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  2. Bhāskara I's sine approximation formula - Wikipedia

    en.wikipedia.org/wiki/Bhāskara_I's_sine...

    The formula is given in verses 17–19, chapter VII, Mahabhaskariya of Bhāskara I. A translation of the verses is given below: [3] (Now) I briefly state the rule (for finding the bhujaphala and the kotiphala, etc.) without making use of the Rsine-differences 225, etc. Subtract the degrees of a bhuja (or koti) from the degrees of a half circle (that is, 180 degrees).

  3. Law of continuity - Wikipedia

    en.wikipedia.org/wiki/Law_of_continuity

    The law of continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler.It is the principle that "whatever succeeds for the finite, also succeeds for the infinite". [1]

  4. Spherical trigonometry - Wikipedia

    en.wikipedia.org/wiki/Spherical_trigonometry

    Construct the great circle from A that is normal to the side BC at the point D. Use Napier's rules to solve the triangle ABD: use c and B to find the sides AD and BD and the angle ∠BAD. Then use Napier's rules to solve the triangle ACD: that is use AD and b to find the side DC and the angles C and ∠DAC. The angle A and side a follow by ...

  5. 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.

  6. cis (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Cis_(mathematics)

    cis is a mathematical notation defined by cis x = cos x + i sin x, [nb 1] where cos is the cosine function, i is the imaginary unit and sin is the sine function. x is the argument of the complex number (angle between line to point and x-axis in polar form).

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  8. Degree of a continuous mapping - Wikipedia

    en.wikipedia.org/wiki/Degree_of_a_continuous_mapping

    The degree of a map between general manifolds was first defined by Brouwer, [1] who showed that the degree is homotopy invariant and used it to prove the Brouwer fixed point theorem. Less general forms of the concept existed before Brouwer, such as the winding number and the Kronecker characteristic (or Kronecker integral ).

  9. Chord (geometry) - Wikipedia

    en.wikipedia.org/wiki/Chord_(geometry)

    In the 2nd century AD, Ptolemy compiled a more extensive table of chords in his book on astronomy, giving the value of the chord for angles ranging from ⁠ 1 / 2 ⁠ to 180 degrees by increments of ⁠ 1 / 2 ⁠ degree. Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the ...

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