# Math Help - Using Polar coordinates for leaf design

1. ## Using Polar coordinates for leaf design

I am looking for a polar coordinate equation that would develop this leaf design.

I have come up with is r= 1 + sin(x) + sin(x)2 , where x = degrees in radians but, it does not give the pointy tail. Too circular
(and has a heart shape bump, but that's okay because most leaves have that heart shape).

Anyone have any clue as to what infinite expansion I could use to get that bend to the point? i.e. r= a0 + a1sin(x) + a2sin(x)2 + a3sin(x)3 + ......that could be thrown my way? I only need to degree 4 or 5 in sin(x) as a loose approximation to get the flavor.

Thanks!
Walter Poelzing - Math Teacher

2. ## Re: Using Polar coordinates for leaf design

Something like 3 - sqrt(abs(cos(t))) + sin(t)/2 + sin(t)^3 ?

Hope I'm not missing the point

3. ## Re: Using Polar coordinates for leaf design

Thanks. That is very creative with the absolute value function in the sin function. Now, I'm going to see if I can create a stronger point! -W

4. ## Re: Using Polar coordinates for leaf design

only "leaf" design I could find ...

Cannabis Curve -- from Wolfram MathWorld