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  2. List of trigonometric identities - Wikipedia

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

    These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.

  3. Parallel curve - Wikipedia

    en.wikipedia.org/wiki/Parallel_curve

    In computer-aided design the preferred term for a parallel curve is offset curve. [ 2 ] [ 3 ] [ 4 ] (In other geometric contexts, the term offset can also refer to translation . [ 5 ] ) Offset curves are important, for example, in numerically controlled machining , where they describe, for example, the shape of the cut made by a round cutting ...

  4. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    In Euclidean geometry, the two acute angles in a right triangle are complementary because the sum of internal angles of a triangle is 180 degrees, and the right angle accounts for 90 degrees. The adjective complementary is from the Latin complementum , associated with the verb complere , "to fill up".

  5. Intersection (set theory) - Wikipedia

    en.wikipedia.org/wiki/Intersection_(set_theory)

    That is, for any sets ,, and , one has = () = () Inside a universe , one may define the complement of to be the set of all elements of not in . Furthermore, the intersection of A {\displaystyle A} and B {\displaystyle B} may be written as the complement of the union of their complements, derived easily from De Morgan's laws : A ∩ B = ( A c ...

  6. Law of sines - Wikipedia

    en.wikipedia.org/wiki/Law_of_sines

    In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law, ⁡ = ⁡ = ⁡ =, where a, b, and c are the lengths of the sides of a triangle, and α, β, and γ are the opposite angles (see figure 2), while R is the radius of the triangle's circumcircle.

  7. Midpoint - Wikipedia

    en.wikipedia.org/wiki/Midpoint

    Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction.The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the ...

  8. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles.

  9. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    This is a list of formulas encountered in Riemannian geometry. Einstein notation is used throughout this article. This article uses the "analyst's" sign convention for Laplacians, except when noted otherwise.

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