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  2. Angular defect - Wikipedia

    en.wikipedia.org/wiki/Angular_defect

    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 ...

  3. Caster angle - Wikipedia

    en.wikipedia.org/wiki/Caster_angle

    Front suspension of a race car ‍ — the caster angle is formed by the line between upper and lower ball joint An example of a chopper with a raked fork at an extreme caster angle The caster angle [ 1 ] or castor angle [ 2 ] is the angular displacement of the steering axis from the vertical axis of a steered wheel in a car , motorcycle ...

  4. Rake angle - Wikipedia

    en.wikipedia.org/wiki/Rake_angle

    Negative rake: A tool has a negative rake angle when the face of the cutting tool slopes away from the cutting edge at outer side. Positive rake angles generally: Make the tool more sharp and pointed. This reduces the strength of the tool, as the small included angle in the tip may cause it to chip away. Reduce cutting forces and power ...

  5. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides. 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.

  6. Non-Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Non-Euclidean_geometry

    In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.

  7. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    Angle trisection is the construction, using only a straightedge and a compass, of an angle that is one-third of a given arbitrary angle. This is impossible in the general case. For example, the angle 2 π /5 radians (72° = 360°/5) can be trisected, but the angle of π /3 radians (60°) cannot be trisected. [8]

  8. Mathematical visualization - Wikipedia

    en.wikipedia.org/wiki/Mathematical_visualization

    Mathematical visualization is used throughout mathematics, particularly in the fields of geometry and analysis. Notable examples include plane curves, space curves, polyhedra, ordinary differential equations, partial differential equations (particularly numerical solutions, as in fluid dynamics or minimal surfaces such as soap films), conformal ...

  9. Conformal map - Wikipedia

    en.wikipedia.org/wiki/Conformal_map

    In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths.. More formally, let and be open subsets of .A function : is called conformal (or angle-preserving) at a point if it preserves angles between directed curves through , as well as preserving orientation.

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