
- Cool Math 4 Kids – Geometry and Math Art presents the basics of tessellations, polyhedra, and fractals in kid-friendly language. These complex ideas are presented in a way that young people can understand and begin to experiment with.
- Linking Math with Art through the Elements of Design introduces students to the basic principles of design and geometry through these online activities. This document is mostly oriented toward students in the primary and intermediate grades, with some adaptations provided for working with middle and high school students.
- Math and the Art of M.C. Escher celebrates Escher’s vast collection of work, which encompasses almost every category in the math art world. This site includes both examples of Escher’s work (sorted by category) as well as activities for teachers and students seeking to connect their mathematical understandings with artistic projects.
- Math and Art is developed for those interested in exploring the connections between art and mathematics. The site contains resources for educators, links to organizations, and other math websites. In addition to being a great spot to search for resources, it’s also an open forum for those wishing to contribute.
- Math Art Fun provides a simple, yet comprehensive, overview of the different types of math art, and how each relates to learning important concepts in both math and art. Though this is a commercial site that offers many products for sale, it is also particularly useful for teachers looking to integrate art into their mathematics curriculum with little or no idea of where to begin. This site will answer your questions and give you lots of options for how to proceed.
- Mathematical Imagery offers a vast collection of math art that is catalogued in albums on this website presented by the American Mathematical Society. Though it doesn’t delve into the historical connections between math and art, this is a great site for current examples of how the two fields remain integrated today.
- Mathematics Museum showcases work that demonstrates the connections between art and mathematics. Find a variety of galleries, interactive displays, and interesting math problems that will puzzle and engage.
The Golden Ratio
- Fibonacci and the Golden Section in Art, Architecture, and Music provides information and examples about how the Golden Ratio has made intentional and unintentional appearances in everything from elaborate and famous works of art, architecture, and music, to everyday buildings and tools. Examples and suggestions of resources for further exploration are also provided.
- Golden Mean Art incorporates different media and more current artistic works in your lessons about the Golden Ratio. This site provides examples of modern photography, colored pencil, and ink drawings, as well as some of the more classic examples of the golden ratio in art history.
- Golden Mean – Math Integration features an interdisciplinary lesson that incorporates math, art, and technology. Lesson resources are provided, as well as examples of student work. It’s designed for high school students, but could be easily adapted to fit younger students.
- Nature by Numbers, an entertaining animated video, is an engaging way to show students the connections between math and art. Don’t miss this beautifully animated short film that illustrates the golden ratio, the Fibonacci sequence, and other mathematical concepts using nature.
- The Math Forum offers a clear, concise explanation for beginners that teachers who feel a bit uncertain about the mathematics will appreciate. Though not explicitly art-focused, this site will give you the basic mathematical understanding you need to use the golden ratio to integrate art and math in your curriculum.
- Interactive Tessellate! allows users with java-capable browsers to make both regular and non-regular tessellations (but unfortunately is not capable of making semi-regular tessellations). It’s intuitive to use and contains clear directions for those needing more guidance. Curricular connections are provided for educators.
- The Metropolitan Museum of Art: Islamic Art and Geometric Design provides background on regular tessellation techniques used in Islamic Art, as well as several examples of famous pieces and suggestions for educational activities.
- Pattern Blocks – Exploring Tessellations is an interactive pattern blocks program that allows users with java-capable browsers to experiment with regular and semi-regular tessellations. Though the program is intuitive, instructions are not provided, so adults working with younger children may want to develop a lesson or series of lessons to teach students how to place and manipulate the pattern blocks on the screen.
- Tessellations.org focuses on using tessellations in the classroom (including several techniques students can use to create tessellations at all ages). The helpful site contains lessons and tutorials, and invites contributions from teachers working with their students on tessellations. It’s entirely-kid friendly in its examples, and the site is willing to post your students’ tessellation projects on its “School Gallery” page.
- Totally Tessellated explores the history of tessellations, before, after, and including M.C. Escher’s work. Learn what you need to know about the history and techniques behind tessellation artwork, and see what both mathematicians and artists have done to explore the complex nature of tessellations.
- What is a Tessellation? provides a clear and concise explanation of the mathematics of tessellations, so they can be more than just another art project. If you think tessellations are cool, but want more information on their mathematical significance, this site is a great place to start.
- A Fractals Unit for Elementary and Middle School Students enables educators to adjust their math curricula to reflect the current field of mathematics. Learn why every math teacher should think about incorporating fractals into their curriculum. Then, use the well-developed resources provided here to do so.
- Exploring Fractals helps teachers tailor an exploration of fractals to students of all ages (as young as fifth grade). Lessons and web resources (including web quests) are provided for teachers trying to make fractals interesting and accessible to their students.
- Fractals and Proportional Reasoning uses the art of fractals to teach middle school students proportional reasoning. This detailed unit plan will help teachers make fractals more than just cool math art.
- Fractal Foundation is a non-profit organization developed to inspire interest in connecting math, art, and science through the study of fractals. Explore your own interests in fractals, and learn how to connect that interest to others through teacher resources and professional development opportunities.
- Fractals in Nature walks the user through the geometry of fractals as seen in nature, and provides stunning images to illustrate the interconnectedness of math, art, and the natural world.
- Fractal World Gallery offers an enormous collection of fractal art on the web: hundreds of high quality images of fractal designs are available.
- Classroom Polyhedra Activities will bring polyhedra to life and allow students to create their own models using paper and other common classroom supplies. Activities range in levels of complexity and skills required for construction.
- Investigations with Polyhedra helps make geometry more concrete and accessible. This well-developed unit plan is appropriate for students in grades 7-12.
- Polyhedra and Art details the historical presence of polyhedra in important works of art and artistic movements. Lots of examples from Pre-Renaissance movements through the twentieth century are provided by this informative site.
- Geometry and Art: Perspective Drawing is a high school geometry unit plan designed to teach the concept of lines and planes in space through art. Unit and lessons are aligned to math and art standards and lesson materials for copying and classroom display are provided.
- Perspective Drawing suggests some simple drawing activities to explore the relationship between the vanishing point and parallel lines for math students. Links are also provided for students to identify parallel lines and similar figures in some classic pieces of art.
- The Geometry of Perspective Drawing on the Computer is published by the University of Utah and appropriate for those in high school mathematics and beyond. This article investigates the mathematics behind computer programs that create perspective drawings and includes some problems to challenge readers to apply what they’ve learned.
Braids and Knots
- Algorithms, Braids, and Kolam Figures uses the familiar topic of braids to teach properties of math and algorithms to elementary school students. Resources provided here will help you incorporate math into something many of your students already create as crafts.
- Knot Plot examines knots and knot tying from a mathematical perspective. This site contains simple and higher-dimensional knot tying examples and knot activities for students to try. Activities are appropriate for high school students through higher-level mathematicians. Knot-tying activities are mostly computer simulations.
- Untangling the Mathematics of Knots offers a wealth of knot tying activities related to mathematics. Lessons involve mostly kinesthetic, rope-tying tasks, and make this an excellent spot to start exploring the mathematics of knots with intermediate and middle level students needing concrete examples.
- Modular Mania is Meenakshi Mukerji’s origami art site, and it’s one of the top modular origami sites on the web. The galleries provide lots of impressive examples of modular origami, including polyhedra and other designs with clear connections to mathematics.
- Origami and Math provides an overview of how to make the connection between the art of paper folding and mathematics, with activities ranging from basic to complex.
- Origami Tessellations demonstrates the merger of modular origami with tessellation artwork and other elements of geometric design. Explore the crossover of different approaches to math art here.
- Paper Folding Geometry helpfully connects paper folding activities to key concepts in geometry. Those teaching math can easily search for these activities by the mathematical concept they connect to. Most activities are appropriate for middle and high school students.
- Geometry in Art and Architecture traces the evolution of western art and architecture as it collides with mathematics. With lots of pictures and examples along the way, this site moves chronologically from the Egyptian pyramids to the intersection of math, art, and architecture today.
- Math-Kitechture is designed to help students use architecture to do math. Lessons incorporate computer-aided design (CAD) and work submitted by students can be displayed here in an online gallery.
- Perfect Buildings: The Maths of Modern Architecture has long been connected to mathematical ideas, and the display of mathematics through art. This article is dedicated to exploring the presence of art in the most groundbreaking and modern works of architecture.
- The International Society for Arts, Mathematics, and Architecture is a non-profit organization developed to enhance the integration of education relating to mathematics, architecture, and the arts. Membership is free and many resources are provided.
- Explore Mandala provides an easy to use, interactive tool to create mandalas provided by the Rubin Museum of Art. No additional programs for your computer or downloads are required to experiment with this tool, and finished products can be printed for decoration or mathematical analysis.
- Geometry and Art: Mandala is a geometry unit designed for high school students that teaches geometric modeling and the properties of circles and symmetry demonstrated by the mandala. The unit is aligned to national math standards.
- Radial Design incorporates symmetry and radial design into a mandala construction lesson plan. Student examples of finished products are provided. This lesson was designed for middle school math classrooms, but adaptations for elementary and high school classrooms are provided as links.
- The Mandala Project is dedicated to promoting unity and diversity through mandala artwork. Though not specifically math focused, the gallery on this site has over a thousand examples of mandalas, and is a great place to submit student work for display.
- Euclidean Geometry of Crop Circles summarizes Gerald Hawkins’ work on crop circle theorems based on the principles of Euclidean Geometry. It’s an interesting look at geometry and the way that research and discovery in mathematics is ongoing today. It’s not just a thing of the past as young math students often believe.
- Pi Appears in Crop Circle, an article published by the mathematics magazine, Plus, details the mathematical significance of a crop circle that encodes the number for pi out to ten digits. This article has the potential to be a highly engaging and interesting way to start an investigation of pi for middle or high school math students.
- Temporary Temples is an online image library of crop circles, and it’s one of the best on the web. Thumbnails make it easier to search images (which are also sorted by date) for those looking to tie examples into their work in mathematics.