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  2. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Millennium Prize Problems: 7: 6 [6] Clay Mathematics Institute: 2000 Simon problems: 15 < 12 [7] [8] Barry Simon: 2000 Unsolved Problems on Mathematics for the 21st Century [9] 22 – Jair Minoro Abe, Shotaro Tanaka: 2001 DARPA's math challenges [10] [11] 23 – DARPA: 2007 Erdős's problems [12] > 934: 617: Paul Erdős: Over six decades of ...

  3. Langley's Adventitious Angles - Wikipedia

    en.wikipedia.org/wiki/Langley's_Adventitious_Angles

    In 2015, an anonymous Japanese woman using the pen name "aerile re" published the first known method (the method of 3 circumcenters) to construct a proof in elementary geometry for a special class of adventitious quadrangles problem. [7] [8] [9] This work solves the first of the three unsolved problems listed by Rigby in his 1978 paper. [5]

  4. Elementary mathematics - Wikipedia

    en.wikipedia.org/wiki/Elementary_mathematics

    Two-dimensional geometry is a branch of mathematics concerned with questions of shape, size, and relative position of two-dimensional figures. Basic topics in elementary mathematics include polygons, circles, perimeter and areas.

  5. Angle trisection - Wikipedia

    en.wikipedia.org/wiki/Angle_trisection

    There are angles that are not constructible but are trisectible (despite the one-third angle itself being non-constructible). For example, ⁠ 3 π / 7 ⁠ is such an angle: five angles of measure ⁠ 3 π / 7 ⁠ combine to make an angle of measure ⁠ 15 π / 7 ⁠, which is a full circle plus the desired ⁠ π / 7 ⁠.

  6. Gradian - Wikipedia

    en.wikipedia.org/wiki/Gradian

    In trigonometry, the gradian – also known as the gon (from Ancient Greek γωνία (gōnía) ' angle '), grad, or grade [1] – is a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees.

  7. Thales's theorem - Wikipedia

    en.wikipedia.org/wiki/Thales's_theorem

    In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid 's Elements . [ 1 ]

  8. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A. The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively. See below under Mnemonics. Sine (denoted sin), defined as the ratio of the side opposite the angle to the hypotenuse.

  9. Regiomontanus' angle maximization problem - Wikipedia

    en.wikipedia.org/wiki/Regiomontanus'_angle...

    In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem [1] posed by the 15th-century German mathematician Johannes Müller [2] (also known as Regiomontanus). The problem is as follows: The two dots at eye level are possible locations of the viewer's eye. A painting hangs from a wall.

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