Three-Leaved Rose

Simple is beautiful. This universal principle is valid in mathematics and geometry too!

Equation for three-leaved-rose (trifolium) in polar coordinates is

r = a cos (3θ )


where “a” is a constant and the angle θ is measured from the x-axis.

If you want one of the lobes to lie on the negative x-axis the equation is

r = -a cos (3θ )


In general,

r = a cos (nθ)


r = a sin (nθ)

has n leaves if n is odd.


About Suresh Emre

I have worked as a physicist at the Fermi National Accelerator Laboratory and the Superconducting Super Collider Laboratory. I am a volunteer for the Renaissance Universal movement. My main goal is to inspire the reader to engage in Self-discovery and expansion of consciousness.
This entry was posted in geometry, tutorial and tagged , . Bookmark the permalink.