Definition:Trifolium

Trifolium

The trifolium is the instance of the rhodonea curve for $n = 3$:

Cosine Form

The trifolium can be defined by the polar equation in the form:

$r = a \cos 3 \theta$

where:

$0 \le \theta \le \pi$

Sine Form

The trifolium can be defined by the polar equation in the form:

$r = a \sin 3 \theta$

where:

$0 \le \theta \le \pi$

Also known as

The trifolium is also seen referred to as a three-leaved rose, or three-petalled rose.

Also see

• Definition:Quadrifolium

• Results about trifolium curves can be found here.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rose

• Weisstein, Eric W. "Trifolium." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Trifolium.html