# Thread: create a 4-leaf clover by polar coordinates

1. ## create a 4-leaf clover by polar coordinates

hi,
what can be the polar equation whose graph is just like a 4-leaf clover as in the attachment?

2. Hello spring

Welcome to Math Help Forum!
Originally Posted by spring
hi,
what can be the polar equation whose graph is just like a 4-leaf clover as in the attachment?
I produced the attached graph in Excel, using the polar equation
$r = \sin2\theta + \tfrac14\sin6\theta$
Is that close enough to what you wanted?

3. cant be closer than this!
i thought there must be something addition of two "sin"s and their coefficients should be different from each other. this solution makes me happy...
thank you...

but i want to know how can you produce a polar coordinated graph in excel?

4. Hello spring
Originally Posted by spring
...but i want to know how can you produce a polar coordinated graph in excel?
I'm using a fairly old version of Excel. (I bought Office 2007 and tried to like it but hated it, so I reverted to my earlier 2000 version.)

1. Set up two columns of values: $\theta$ and $r=f(\theta)$. Use values of $\theta$ from $0$ to $2\pi$.

2. Create two further columns $x = r\cos\theta$ and $y = r\sin\theta$.

3. Use the XY (Scatter) graph-type using the $x$ and $y$ values, choosing the 'smoothed lines without markers' sub-type.

5. attached graph in St. Patrick green ...

6. hmm, got it!
excel is incredible sometimes.
i will try to produce the equation by skeeter.

by the way,
"work smart, not hard."
like it.

7. Originally Posted by skeeter
attached graph in St. Patrick green ...
Faith and begorrah! 'Tis a handsome colour. Yes, indeed!

8. ## Re: create a 4-leaf clover by polar coordinates

Hi there, first post, i'm in the middle of doing that very design but my clover isn't as tidy as yours, just wondering what i'm doing wrong.

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# full clover leaf graph

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