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In spherical trigonometry, the law of cosines and derived identities such as Napier's analogies have precise duals swapping central angles measuring the sides and dihedral angles at the vertices. In the infinitesimal limit, the law of cosines for sides reduces to the planar law of cosines and two of Napier's analogies reduce to Mollweide's ...
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle.
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 Euclidean geometry, the intersecting secants theorem or just secant theorem describes the relation of line segments created by two intersecting secants and the associated circle.
The high school exterior angle theorem (HSEAT) says that the size of an exterior angle at a vertex of a triangle equals the sum of the sizes of the interior angles at the other two vertices of the triangle (remote interior angles). So, in the picture, the size of angle ACD equals the size of angle ABC plus the size of angle CAB.
Rubio released a report detailing these same issues, which includes another example where a slide presentation for the Air Force Academy was titled, “Diversity & Inclusion: What it is, why we ...
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