Nephroid

The Nephroide ( from Ancient Greek ὁ νεφρός ho nephros "The Kidney ", according to their shape) is an algebraic curve 6th grade. It is to be described by the equation

The Nephroide formed by rolling of a circle with the radius on the outside of a circle with the radius. This is one of the Nephroide in the class of epicycloids and has the parametric representation

The shape of the curve resembles a kidney ( gr nephros ), with two opposing constrictions. Thus Nephroide at its widest point is twice as wide as at its narrowest. The area of ​​the Nephroide is. Their scope is. The evolute of Nephroide is again a Nephroide, but half the size and 1/4 shot.

Nephroide in daily life

When light strikes an infinitely distant light source, the envelope of light rays laterally on a concave, circular reflective surface, thus forming a part of a Nephroide. Sometimes she is therefore also called " Kaffeetassenkaustik " ( caustic = focal line). They can also watch on the road when the bare rim of a bicycle reflect the light on the floor: As the sunlight hits the cylinder surface of the bicycle rim parallel to an internal surface whose profile has the shape of a half Nephroide and when making easily inserted into the curve, together with the flat surface part of a Nephroide as intersection.