Parker Glynn-Adey

Three-Dimensional Kaleidoscope

Posted in Math by pgadey on 2019/05/05

My highschool student, Lukas Boelling, made this three-dimensional icosahedral/dodecahedral kaleidoscope with his dad, @eric_boelling. Lukas based his models off this excellent paper: Alice through Looking Glass after Looking Glass: The Mathematics of Mirrors and Kaleidoscopes by Roe Goodman. Stay tuned for more models!

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Homework #5 Question 4

Posted in Math by pgadey on 2018/07/20

Consider a solid ball of radius R. Cut a cylindrical hole, through the center of the ball, such that the remaining body has height h. Call this the donut D(R,h). Use Cavalieri’s principle to calculate the volume of D(R,h). Calculate the volumes of D(25,6) and D(50,6).

donut

Several students have asked what D(R,h) looks like. Here are some pictures that I found to illustrate the concept. The donut D(R,h) is the region between the red sphere and blue cylinder. The golden balls below show various views of the donut. The donut should fit between the two planes z=h/2 and z=-h/2, so that it has total height h.

SphericalRingSolid_800napring2

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