The Napkin Ring Problem

youmagine

This model was crafted for week 7 of the Ultimaker design engine challenge. The challenge prompt is: Challenge Prompt #1 - "Eureka!" Design an object that showcases the elegance of math. The two parameter prompts are: Parameter Prompt #1 - Intricate and Parameter Prompt #2 - Exclusive. There's also a gameplay prompt - Reverse! Do the opposite of your selected parameter. I opted to reverse the intricate parameter prompt to be straightforward. The challenge is to create an object that reveals the beauty in math. To me, the beauty in math stems from its patterns and connections. Many examples of repeating patterns and relationships can be found throughout various areas of math, but one that captivates my interest 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 they are of equal heights, their volumes will be identical. This relationship signifies that if you had a cored out golf ball with a height of 5 cm and you hollowed the earth so its height was also 5 cm, they would have the same volume. That's truly mind-boggling to me. The parameter prompt #1 - Intricate, switched to straightforward, is met by the nature of this phenomenon in that simple shapes possess very interesting relationships. The parameter prompt #2 - Exclusive is fulfilled by this design being intended as an addition to someone's personal collection of unique items, making it a great conversation starter.