Take two gears with 3:1 ratio and a handle of length 3 on the smaller gear. The end of the handle traces a circle and the corresponding point on the larger gear traces a trifolium. What do you think happens with other gear ratios? [Wiki bit.ly/2Sadb5o] #50FamousCurves
The trifolium belongs to the family of rose curves defined by the polar equation r=a·sin(kφ) associated with gear ratio k:1. If k is odd, there are k petals, but if k is even, you get 2k petals. Here is the case when k=2. #50FamousCurves
Table of rose curves r=sin(kφ) with k=n/d (gear ratio n:d) and n,d=1,2,...,7. #50FamousCurves
Fun fact: "Folium" is Latin for "leaf". So the name "trifolium" means "three leaves". #50FamousCurves
Tangents to the trifolium. #50FamousCurves
[Source: community.wolfram.com/groups/-/m/t/1…]
How to draw a trifolium?
1) Take two circles with 3:1 radius ratio.
2) Put a handle of length 2 on the smaller circle.
3) Roll the smaller circle around on the inside of the larger circle.
The end of the handle will trace a trifolium. #50FamousCurves
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