Hi Fellows,
As promised … here is the more challenging fuzzle – The Fuzzle_B.
It is a step evolution of the previous one:
https://forums.autodesk.com/t5/fusion-design-validate-document/the-fuzzle/td-p/12732984
Although the theme is very similar, the complexity of the problem is revolutionary higher. In the previous fuzzle post, I joked about the difficulty of entry into MIT and Yale UVs. I am not entirely sure which one would be more exigent; perhaps we are comparing here an in-the-shell-macadamia nut with the M&M button, respectively. Nevertheless, for the sake of sweetening the exercise, I will acknowledge the latter here.
The problem is as follows:
- Devise formulas defining i_th circle tangential to tangential circles inscribed on two vectors of angle 2α and the vector itself.
- The definition should include separate expressions for their radii and coordinate positions.
- The form of the formulas should be as compact and mathematically esthetic as possible.
- The circles to be solved are depicted in red in the following picture.
I will not rush to present the solution. I will also not reveal “how to solve” it … because it would hinder self-development and promote the launguorness of many … not to mention … feed AI Monster.
Notwithstanding … any fast response …. from the field Wizards … will be Very Welcome.
The result of the first ten radii - l=100, α=30°. (all digits but the last are significant)
0, 4.465819873852045
1, 1.4886066246173482
2, 0.49620220820578287
3, 0.1654007360685943
4, 0.05513357868953144
5, 0.018377859563177147
6, 0.006125953187725717
7, 0.0020419843959085726
8, 0.0006806614653028576
9, 0.00022688715510095256
Regards
MichaelT
