Prince Rupert's Cube visualization
Description
Prince Rupert's Cube is a mathematical problem from a few centuries ago. It claims that a cube with sides of length 1 can allow a slightly larger cube to pass through the space it encloses. You can find more information in these links: https://wiki2.org/en/Prince_Rupert%27s_cube+Newton https://geekhaus.com/math103_fall2017/2017/10/05/open-project-prince-ruperts-cube/ The optimal solution to the Prince Ruper's Cube is another cube with sides of length 1.0606601, which is the largest cube that can pass through a cube with sides of length 1. It passes through at an angle of 22.5 degrees, which is 1/16th of a full circle. My visualization of Prince Rupert's Cube is not the optimal solution due to the need to have small amounts of plastic still present to hold the outer part together in one piece. Other visualizations have used loops of plastic to hold the pieces together, such as the one linked above, but that solution is not the optimal solution because it uses an intersection angle of 45 degrees and a cube with sides of length 1.03. My version uses an angle of 23 degrees and requires a cube with sides of length 0.99 to allow for a working, 3D printable, real world visualization. This model consists of three parts: the outer and inner parts of the cube, which can be assembled to form a cube, and the solution, which is the cube that passes through the hole. PRINTING NOTES: ● These files are designed to be printed with sides of length 100mm (4 inch), but the models are 1mm in size, so you will need to scale them up for printing by 100x, which is 10000%. ● Scaling by a different amount may result in parts that cannot be assembled and do not work. ● The small size of the models also explains why they appear to have textured surfaces in Thingiverse, but they are in fact smooth. ● I've included the OpenSCAD file if you need to edit the models.
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