Isogonal trajectory
Encyclopedia
When a family of curve
s intersects another family at a specific constant angle
α, the first family is referred to as an isogonal
family of the second one, and in this case it is said that every family is an isogonal trajectory of the other. It is assumed that α is different from π/2; if α=π/2 both families are orthogonal. If the given family is described by the differential equation
then the isogonal family satisfies the differential equation
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...
s intersects another family at a specific constant angle
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...
α, the first family is referred to as an isogonal
Isogonal
Isogonal is a mathematical term which means "having similar angles". It occurs in several contexts:*Isogonal polygon, polyhedron, polytope or tiling.*Isogonal trajectory in curve theory.*Isogonal conjugate in triangle geometry....
family of the second one, and in this case it is said that every family is an isogonal trajectory of the other. It is assumed that α is different from π/2; if α=π/2 both families are orthogonal. If the given family is described by the differential equation
then the isogonal family satisfies the differential equation