The Circles of Descartes Poster

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The Circles of Descartes Poster
Excl. VAT: £4.99 Incl. VAT: £5.99

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This poster describes the Descartes Circle Theorem and shows some of the beautiful and complex figures, known as Apollonian packings, that can be created using the theorem.

In the early part of the 17th century, Rene Descartes described a simple relationship between the curvatures of four mutually tangent circles. Given the curvatures of three of the circles, it is possible to calculate the curvature of the fourth by a straightforward solution to a quadratic equation. (It may be the coolest thing you'll ever see done with a quadratic equation!)

This allows the construction of fascinating figures know as Apollonian packings, in which an infinite number of circles fit inside a large outer circle. In fact, there are many Apollonian packings for which every circle has integer curvature. Some arrangements lead to intriguing number sequences, such as the squares (1, 4, 9, 16, 25 ...).

Year/Grades 7-12.  c55cm x 86cm (22" x 34")

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Excl. VAT: £4.99 Incl. VAT: £5.99