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  2. Farey sequence - Wikipedia

    en.wikipedia.org/wiki/Farey_sequence

    If 0 < ⁠ p / q ⁠ < 1 then the Ford circles that are tangent to C[p/q] are precisely the Ford circles for fractions that are neighbours of ⁠ p / q ⁠ in some Farey sequence. Thus C[2/5] is tangent to C[1/2], C[1/3], C[3/7], C[3/8], etc. Ford circles appear also in the Apollonian gasket (0,0,1,1). The picture below illustrates this ...

  3. Math circle - Wikipedia

    en.wikipedia.org/wiki/Math_circle

    A math circle is an extracurricular activity intended to enrich students' understanding of mathematics. The concept of math circle came into being in the erstwhile USSR and Bulgaria, around 1907, with the very successful mission to "discover future mathematicians and scientists and to train them from the earliest possible age". [1]

  4. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    6 1 2 1 1 −1 4 5 9. and would be written in modern notation as 6 ⁠ 1 / 4 ⁠, 1 ⁠ 1 / 5 ⁠, and 2 − ⁠ 1 / 9 ⁠ (i.e., 1 ⁠ 8 / 9 ⁠). The horizontal fraction bar is first attested in the work of Al-Hassār (fl. 1200), [35] a Muslim mathematician from Fez, Morocco, who specialized in Islamic inheritance jurisprudence.

  5. Circular segment - Wikipedia

    en.wikipedia.org/wiki/Circular_segment

    The arc length, from the familiar geometry of a circle, is s = θ R {\displaystyle s={\theta }R} The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of θ {\displaystyle \theta } ):

  6. Semicircle - Wikipedia

    en.wikipedia.org/wiki/Semicircle

    The Farey sequence of order n is the sequence of completely reduced fractions which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size. With a restricted definition, each Farey sequence starts with the value 0, denoted by the fraction ⁠ 0 / 1 ⁠ , and ends with the fraction ⁠ 1 / 1 ⁠ .

  7. Circle packing - Wikipedia

    en.wikipedia.org/wiki/Circle_packing

    A compact binary circle packing with the most similarly sized circles possible. [7] It is also the densest possible packing of discs with this size ratio (ratio of 0.6375559772 with packing fraction (area density) of 0.910683). [8] There are also a range of problems which permit the sizes of the circles to be non-uniform.

  8. Number Forms - Wikipedia

    en.wikipedia.org/wiki/Number_Forms

    2 ⁄ 3: 0.666... Vulgar Fraction Two Thirds 2154 8532 ⅕ 1 ⁄ 5: 0.2 Vulgar Fraction One Fifth 2155 8533 ⅖ 25: 0.4 Vulgar Fraction Two Fifths 2156 8534 ⅗ 3 ⁄ 5: 0.6 Vulgar Fraction Three Fifths 2157 8535 ⅘ 4 ⁄ 5: 0.8 Vulgar Fraction Four Fifths 2158 8536 ⅙ 1 ⁄ 6: 0.166... Vulgar Fraction One Sixth 2159 8537 ⅚ 5 ⁄ 6: 0 ...

  9. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    A circle bounds a region of the plane called a disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern

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