Fellow kendama slayers, I am currently a senior in high school and am taking an IB Math Analysis class, which is basically like a slight step above AP classes. I am required to write an IA (Internal Assessment) which is basically just a long essay about math which revolves around any topic I choose. I am trying to incorporate kendama and do something “mathy” with it. The only problem is that the math portion could only be carried so far, it would just be a simple problem and analysis which would give me very low scores. I had several ideas. Testing out different kendama sizes and shapes on different people to see their effect and determine the exact size and shape that would be perfect. Another would be changing string lengths on one kendama and having others try to get it on all cups and the spike to see what the best string size would be. Maybe something to do with the weights and whether lighter or heavier kendamas are better statistically. These were all just beginner ideas and while they may sound good, the math is not anywhere near the depth at which an IB class goes. If anybody could please give me some ideas to spark something that could be taken further that would be very much appreciated. Although no worries, I know that you guys just wanna land some banger tricks (and more power to you).

Mod Hat Engaged @Rutland Moved your thread to The Sesh for visibility. Sessions is usually for events etc. As for your project if you have access to a high speed camera maybe you could do an analysis of the swing and/or rotational speed of various weights of kendama combined with string lengths. Not a math guy but here are some physics related clips that might inspire you. Good luck with your project. This one might not be as obvious as how it would relate to kendama. If you watch a ken rotation for 1 turn airplane in particular you might see it. There are kind of two ways to have a ken rotate for that trick. 1. set it up to spin "flat" with one cup following the other like a circular saw blade's teeth follow one another around the center pivot of the blade (like the edge of a thrown frisbee rotates around its center point); 2. more like the tennis racket in this video.

Thank you so much! This means a lot. I do like the physics application and the rotations do seem like they have some potential.

No worries, glad to help. Did have another thought, Adam Savage made a kendama but IIRC made a mistake (IMO) on the tama. He only drilled it half way through which really messes up how it moves when it's pulled up, rotated, etc. Anyway you might see if you can get a tama without a hole and see what changes as the hole gets closer to the opposite end of the tama (like a traditional tama). e.g. How it the tama rotates for Furiken (Swing in) as the hole deepens.

This is probably a little basic for your project, but Austin Donovan had an interesting perspective on point strategy for KWC. It’s not complex but essentially he described a statistical advantage that one can gain from aiming for fewer, yet higher point value tricks vs more numerous lower difficulty tricks. However the time constraint is a very important variable to consider which leads one to examine the cost/benefit of max number of tricks compared to the lower probability of landing tricks of a higher point value. My guess is there is an exponential increase/decrease similar to Xsquared, but you may be able to complicate this further for your sake.