The Napkin Ring Problem

This model demonstrates the phenomenon known as the napkin ring problem.


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This idea was inspired by Michael Stevens of the YouTube channel Vsauce. Here is a link to the video on the napkin ring problem:


This model was created for week 7 of the Ultimaker design engine challenge. The challenge card is: Challenge card #1 - "Eureka!" Design an object that expresses the beauty of math. the two parameter cards are: Parameter Card #1 - Complex and Parameter Card #2 - Private. There was also a gameplay card - Reverse! β€” Do the opposite of your chosen parameter. I chose to reverse the complex parameter card to be simple.

The challenge was to create an object that shows the beauty in math. To me, the beauty in math comes from its patterns and relationships. There are many examples of repeating patterns and relationships in many different areas in math but one that I find extremely interesting is the napkin ring problem. The napkin ring problem states that if you have two spheres, one small and one large, and you cut a hole in each of them so that they are of equal heights, the volume of each will be equal. This relationship means that if you had a cored out golf ball with a height of 5 cm and you cored the earth so that its height was also 5 cm, they would have the same volume. That is mind blowing to me. The parameter card #1 - Complex, switched to simple, is met by the nature of this phenomenon in that they simple shapes that have a very interesting relationship. The parameter card #2 - Private is met by this design being intended to be an addition to someone's private collection of interesting things. This could make a great conversation piece.

Materials and methods

3D printer



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1283825be94c91c2ca648968f823b7c0?default=blank&size=40BLAKE_S published this design ago