Angle


Read here about the types of mathematical angles that are generally significant when specifying, measuring or analyzing tensegrity structures, and some speculation about the conventional idea of the angle and its specific application in tensegrity structural comprehension.


Overview

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other. Where there is no possibility of confusion, the term "angle" is used interchangeably for both the geometric configuration itself and for its angular magnitude (which is simply a numerical quantity).

Angle Types


Read here about types of angles commonly encountered in tensegrity analysis.

Axial Angle


When a system is spherical the axial angles are at the base of an isosceles triangle whose apex is the central angle subtended by a strut.

If the system is nonspherical, we need, in addition to the stut's chord factor, the radii at its two ends.

Face Angle


This is the traditional angle taught in high school trigonometry, being the angles defined by the polygon as if it is a plane.

Dihedral Angle


A dihedral or torsion angle is the angle between two planes.


Mathworld, http://mathworld.wolfram.com/DihedralAngle.html
Wikipedia articles, dihedral angle,



Dip Angle



A form of a dihedral angle, the dip angle is formed when on a spherical tensegrity structure, where the spherical contour dips inward, incising a polyhedron with a re-entrant angle.

References

Hugh Kenner's chapter on Angles in Geodesic Math and how To use It

Portal To Mathematics
A series on mathematical methods.
Angle, Assur Truss, Cylindrical coordinates, Distance Geometry, Finite Element Method, Graph, Skew, Twist Angle
People: Burkhardt, Connelly, Kenner, Hart, Whiteley