Circles of Apollonius

Figure 1. Apollonius' definition of a circle.

Figure 2. A set of Apollonian circles. Every blue circle intersects every red circle at a right angle, and vice versa. Every red circle passes through the two foci, which correspond to points A and B in Figure 1.

Apollonius' problem may have up to eight solutions. The three given circles are shown in black, whereas the solution circles are colored.

Figure 4. A symmetrical Apollonian gasket, also called the Leibniz packing, after its inventor Gottfried Leibniz.

The circle of Apollonius is any of several types of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for example, counterparts on the surface of a sphere can be defined through stereographic projection.

单词	Circle of Apollonius
释义	Circle of Apollonius 英语百科 Circles of Apollonius The circle of Apollonius is any of several types of circles associated with Apollonius of Perga, a renowned Greek geometer. Most of these circles are found in planar Euclidean geometry, but analogs have been defined on other surfaces; for example, counterparts on the surface of a sphere can be defined through stereographic projection.
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Circle of Apollonius

Circles of Apollonius