What are the characteristics of a circle?

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.

What is the importance of circle?

Circles are still symbolically important today -they are often used to symbolize harmony and unity. For instance, take a look at the Olympic symbol. It has five interlocking rings of different colours, which represent the five major continents of the world united together in a spirit of healthy competition.

What is the origin of a circle?

Origin: the center of a circle. Radius: the distance from the center of a circle to any point on it. Diameter: the longest distance from one end of a circle to the other.

What are the different definitions of Apollonius circles?

There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio (Durell 1928, Ogilvy 1990). 2. One of the eight circles that is simultaneously tangent to three given circles (i.e., a circle solving Apollonius’ problem for three circles ). 3.

What was the problem of Apollonius in geometry?

In Euclidean plane geometry, Apollonius’s problem is to construct circles that are tangent to three given circles in a plane.

What did Apollonius do in his book tangencies?

For example, Euclid in Book III shows how to draw a circle so as to pass through three given points or to be tangent to three given lines; Apollonius (in a work called Tangencies, which no longer survives) found the circle tangent to three given circles, or tangent to any combination of three points, lines, and circles.

Which is the basis of the Apollonius pursuit problem?

This Apollonian circle is the basis of the Apollonius pursuit problem. It is a particular case of the first family described in #2. The Apollonian circles are two families of mutually orthogonal circles.