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2. Farey sequence - Wikipedia

   en.wikipedia.org/wiki/Farey_sequence

   For every fraction ⁠ p / q ⁠ (in its lowest terms) there is a Ford circle C[⁠ p / q ⁠], which is the circle with radius 1/(2q 2) and centre at (⁠ p / q ⁠, ⁠ 1 / 2q 2 ⁠). 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 ...

3. Turn (angle) - Wikipedia

   en.wikipedia.org/wiki/Turn_(angle)

   degrees. 360°. gradians. 400 g. The turn (symbol tr or pla) is a unit of plane angle measurement that is the angular measure subtended by a complete circle at its center. It is equal to 2π radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) [1] or to one revolution (symbol rev or ...

4. Rhind Mathematical Papyrus - Wikipedia

   en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus

   Also bear in mind that the fraction 2/3 is the single exception, used in addition to integers, that Ahmes uses alongside all (positive) rational unit fractions to express Egyptian fractions. The 2/n table can be said to partially follow an algorithm (see problem 61B) for expressing 2/n as an Egyptian fraction of 2 terms, when n is composite.

5. Packing problems - Wikipedia

   en.wikipedia.org/wiki/Packing_problems

   The hexagonal packing of circles on a 2-dimensional Euclidean plane. These problems are mathematically distinct from the ideas in the circle packing theorem.The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere.

6. Ancient Egyptian mathematics - Wikipedia

   en.wikipedia.org/wiki/Ancient_Egyptian_mathematics

   An interesting feature of ancient Egyptian mathematics is the use of unit fractions. [7] The Egyptians used some special notation for fractions such as ⁠ 1 / 2 ⁠, ⁠ 1 / 3 ⁠ and ⁠ 2 / 3 ⁠ and in some texts for ⁠ 3 / 4 ⁠, but other fractions were all written as unit fractions of the form ⁠ 1 / n ⁠ or sums of such unit ...

7. Descartes' theorem - Wikipedia

   en.wikipedia.org/wiki/Descartes'_theorem

   In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who stated it in 1643.