Angle

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 http://en.wikipedia.org/wiki/Geometry geometry, an angle is the figure formed by two rays sharing a common endpoint, called the http://en.wikipedia.org/wiki/Vertex_%28geometry%29 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 http://en.wikipedia.org/wiki/Torsion_of_a_curve torsion angle is the http://en.wikipedia.org/wiki/Angle angle between two http://en.wikipedia.org/wiki/Plane_%28mathematics%29 planes.

Mathworld, http://mathworld.wolfram.com/DihedralAngle.html Wikipedia articles, http://en.wikipedia.org/wiki/Dihedral_angle%7Cdihedral 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 | http://books.google.com/books?id=arwzU5ZjE1YC&pg=PA118&lpg=PA118&dq=%22shows+that+when+the+system+is+spherical+the+axial+angles%22&source=bl&ots=xYLSlypbuX&sig=ZUJBFOJZcSIAWxBUkLBQewkdz8U&hl=en&ei=DGqMTLDcC4eCswbX1KD-AQ&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBIQ6AEwAA#v=onepage&q=%22shows%20that%20when%20the%20system%20is%20spherical%20the%20axial%20angles%22&f=false

Category:Portal To Mathematics | math | coordinates