# create a 4-leaf clover by polar coordinates

• Mar 14th 2010, 04:17 AM
spring
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?
• Mar 14th 2010, 10:29 AM
Hello spring

Welcome to Math Help Forum!
Quote:

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?

• Mar 14th 2010, 11:21 AM
spring
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?
• Mar 14th 2010, 02:43 PM
Hello spring
Quote:

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.

• Mar 14th 2010, 03:07 PM
skeeter
attached graph in St. Patrick green ...
• Mar 14th 2010, 03:30 PM
spring
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. (Smirk)
• Mar 15th 2010, 01:07 AM