“Canned” MathematicsHow 3D Printing Can Support Mathematical Learning

Matt Roscoe

SEOMTC Summer ImmersionAthens, OH

June 7, 2016

1 3D Printing Opportunities

2 Mathematical Learning Supported by 3D PrintingWhat is the same? What is different?What is the question?What are the bigger questions?!#?

3 3D Printing: Share Your Inspiration

3D Printing Opportunities

Where can I make 3D prints?

University of Montana Mansfield Library PawprintPrinter: Makerbot Replicator Z18.http://www.lib.umt.edu/pawprint/3DPrinting

Missoula Public Library MakerspacePrinters: Makerbot Replicator 2, CubePro Triohttp://www.missoulapubliclibrary.org/makerspace

Many Other Locations Onlinehttp://3dprintingforbeginners.com/3d-printing-stores/

3D Printing Opportunities

Where can I make 3D prints?

University of Montana Mansfield Library PawprintPrinter: Makerbot Replicator Z18.http://www.lib.umt.edu/pawprint/3DPrinting

Missoula Public Library MakerspacePrinters: Makerbot Replicator 2, CubePro Triohttp://www.missoulapubliclibrary.org/makerspace

Many Other Locations Onlinehttp://3dprintingforbeginners.com/3d-printing-stores/

3D Printing Opportunities

3D Printing Opportunities

What does it cost?

$ 0.10 per gram plus $1.00 per model

3D Printing Opportunities

What does it cost?

$ 0.10 per gram plus $1.00 per model

3D Printing Opportunities

What will it print?

Any scalable .stl or .obj file in a multitude of colors.

3D Printing Opportunities

What will it print?

Any scalable .stl or .obj file in a multitude of colors.

3D Printing Opportunities

How do I create a scalable .stl or .obj file?

Software: Mathematica, Maple, MatLab, etc.Freeware: Google Sketchup, Tinkercad, andhttp://www.3ders.org/3d-software/3d-software-list.html

3D Printing Opportunities

How do I create a scalable .stl or .obj file?

Software: Mathematica, Maple, MatLab, etc.Freeware: Google Sketchup, Tinkercad, andhttp://www.3ders.org/3d-software/3d-software-list.html

3D Printing Opportunities

Are there any free .stl or .obj files already created?

https://www.thingiverse.com/

3D Printing Opportunities

Are there any free .stl or .obj files already created?

https://www.thingiverse.com/

3D Printing Opportunities

What objects should I print to support mathematical learning?

Objects that increase access to difficult mathematics topicsObjects that allow for direct inquiryObjects that are “low floor and high ceiling”Objects that are reusableObjects that currently unavailable from other outlets

3D Printing Opportunities

What objects should I print to support mathematical learning?

Objects that increase access to difficult mathematics topicsObjects that allow for direct inquiryObjects that are “low floor and high ceiling”Objects that are reusableObjects that currently unavailable from other outlets

Mathematical Learning Supported by 3D PrintingWhat is the same? What is different?

In front of you are some different cylinders. Investigate thecylinders and form some conjectures. What, do you think, is thesame for all cylinders? What, do you think, is different? What,do you think, is the question the set might be asking?

Mathematical Learning Supported by 3D PrintingWhat is the same? What is different?

Find the height, h, radius, r , surface area, S and volume, V , forthe right circular cylinder that your group has been given usingcareful measurement and calculation. Measure in centimeters.Add your results to the chart at the front of the room.

S “ 2πr2 ` 2πrh

V “ πr2h

Mathematical Learning Supported by 3D PrintingWhat is the question?

Which right circular cylinder with a fixed volume of 500 cubiccentimeters is the most efficient in terms of minimizing surfacearea? How might we take an algebraic approach? Recall:

S “ 2πr2 ` 2πrh

V “ πr2h

Mathematical Learning Supported by 3D PrintingWhat are the bigger questions?!#?

On the table in front of you, there are a number of cylinderseach containing a product of a different volume. Whatmathematical questions, related to those we have alreadyasked, could we ask of these cylinders?

3D Printing: Share Your Inspiration

In what other ways could 3D printing support mathematicallearning?