Making math tangible with Maple and 3-D printers - User Case Studies - Maplesoft
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User Case Study: Making math tangible with Maple and 3-D printers

Building goblets with Maple helps students learn Calculus 2 concepts

Maple has long been used in the classroom to help students learn mathematics through visualizations, real-world applications, interactive explorations, and other techniques that makes mathematics more concrete for the students. Now, with the advent of 3-D printing, instructors have another means of making mathematics more tangible to their students. And this time, "tangible" is meant literally.

Dr. Philip Yasskin, professor of mathematics at Texas A&M University, has started combining Maple with 3-D printing to teach his students about solids of revolution. His Honors Calculus 2 class recently completed a project in which they designed goblets as solids of revolution, and then actually constructed the goblet so they could see, and touch, the results.

Students were asked to design a drinking glass or vase as a solid of revolution satisfying certain restrictions on the liquid capacity, volume of glass, thickness, and location of the center of mass. The students used Maple and the integration techniques they learned in Calculus 2 to define the mathematical expression whose volume of revolution met the requirements. They then graphed both the 2-D curve and the 3-D volume of revolution using Maple's extensive plotting facilities. Once they were satisfied with both the mathematics and aesthetics of their solutions, they exported the 3-D graph from Maple into a file format understood by the 3-D printer, and printed out their object.

"The students were absolutely thrilled to learn that they would be able to actually build the goblets they had designed in Maple," said Dr. Yasskin. "Maple has always been helpful in developing the students' mathematical intuition in general, and the 3-D visualizations in Maple are extremely valuable when it comes to learning about topics like solids of revolution. But Maple lets us go even further, taking that extra step from a virtual representation to a solid object and making a traditionally difficult topic much more understandable for the students."

Dr. Yasskin is also involved in other education projects that use Maple in innovative ways. He is the founder and director of the Summer Educational Enrichment in Math (SEE-Math), an outreach program from the Texas A&M University Math Department that offers enrichment opportunities to middle school students. Each summer, talented students entering grades 6, 7, and 8 spend two weeks exploring mathematical ideas from algebra, geometry, graph theory, topology, and more. A popular activity in the course is computer animation, where students use Maple's visualization tools and programming language to create their own animated movies, such as growing flowers, sliding penguins, and spaceship battles. In the process, the students learn and use new mathematical skills and practise thinking algorithmically. Maplesoft supports SEE-Math every year by donating Maple licenses as prizes for the best animations.

For more information on using Maple together with 3-D printers, read the Maple Tips and Techniques article.

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Highlights

• Mathematics Professor Dr. Philip Yasskin combined Maple with 3D printing to teach his Honors Calculus 2 class about solids of revolution.
• Students completed a project in which they used Maple to design goblets as solids of revolution, and then actually constructed the goblet so they could see, and touch, the results.
• Students graphed the 2-D curve and 3-D volume of revolution using Maple's plotting features, and ultimately exported the 3-D graph from Maple to print out their object.