Cotes's spiral

In physics and in the mathematics of plane curves, Cotes's spiral (also written Cotes' spiral and Cotes spiral) is a family of spirals named after Roger Cotes. The shape of spirals in the family depends on the parameters, and the curve equation in polar coordinates can take one of five forms: A, k and ε are arbitrary real number constants. A determines the size, k determines the shape, and ε determines the angular position of the spiral. Cotes referred to the different forms as "cases". The curves above correspond to his cases 1, 5, 4, 2, 3 respectively.

Cotes's spiral

In physics and in the mathematics of plane curves, Cotes's spiral (also written Cotes' spiral and Cotes spiral) is a family of spirals named after Roger Cotes. The shape of spirals in the family depends on the parameters, and the curve equation in polar coordinates can take one of five forms: A, k and ε are arbitrary real number constants. A determines the size, k determines the shape, and ε determines the angular position of the spiral. Cotes referred to the different forms as "cases". The curves above correspond to his cases 1, 5, 4, 2, 3 respectively.