Spherical geometry other geometric concepts are defined as in plane geometry, but with straight lines replaced by great circles. Thus, in spherical geometry, angles are defined between great circles, resulting in a spherical trigonometry that differs from ordinary trigonometry in many respects; for example, the sum of the interior angles of a triangle exceeds 180 degrees. Spherical geometry is "not" elliptic geometry, but is rather a "subset" of elliptic geometry. For example, it shares with that geometry the property that a line has no parallels through a given point. Contrast this with Euclidean geometry, in which a line has one parallel through
Vibrations of a circular membrane equation with zero boundary conditions, Due to the circular geometry of formula_1, it will be convenient to use cylindrical coordinates, formula_13 Then, the above equations are written as Here, formula_16 is a positive constant, which gives the speed at which transverse vibration waves propagate in the membrane. In terms of the physical parameters, the wave speed, c, is given by where formula_18, is the radial membrane resultant at the membrane boundary (formula_19), formula_20, is the membrane thickness, and formula_21 is the membrane density. If the membrane has uniform tension, the uniform tension force at a given radius, formula_22 may be