Ultimaker uses functional, analytical and tracking cookies. Tracking cookies enhance your experience on our website and may also collect your personal data outside of Ultimaker websites. If you agree with the use of tracking cookies, click “I agree, continue browsing”. You can withdraw your consent at any time. If you do not consent with the use of tracking cookies, click “Refuse”. You can find more information about cookies on our Privacy and Cookie Policy page.
Integrating 3D printing and The Goblet Project
Christopher Hanusa
University
Mathematics
Pioneer Chris Hanusa shares one way he integrated 3D printing into his Integral Calculus class.
In Fall 2017, I volunteered to teach Integral Calculus because I wanted to integrate 3D printing into its curriculum. Today I will share with you how I worked "The Goblet Project" into my calculus curriculum.
Later in the session, there were two successive talks on The Goblet Project, by Brenda Edmonds, Cathleen O'Neil, and Rob Grondahl, and by Scott Dunn, Douglas Meade, and Philip Yasskin. The goal of this project is to make tangible the concept of solids of revolution.
Solids of revolution
A solid of revolution is a three-dimensional object formed by taking a two-dimensional region in the plane, and choosing to rotate it around an axis into a three-dimensional object. A common method for teaching this concept involves drawing representations of the 3D objects on a blackboard, hoping that the students are able to understand their intricacies.
The key idea involved in The Goblet Project is that when you rotate a solid that looks like
The students were tasked with designing a goblet that satisfies the following criteria:
The goblet must be a solid of revolution created by revolving a piecewise-defined function.
The goblet must hold 150–200 cm3 (cubic centimeters) of liquid.
The height of the goblet must be no more than 20 cm.
The stem thickness must be at least 0.8 cm at its thinnest point.
The base diameter of the goblet must be at least 1/3 of the height of the goblet, so that it does not fall over.
In addition to designing a theoretical goblet satisfying the requirements, I required that the students create a virtual 3D model of their goblet and send it to me as an STL file. This allowed me to print the digital representation of the goblet on a 3D Printer. I also asked the students to write a two-page discussion explaining their learning process and verifying that their goblet satisfied the project specifications.
Since everyone is used to thinking of graphs of functions of x, the goblets are actually formed lying on their sides, rotating functions of x around the x-axis. The Mathematica file first teaches the students how to use the Plot command to display the pieces of their bounding curves:
This gives the following visualization:
Then the file helps the students to define the piecewise-defined functions for the outer boundary and the inner boundary using the Piecewise command:
I then provided the students with the code that makes the polygonal faces of the goblet based on these piecewise-defined functions and certain parameters that help to make the surface smoother or coarser. The final version looks like this:
Then the most magical part of using Mathematica is that this virtual goblet can be 3D printed by simply exporting to STL format:
For my two classes with 40–50 students by this point, I needed to print out 17 different goblets. I enlisted two students to help keep the printing process going. They helped remove goblets that finished and restart the printers with new models.
To print the 17 goblets took a whole week of constant printing on three machines since there were the standard 3D printing issues along the way. Sometimes the filament ran out, sometimes the print broke because of a thin stem, sometimes the model had too much overhang to be able to print correctly which meant certain filaments didn't work.
It's showtime!
Once the goblets were all printed, it was time for the most satisfying part of the project—the reveal! I bought all the goblets to class and the students got to hold their goblets for the first time.
My favorite part about class projects is how diverse the final results always are. I am lucky to be teaching such amazing students who work hard, take ownership of their work, and thrive when given high expectations, which they always exceed.
I asked for some feedback from the students about the project. They had the following comments:
"It's amazing to see your goblet come alive through the art of 3D printing."
"I got to apply the math I learned."
"I finally had a reason to learn how to calculate volume."
"This project helps to visualize the disk and washer method."
"I had never used Mathematica before; working in groups made it possible."
"This project opened up a new passion for 3D printing."
"Cool!"
I asked the students if given the chance, would they want to do the project again. It was an overwhelming YES! Furthermore, most students said that the difficulty was just right. It was not overly simple, but it did require problem solving and applying the math that they had just learned.
The next time I teach Integral Calculus, I will work to use this module again. But I would do a few things differently. I would change the height to 17cm because that's the maximum height of the 3D printer! I would require that the minimal diameter of the stem be 1.5cm so that the prints won’t break. I would also require that there be no vertical tangents to the piecewise-defined curves because that is where the 3D printer had issues with printing. I would also want to give students a choice of colors for their final prints. I definitely will want to have student helpers again, because they made the printing process much less stressful on my part.
Summary
Why use The Goblet Project in your own classes? The Goblet Project involves
Groupwork: Students must work in teams of two or three
Problem solving: Students are given constraints that restricted the possible solutions and the students needed to work together to ensure that the criteria were satisfied
Creativity: Most teams wanted to create a goblet that was unique and matched an aesthetic that they shared
Functional visualization: In order for their goblet to match their ideal, teams needed to determine which mathematical functions would lead to the shapes they desired. This meant a deeper understanding of the shape and properties of functions. They also earned a deeper understanding of piecewise-defined functions
Solving equations: Goblets were formed by piecing together different equations. In order for the pieces to be assembled with no gaps, the teams would need to find where two adjacent graphs intersect, which required (gasp!) solving equations
Computer programming and design: The students learned the basics of the computational software Mathematica, and programmed the computer to create the final 3D model
3D printing: The students learned the principles of 3D printing / additive manufacturing
Enthusiasm: Students were extremely engaged — this project stimulated interest and enthusiasm in mathematics
Feel free to incorporate The Goblet Project into your own classes.
Christopher Hanusa is a mathematician, mathematics educator, and mathematical artist. To learn more about his teaching and research, visit his Queens College website; to learn more about his portfolio of mathematical art and jewelry, visit Hanusa Design.
Naturalis Biodiversity Center: Prehistoric prints, cutting-edge technology
Naturalis Biodiversity Center, the Netherlands’ national natural history museum, is using 3D printing to create both partial and full dinosaur skeletons for public display.
History
Informal learning
Feel the Action: Learn about how a college is changing lives in ways we can touch!
A 3D printing club emerges at College of the Dessert to help make ideas accessible to all students
Special education
Technology
How the tools we use influence the designs we make
Michael Delaney writes about his iterative process of integrating electronics and 3D printing in his programmable quadcopter project.
Informal learning
Technology
Bringing 3D printing to the Metropolitan Museum of Art
Part of the mission from Ultimaker North America's Community team is to help educators get up and running with 3D printing and to help them find meaningful ways to integrate the technology into their curriculum while celebrating their successes. When we w
Secondary education
History
3D printing as part of the Smithsonian Learning Lab
Pioneer Christopher Sweeney shares the work he did with 3D printing and the Smithsonian Learning Lab to create collections of educational resources, organized and structured for teaching and learning.
Informal learning
Art
Harvard calculus courses use 3D printed models to engage students
What is the best way to teach concepts like surface area and volume relating to mathematical objects in a three-dimensional world? The curricular design team at Harvard University thinks the...
University
Mathematics
3D Design in Mathematica: Tea Light Holders
If it’s happening in Ultimaker’s world, you can find out about it here. 3D printing stories about inspiring moments, original 3D printed projects and much much more.
Informal learning
Mathematics
Code your 3D designs with Tinkercad’s new Codeblocks app
Tinkercad released Codeblocks last June, and now that it's out of Beta, Pioneer Rob Morrill tells us how he uses it.
Informal learning
Technology
Modifying an STL with Tinkercad
When Ultimaker Pioneer Alex Larson contacted me about the Ultibot-D project, I was super excited. As a teacher and parent, I am a huge cheerleader for risk. I printed the base models at ⅕ scale and gave it to my students to explore
Primary education
Technology
Math Camp: Having fun doing stuff
Pioneer Dr Toni Szymanski writes about summer fun at camp with 4th and 5th graders, math, and 3D printing.
Primary education
Mathematics
GlitchCraft
Guest blogger Astrida Valigorsky writes about combining the old and the new at Timothy Belliveau's GlitchCraft class where students combined 3D printing and glass blowing.
Informal learning
Technology
Using Basecamp to manage your classroom/makerspace projects and print queue
Pioneer Andrew Woodbridge uses Basecamp to organize his students' projects, and he explains how you can too.
Secondary education
Technology
A unique 3D printing collaboration between mathematics and chemistry faculty
Passing it on. After integrating 3D printing into her own math courses, Kristen Schreck helps spread 3D printing across disciplines at Saint Xavier University.
University
Science
Living world monuments assignment
Pioneer Joanne Barrett shares about a middle school project that combines 3D printing, Augmented Reality, History, and Art.
Secondary education
History
My reintroduction to Netfabb
A recent NetFabb workshop convinced the writer that they can't live without this application. See why it's time to take another look at Netfabb.
Secondary education
Technology
Wrench Engineering
Inspired by NASA printed in space wrench, Pioneer Rob Morrill gave his fifth graders a design challenge to design their own real-world tool.
Primary education
Engineering
Integrating 3D printing and The Goblet Project
Pioneer Chris Hanusa shares one way he integrated 3D printing into his Integral Calculus class
University
Mathematics
3D printers in the public library: Finland ahead of the curve
US Professor Joshua Pearce, sponsored by Fulbright Finland for Research, shares his first impressions of Finnish libraries.
Informal learning
Technology
Lessons in letting go - releasing student energy speeds creation and use of our art and innovation lab
Pioneer John Nordell enlisted his students to put the Art and Innovation Lab together. The result was one of the best experiences he has had as an educator.
University
Technology
Teacher training for 3D printing
Pioneer Dr. Toni Szymanski thought that 3D printing could engage students in math classes. To test this out, she had to learn all about 3D printing first.
Secondary education
Mathematics
Digital fabrication informs ceramics decorative process
Pioneer Young Kim blends his classical arts background with digital fabrication to create a ceramic project that incorporates 3D printing.
Secondary education
Art
Modeling rocks at iCREATE
iCREATE's Tiffany Huang shared an iCREATE success story about Jackie Zheng.
Secondary education
Science
Elementary-College Engineering Design partnership
Pioneer Matthew Wigdahl writes about how his fifth graders and local undergraduate engineering students learn from each other.
Primary education
Engineering
Introducing Ultimaker’s Core Lessons Set for STEAM Educators
Designed by the Ultimaker North America Community Team, our new Core Lessons: STEAM Set is a resource for educators who need inspiration and ideas when they bring 3D printing into their classrooms.
Primary education
Technology
Empower one MakerGirl, empower the world
how the group traveled 10,000 miles around the country to help bring 3D printing workshops to over 1,000 young girls. In this week's post we catch up with the organization that is still working to create a new generation of confident, creative women leade
Primary education
Technology
Building a mobile maker space: part 2—up and rolling
So what exactly does a Mobile MakerSpace look like? That's the question I had to ask myself once I began the project of bringing 3D printing technology to virtual students. When we started this project, we knew we needed something that would be easy to
Secondary education
Technology
Building a mobile makerspace: part 1— getting started
Pioneer Wendy Aracich is putting together and implementing a mobile MakerSpace for her virtual school of 4000 students spread across the state of Georgia.
Secondary education
Technology
Tactile Problem/Solution Bank Community Project
3D modeling and printing should be accessible of every educator so that they may offer their students tactile means to understand spatial concepts.
Secondary education
Languages
Design Engine community project
We want to challenge educators and students to help evolve the Design Engine game. We want to see how you're using or modifying the game with your students, and we want to incorporate your ideas into the next edition.
Informal learning
Technology
Upcycling community project
Upcycling challenges students and educators to use their creativity and 3D printing skills to breathe new life into a few familiar objects.
Informal learning
Technology
Construct3D to Kamehameha Ed Tech Conference
Last year Pioneer Greg Kent traveled from Hawaii to North Carolina to attend Construct3D 2017. We thought we'd share his reflections with you now since we recently announced Construct3D 2018
Secondary education
Technology
Ocean Plastic Community Project
The Ultimaker Community Team will be launching a series of interdisciplinary projects over the next few months that challenge students to research, explore, design, and 3D print. Ocean Plastic is the first project of this series.
Secondary education
Geography
3D printed fractals at JMU 3SPACE
Pioneer Professor Laura Taalman, (a.k.a. mathgrrl), reviews a multi-week study of fractals by general education math students in the JMU 3D printing classroom.
University
Mathematics
Using drones and 3D printing to develop design thinking during a summer robotics camp
Pioneer Yuriy Drubinskiy writes about his experience leading a summer program and how creating drones with 3D printing brings form, structure, and design together.
Secondary education
Technology
Introducing the Ultimaker Design Engine Starter Pack
Presenting the Ultimaker Design Engine Starter Pack: a game created to provoke, inspire, and entertain students, educators, 3D designers, artists, and engineers of all experience levels!
Informal learning
Technology
Davidson Desktop Doohickeys: Puzzle cubes
Pioneer Adam Davidson writes about a project in his curriculum that is a rite of passage for his high school's engineering program students. He explains at how it started and what caused it to change
Secondary education
Engineering
3D printing with UMaine Bioengineering students
If it’s happening in Ultimaker’s world, you can find out about it here. 3D printing stories about inspiring moments, original 3D printed projects and much much more.
University
Science
3D printing, Arduino, and Star Wars: A guide to K-12 STEAM engagement
If it’s happening in Ultimaker’s world, you can find out about it here. 3D printing stories about inspiring moments, original 3D printed projects and much much more.
Secondary education
Technology
3D printable molecular models
Tandy Grubbs, Professor of Chemistry, writes about how chemistry students at Stetson University are taking advantage of 3D printing to better visualize the molecular world.
University
Science
Nautilus cam ball launcher
Design process is about discovery through iteration. Pioneer Brad Whitehead describes how his FTC robotics team learned this while working on a unique ball launcher.
Special education
Technology
Animal Adaptations
If it’s happening in Ultimaker’s world, you can find out about it here. 3D printing stories about inspiring moments, original 3D printed projects and much much more.
Primary education
Technology
3D water rockets
Pioneer Tim Cooper explains what to do with a First Lego League team in the off season when they love rockets and 3D printing.
Primary education
Science
Three reasons for open source tech in your 3D printing classroom
Pioneer Joshua Pearce explains why educators should consider using free and open source options in and out of the 3D printing classroom.
University
Technology
Our 3D printing journey in Multivariable Calculus
Here’s a story of the next generation of 3D printing pioneers exploring the 3D printing technology in Multivariable Calculus with the Ultimaker 2+.
University
Mathematics
#1 reason to love math: 3D printed puzzles
Pioneer Andreas Kaiser writes about the power of puzzles in the classroom and how recreating or designing puzzles is a perfect fit for his engineering students.
Secondary education
Mathematics
Thinking about the environment
The learning curve associated with 3D printing can produce a lot of 3D printed waste. It's time to start exploring and thinking about more sustainable options.
Informal learning
Geography
Why I use 3D printing in the classroom (and why you should too!)
While 3D printing is not new to designers, engineers and other professionals in need of rapid prototyping tools, it is still a new and exciting technology for our students. Pioneer Grace Bennett shares why teachers should get started with 3D printing.
Secondary education
Technology
3D printing artifacts from the Penn Museum
The chance to hold a 3D printed historical artifact in our hands is one of the greatest ways to boost students' engagement with science, engineering, and culture. Learn how challenging and exciting it can really be.
Secondary education
History
Managing an open 3D printing lab
What’s it like to be a student administrator for a 3D printing lab space? What kind of knowledge and experiences could you offer to students at your own school by hiring them for such position?
