An Area Relationship of the Parabola and its Focal Circle | Steve Wait – December 28, 2020

Sectioning a conical surface with generator angle of 47.34508022773829+° yields a Latus Rectum bounded Parabola area equal to that of the Circle sectioned from the center of the Focal (Dandelin) Sphere. Pi is not requisite in determining this generator angle. Its value accomplished by creating a Parabola area equal that of its Focal Circle and placing it in correct geometric orientation forming the conic. Thus, Circle area may be found via its relationship with Parabola area. Subsequent simplification affirms with the value of pi.

(Latus Rectum length)(Focal length)(2/3)        = Area of Parabola

((8)((tan47.345+°)2)(r2))/3           = Area of Circle

         ((8)((1.0854+)2)(r2))/3          = Area of Circle

            ((8)(1.1780+)(r2))/3           = Area of Circle

  ((9.4247+)(r2))/3           = Area of Circle

(π)(r2)            = Area of Circle