The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body. To describe such an orientation in 3-dimensional Euclidean space three parameters are required. They can be given in several ways, Euler angles being one of them; see charts on SO(3) for others. Euler angles are also used to describe the orientation of a frame of reference (typically, a coordinate system or basis) relative to another. They are typically denoted as α, β, γ, or φ, θ, ψ. Euler angles represent a sequence of three elemental rotations, i.e. rotations about the axes of a coordinate...

In elementary plane geometry, the power of a point is a real number h that reflects the relative distance of a given point from a given circle. Specifically, the power of a point P with respect to a circle O of radius r is defined by (Figure 1) h = s 2 − r 2 , {\displaystyle h=s^{2}-r^{2},} where s is the distance between P and the center O of the circle. By this definition, points inside the circle have negative...