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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.

3. Mathematical beauty - Wikipedia

   en.wikipedia.org/wiki/Mathematical_beauty

   In a general Math Circle lesson, students use pattern finding, observation, and exploration to make their own mathematical discoveries. For example, mathematical beauty arises in a Math Circle activity on symmetry designed for 2nd and 3rd graders, where students create their own snowflakes by folding a square piece of paper and cutting out ...

4. Circular coloring - Wikipedia

   en.wikipedia.org/wiki/Circular_coloring

   In graph theory, circular coloring is a kind of coloring that may be viewed as a refinement of the usual graph coloring. The circular chromatic number of a graph , denoted can be given by any of the following definitions, all of which are equivalent (for finite graphs). is the infimum over all real numbers so that there exists a map from to a ...

5. Geometric series - Wikipedia

   en.wikipedia.org/wiki/Geometric_series

   Each of the purple squares has 1/4 of the area of the next larger square (1/2× 1/2 = 1/4, 1/4×1/4 = 1/16, etc.). The sum of the areas of the purple squares is one third of the area of the large square. Another geometric series (coefficient a = 4/9 and common ratio r = 1/9) shown as areas of purple squares.

6. Josephus problem - Wikipedia

   en.wikipedia.org/wiki/Josephus_problem

   Josephus problem. In computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. Such games are used to pick out a person from a group, e.g. eeny, meeny, miny, moe. A drawing for the Josephus problem sequence for 500 people and skipping value of 6.

7. Pie chart - Wikipedia

   en.wikipedia.org/wiki/Pie_chart

   Pie chart. Pie chart of populations of English native speakers. A pie chart (or a circle chart) is a circular statistical graphic which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area) is proportional to the quantity it represents.

8. Circular arc - Wikipedia

   en.wikipedia.org/wiki/Circular_arc

   A circular sector is shaded in green. Its curved boundary of length L is a circular arc. A circular arc is the arc of a circle between a pair of distinct points.If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle ...

9. Circle graph - Wikipedia

   en.wikipedia.org/wiki/Circle_graph

   A graph is a circle graph if and only if it is the overlap graph of a set of intervals on a line. This is a graph in which the vertices correspond to the intervals, and two vertices are connected by an edge if the two intervals overlap, with neither containing the other. The intersection graph of a set of intervals on a line is called the ...