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Rotated quadrifolium
Quadrifolium created with gears

The quadrifolium (also known as four-leaved clover[1]) is a type of rose curve with n=2. It has the polar equation:

with corresponding algebraic equation

Rotated by 45°, this becomes

with corresponding algebraic equation

In either form, it is a plane algebraic curve of genus zero.

The dual curve to the quadrifolium is

Dual quadrifolium

The area inside the curve is , which is exactly half of the area of the circumcircle of the quadrifolium. The length of the curve is about 9.6884.[2]

NotesEdit

  1. ^ C G Gibson, Elementary Geometry of Algebraic Curves, An Undergraduate Introduction, Cambridge University Press, Cambridge, 2001, ISBN 978-0-521-64641-3. Pages 92 and 93
  2. ^ Quadrifolium - from Wolfram MathWorld

ReferencesEdit

  • J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. p. 175. ISBN 0-486-60288-5.

External linksEdit