Search results
Results from the WOW.Com Content Network
For a polyhedron, the defect at a vertex equals 2π minus the sum of all the angles at the vertex (all the faces at the vertex are included). If a polyhedron is convex, then the defect of each vertex is always positive. If the sum of the angles exceeds a full turn, as occurs in some vertices of many non-convex polyhedra, then the defect is ...
In biochemistry, a Ramachandran plot (also known as a Rama plot, a Ramachandran diagram or a [φ,ψ] plot), originally developed in 1963 by G. N. Ramachandran, C. Ramakrishnan, and V. Sasisekharan, [1] is a way to visualize energetically allowed regions for backbone dihedral angles ( also called as torsional angles , phi and psi angles ) ψ ...
The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles , see Trigonometric functions . Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine , or on the differential equation f ″ + f = 0 ...
The taper angle provided is called the Draft angle. The value of the draft angle depends upon the complexity of the pattern, the type of molding (hand molding or machine molding), height of the surface, etc. Draft provided on the casting is usually 1 to 3 degrees on external surfaces (5 to 8 internal surfaces). [7]
To find the angle of a rotation, once the axis of the rotation is known, select a vector v perpendicular to the axis. Then the angle of the rotation is the angle between v and Rv. A more direct method, however, is to simply calculate the trace: the sum of the diagonal elements of the rotation matrix.
This is a list of graphical methods with a mathematical basis. Included are diagram techniques, chart techniques, plot techniques, and other forms of visualization . There is also a list of computer graphics and descriptive geometry topics .
A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.
Dynkin diagrams have been drawn in a number of ways; [15] the convention followed here is common, with 180° angles on nodes of valence 2, 120° angles on the valence 3 node of D n, and 90°/90°/180° angles on the valence 3 node of E n, with multiplicity indicated by 1, 2, or 3 parallel edges, and root length indicated by drawing an arrow on ...