Q:

# How many lines of symmetry are in a circle?

A:

Circles have an infinite number of lines of symmetry. Any line that bisects a circle through its center is a line of symmetry. Circles are the only Euclidean shape with this property.

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Credit: Procsilas Moscas CC-BY 2.0

Circles have fascinated mathematicians since the time of early Greek culture, and other cultures have pondered circles as well. Circles have an infinite number of edges, and they cannot be described with classic geographical techniques. Pi, the ratio of a circle's area to its radius, pops up throughout seemingly unrelated areas of mathematics.

Many mathematicians and philosophers independently found that circles can be described as having an infinite number of edges, and this conception is useful when considering lines that touch circles at only one point, of which there are an infinite number.

Despite the fact that circles are often considered the simplest shape, they are mathematically complex. Pi is an irrational number; it cannot be expressed completely using standard numbers. The fact that they have an infinite number of edges made them difficult for early mathematicians to comprehend. Unlike other shapes, their area cannot be precisely calculated if the radius is a rational number. Because of this, circles have often been considered a special shape that are different from other shapes.

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