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  2. Additional Mathematics - Wikipedia

    en.wikipedia.org/wiki/Additional_Mathematics

    Additional Mathematics is a qualification in mathematics, commonly taken by students in high-school (or GCSE exam takers in the United Kingdom). It features a range of problems set out in a different format and wider content to the standard Mathematics at the same level.

  3. Menelaus's theorem - Wikipedia

    en.wikipedia.org/wiki/Menelaus's_theorem

    A proof given by John Wellesley Russell uses Pasch's axiom to consider cases where a line does or does not meet a triangle. [4] First, the sign of the left-hand side will be negative since either all three of the ratios are negative, the case where the line DEF misses the triangle (see diagram), or one is negative and the other two are positive, the case where DEF crosses two sides of the ...

  4. Pythagorean triple - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_triple

    The corresponding parabola intersects the b-axis at right angles at b = 2n, and hence its reflection upon interchange of a and b intersects the a-axis at right angles at a = 2n, precisely where the parabola for n is reflected at the a-axis. (The same is of course true for a and b interchanged.)

  5. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    The supplement of an interior angle is called an exterior angle; that is, an interior angle and an exterior angle form a linear pair of angles. There are two exterior angles at each vertex of the polygon, each determined by extending one of the two sides of the polygon that meet at the vertex; these two angles are vertical and hence are equal.

  6. Internal and external angles - Wikipedia

    en.wikipedia.org/wiki/Internal_and_external_angles

    The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...

  7. Longitude by chronometer - Wikipedia

    en.wikipedia.org/wiki/Longitude_by_chronometer

    Time sight is a general method for determining longitude by celestial observations using a chronometer; these observations are reduced by solving the navigational triangle for meridian angle and require known values for altitude, latitude, and declination; the meridian angle is converted to local hour angle and compared with Greenwich hour angle.

  8. Simple harmonic motion - Wikipedia

    en.wikipedia.org/wiki/Simple_harmonic_motion

    Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the displacement (and even so, it is only a good approximation when the angle of the swing is small; see small-angle ...

  9. Relation (mathematics) - Wikipedia

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

    Transitive Closures of Binary Relations I (PDF). Prague: School of Mathematics – Physics Charles University. Archived from the original (PDF) on 2013-11-02. Halmos, Paul R. (1968). Naive Set Theory. Princeton: Nostrand. Kilp, Mati; Knauer, Ulrich; Mikhalev, Alexander (2000). Monoids, Acts and Categories: with Applications to Wreath Products ...