Definition:Rhodonea Curve
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Definition
A rhodonea curve is a curve defined by either one of the polar equations:
| \(\ds r\) | \(=\) | \(\ds a \cos n \theta\) | ||||||||||||
| \(\ds r\) | \(=\) | \(\ds a \sin n \theta\) |
It consists of a number of loops meeting at a central point.
Order
The number $n$ is the order of $R$.
Petal
Each of the loops of a rhodonea curve is referred to as a petal.
Also known as
A rhodonea curve is also known as:
- a rose (but this term is ambiguous)
- a rosette
- a rose of Grandi, for Guido Grandi who investigated it.
Also see
- Results about rhodonea curves can be found here.
Historical Note
The rhodonea curves were investigated between $1723$ and $1728$ by Guido Grandi.
Linguistic Note
The word rhodonea derives from the Ancient Greek word ῥόδον, meaning rose.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): rose
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): rose
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rose
- Weisstein, Eric W. "Rose." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Rose.html