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Seven circles theorem – A chain of six circles tangent to a seventh circle and each to its 2 neighbors Six circles theorem – Relates to a chain of six circles together with a triangle Smallest circle problem – Finding the smallest circle that contains all given points Pages displaying short descriptions of redirect targets
Those who wish to adopt the textbooks are required to send a request to NCERT, upon which soft copies of the books are received. The material is press-ready and may be printed by paying a 5% royalty, and by acknowledging NCERT. [11] The textbooks are in color-print and are among the least expensive books in Indian book stores. [11]
Book 3 of Euclid's Elements deals with the properties of circles. Euclid's definition of a circle is: A circle is a plane figure bounded by one curved line, and such that all straight lines drawn from a certain point within it to the bounding line, are equal. The bounding line is called its circumference and the point, its centre.
Every blue circle intersects every red circle at a right angle. Every red circle passes through the two points C, D, and every blue circle separates the two points. In geometry, Apollonian circles are two families of circles such that every circle in the first family intersects every circle in the second family orthogonally, and vice versa.
The standard 1-torus is just the circle: T 1 = S 1. The torus discussed above is the standard 2-torus, T 2. And similar to the 2-torus, the n-torus, T n can be described as a quotient of R n under integral shifts in any coordinate. That is, the n-torus is R n modulo the action of the integer lattice Z n (with the action being taken as vector ...
[9] [10] The link itself is much older and has appeared in the form of the valknut, three linked equilateral triangles with parallel sides, on Norse image stones dating back to the 7th century. [11] The Ōmiwa Shrine in Japan is also decorated with a motif of the Borromean rings, in their conventional circular form. [ 2 ]
The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and an equant (•). In both Hipparchian and Ptolemaic systems, the planets are assumed to move in a small circle called an epicycle , which in turn moves along a larger circle called a ...
For three circles denoted by C 1, C 2, and C 3, there are three pairs of circles (C 1 C 2, C 2 C 3, and C 1 C 3). Since each pair of circles has two homothetic centers, there are six homothetic centers altogether. Gaspard Monge showed in the early 19th century that these six points lie on four lines, each line having three collinear points.