page_title: Nephroid
section_title: Nephroid as caustic of one half of a circle
hierarchical_section_title: Nephroid / Nephroid as caustic of one half of a circle
caption_attribution_description: Français&#160;: Caustique dans un liquide
context_page_description: In geometry, a nephroid is a specific plane curve whose name means 'kidney-shaped'. Although the term nephroid was used to describe other curves, it was applied to the curve in this article by Proctor in 1878.
  A nephroid is an algebraic curve of degree 6. It can be generated by rolling a circle with radius on the outside of a fixed circle with radius. Hence, a nephroid is an epicycloid.
context_section_description: The considerations made in the previous section give a proof for the fact, that the caustic of one half of a circle is a nephroid.
  If in the plane parallel light rays meet a reflecting half of a circle (see diagram), then the reflected rays are tangent to a nephroid.
  proof
  The circle may have the origin as midpoint (as in the previous section) and its 
  radius is . The circle has the parametric representation 
  The tangent at the circle point  has normal vector  . The reflected ray has the normal vector (see diagram)  and containing circle point . Hence the reflected ray is part of the line with equation 
  which is tangent to the nephroid of the previous section at point 
   (see above).
caption: Nephroid caustic at bottom of tea cup
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