1 / 14

3D Printing of Spherical Harmonic Manipulatives for the Classroom

Delve into the realm of 3D printing with a focus on spherical harmonic manipulatives for educational purposes. Discover the evolution of 3D printing technologies, their applications, and the potential for innovative classroom resources. Learn about the intricate world of Spherical Harmonics and their visualization using 3D objects. Explore the process of creating, printing, and utilizing these manipulatives in Quantum Mechanics and Atomic Physics studies. Uncover the possibilities for incorporating 3D mathematical abstractions into teaching and experimentation. View diagrams and resources at the provided website for further insights.

brosh
Download Presentation

3D Printing of Spherical Harmonic Manipulatives for the Classroom

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 3D Printing of Spherical Harmonic Manipulatives for the Classroom Josh Grossman Abigail Taylor ‘13

  2. 3D printing • a.k.a. additive manufacturing build up material • Types: • Extrusion • Binding granular material • Lamination • Light polymerization computer file (STL) 3D object

  3. 3D printing • Initiated in 1980’s • Research → industry→ DIY • Exponential price drop • Recently, rapid progress in capability • materials, resolution, speed, … • Rapidly expanding market • Used for prototyping and distributed manufacturing • Compare: home/office publishing (2D printing) • with resources of Internet

  4. Printer #1: MakerBot Replicator • Extrusion: fused deposition modeling (FDM) • In-house; inexpensive Thanks to Alan Jamieson, SMCM Comp Science

  5. Printer #2: Shapeways service • Bound granular material: selective laser sintering (SLS) • Other materials & methods available • Upload file, make payment, receive objects in mail • Better resolution than MakerBot Replicator • Much higher marginal cost per item, but don’t have to buy printer • Marketplace uploading and purchasing designs • SMCM MakerBot printer broke during project

  6. Example project:manipulatives of spherical harmonics

  7. Spherical Harmonics • Angular solutions to Laplace’s equation • Specified by l, m • l = 0, 1, 2, … and m = -l, …, l • Associated Legendre polynomials • Legendre polynomials

  8. Spherical Harmonics • Often initially confusing to students • Geometric properties not immediately evident

  9. Spherical Harmonics

  10. Process Equations Export["00441.STL", RegionPlot3D[315*Abs[SphericalHarmonicY[0,0,ArcCos[z/(x^2+y^2+z^2)^(1/2)],ArcTan[y/x]]^2]<(x^2+y^2+z^2)^(1/2)<315*Abs[SphericalHarmonicY[0,0,ArcCos[z/(x^2+y^2+z^2)^(1/2)],ArcTan[y/x]]^2]+1.1,{x,-45,45},{y,-45,45},{z,-45,45},PlotPoints->150]] Mathematica STL file Additional processing (optional) e.g. ReplicatorG for MakerBot Software converts for printing Finishing (optional) Print

  11. MakerBot models • Honeycomb for solid interiors • Overhangs problematic → print ½’s or ¼’s, then glue • Zero thickness at origin → • Individual plastic strands apparent → sand and paint ~$1 each

  12. Shapeways models • Add thickness $15-$45 each

  13. Uses • Spherical harmonic manipulatives used in Quantum Mechanics class and Atomic Physics study group • Illustrated geometric features • Prompted student discussion

  14. What’s next? • Models of other 3D mathematical abstractions • PvT phase surfaces for Thermodynamics classes, … • Real objects for experiments • Gears, wheels, moment of inertia test objects, … What would you do? diagram from Hyperphysics http://faculty.smcm.edu/jmgrossman/research/ed/3Dprinting.html Fluid filters by user sideritson Thingiverse By user ngoodger on Thingiverse

More Related