Sphere Surface Dissection, Baseball, Tennis Ball, Math

thingiverse

Printing Advice: Please use support and raft. Cutting a spherical surface into two equal pieces may seem impossible at first glance, but there are many ways to do it using the symmetries of a sphere. Scott Elliot has created an impressive OpenScad code that performs such a dissection. From a K-12 educational perspective, I'm curious about how to dissect a spherical surface in Fusion 360 or similar 3D CAD environment. It turns out that cutting a spherical surface is an appealing effort on Fusion 360 after some mathematical tweaking. We can start with a hollow sphere and a cube of equal dimensions. Centering the hollow sphere and the cube, we sketch a circle on a cube surface whose diameter needs to be such that if we make another circle of the same diameter on another orthogonal cube surface, the two circles are tangent to each other in space. A bit of algebra using old Pythagoras leads us to the conclusion: the circle diameter is the diameter of the outer sphere divided by sqrt(2). This itself is an interesting math project for middle and secondary students. We need only half of that circle plus two tangent lines for a "U" curve to split the sphere into two pieces. These two pieces have the same outer surface but are not exactly the same due to thickness. Take the half with even thickness, construct a plane along the edge curve, sketch a 45-degree right triangle, and then perform a sweep cut along the whole path around the opening. Now we have one half of the spherical surface with some thickness. It takes two to make a hollow ball. This should be an intermediate design project for students aged 6-16 with some guidance as presented above. Have fun and try to come up with another way to do it! References: 1. A Brief History of the Baseball, https://www.smithsonianmag.com/arts-culture/a-brief-history-of-the-baseball-3685086/ 2. Baseball, https://en.wikipedia.org/wiki/Baseball_(ball) 3. Elliot, Scott (2010). OpenScad code for spherical bisection, available at https://www.thingiverse.com/thing:3068/#files 4. Gardner Martin. (2001). The Colossal Book of Mathematics. New York, NY: W.W. Norton & Co.