Monday, July 21, 2014

Machi and Garden Hose

From the post "And Some More Auntie Gravy", we have

\(a<0\),    \(|a|≥\cfrac{L}{\pi}\)    and

 \(|a|>b>0\)

for

\(r=a+bcos(\theta)\)

If we plot r=-5+2.5cos(x) on a polar plot we have,


The high curvature up top compared to the low flat line below suggest that this shape might lift.  Ever seen a garden hose rise when turned on?  Below shows the same curve with a circle superimposed.


Very nice machi shaped curve, indeed.