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Each circle is labeled by an integer i, its position in the sequence; it has radius ρ i and curvature ρ −i. When the four radii of the circles in Descartes' theorem are assumed to be in a geometric progression with ratio , the curvatures are also in the same progression (in reverse). Plugging this ratio into the theorem gives the equation
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Theorems about circles" The following 21 pages are in this category, out ...
By Barbier's theorem, the body's perimeter is exactly π times its width, but its area depends on its shape, with the Reuleaux triangle having the smallest possible area for its width and the circle the largest. Every superset of a body of constant width includes pairs of points that are farther apart than the width, and every curve of constant ...
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...
Print/export Download as PDF; Printable version; ... Pages in category "Theorems about triangles and circles" The following 18 pages are in this category, out of 18 ...
Circle theorem may refer to: Any of many theorems related to the circle; often taught as a group in GCSE mathematics. These include: Inscribed angle theorem. Thales' theorem, if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Alternate segment theorem. Ptolemy's theorem.
Print/export Download as PDF; Printable version; ... Pages in category "Theorems about quadrilaterals and circles" The following 6 pages are in this category, out of ...
This problem is known as the primitive circle problem, as it involves searching for primitive solutions to the original circle problem. [9] It can be intuitively understood as the question of how many trees within a distance of r are visible in the Euclid's orchard , standing in the origin.
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