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  2. Angular defect - Wikipedia

    en.wikipedia.org/wiki/Angular_defect

    Classically the defect arises in two contexts: in the Euclidean plane, angles about a point add up to 360°, while interior angles in a triangle add up to 180°. However, on a convex polyhedron , the angles of the faces meeting at a vertex add up to less than 360° (a defect), while the angles at some vertices of a nonconvex polyhedron may add ...

  3. Mnemonics in trigonometry - Wikipedia

    en.wikipedia.org/wiki/Mnemonics_in_trigonometry

    Quadrant 2 (angles from 90 to 180 degrees, or π/2 to π radians): ... CAST still goes counterclockwise but starts in quadrant 4 going through quadrants 4, 1, 2, then 3.

  4. Ackermann steering geometry - Wikipedia

    en.wikipedia.org/wiki/Ackermann_steering_geometry

    Ackermann geometry. The Ackermann steering geometry (also called Ackermann's steering trapezium) [1] is a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii.

  5. Caster angle - Wikipedia

    en.wikipedia.org/wiki/Caster_angle

    Arthur Krebs proposed placing the front axle of a car at a positive caster angle in his UK patent of 1896, entitled Improvements in mechanically propelled vehicles. In it he stated it was intended "To ensure stability of direction by means of a special arrangement of fore-carriage, that is to say, to re-establish automatically the parallelism of the two axles of the vehicle when there is no ...

  6. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    The trace of a rotation matrix is equal to the sum of its eigenvalues. For n = 2, a rotation by angle θ has trace 2 cos θ. For n = 3, a rotation around any axis by angle θ has trace 1 + 2 cos θ. For n = 4, and the trace is 2(cos θ + cos φ), which becomes 4 cos θ for an isoclinic rotation.

  7. Spherical trigonometry - Wikipedia

    en.wikipedia.org/wiki/Spherical_trigonometry

    Case 3: two sides and an opposite angle given (SSA). The sine rule gives C and then we have Case 7. There are either one or two solutions. Case 4: two angles and an included side given (ASA). The four-part cotangent formulae for sets (cBaC) and (BaCb) give c and b, then A follows from the sine rule. Case 5: two angles and an opposite side given ...

  8. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    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.

  9. Delaunay triangulation - Wikipedia

    en.wikipedia.org/wiki/Delaunay_triangulation

    In the plane (d = 2), if there are b vertices on the convex hull, then any triangulation of the points has at most 2n – 2 – b triangles, plus one exterior face (see Euler characteristic). If points are distributed according to a Poisson process in the plane with constant intensity, then each vertex has on average six surrounding triangles.