The theorem for these shapes named after Descartes is used to generate the inner and outer Soddy ones.
The theorem for these shapes named after Descartes is used to generate the inner and outer Soddy ones. A family of these shapes forms the solution to the differential equation y prime equals negative x over y, and Apollonius demonstrated that this shape is formed by the locus of points k times as distant from one fixed point as they are from another. The osculating type is used to find the curvature of paths at a point, and in Ancient Greece many attempted the impossible problem of drawing a square with the same area as one. In polar coordinates, this is the graph of r equals one, whose coordinates are cosine of theta comma sine of theta and which is called the "unit" example of these figures. This is also generated by the equation x squared plus y squared equals r squared. Name these two-dimensional shapes with a fixed radius.
The theorem for these shapes named after Descartes is used to generate the inner and outer Soddy ones.
circles