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2. Farey sequence - Wikipedia

   en.wikipedia.org/wiki/Farey_sequence

   Two Ford circles for different fractions are either disjoint or they are tangent to one another—two Ford circles never intersect. 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 ...

3. Continued fraction - Wikipedia

   en.wikipedia.org/wiki/Continued_fraction

   Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...

4. Fraction - Wikipedia

   en.wikipedia.org/wiki/Fraction

   A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or ⁠ ⁠, where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include ⁠ 1 2 ⁠, − ⁠ 8 5 ⁠, ⁠ −8 5 ⁠, and ⁠ 8 −5 ⁠.

5. Area of a circle - Wikipedia

   en.wikipedia.org/wiki/Area_of_a_circle

   Another proof that uses triangles considers the area enclosed by a circle to be made up of an infinite number of triangles (i.e. the triangles each have an angle of d𝜃 at the centre of the circle), each with an area of ⁠ 1 / 2 ⁠ · r 2 · d𝜃 (derived from the expression for the area of a triangle: ⁠ 1 / 2 ⁠ · a · b · sin𝜃 ...

6. Locus (mathematics) - Wikipedia

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

   In this example, P is 8 cm from l. In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions. [1][2] The set of the points that satisfy some property is often called the ...

7. Magic circle (mathematics) - Wikipedia

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

   Magic circles were invented by the Song dynasty (960–1279) Chinese mathematician Yang Hui (c. 1238–1298). It is the arrangement of natural numbers on circles where the sum of the numbers on each circle and the sum of numbers on diameters are identical. One of his magic circles was constructed from the natural numbers from 1 to 33 arranged ...