Circles

Perhaps the most beautiful geometric figure is the circle. A circle can be defined as the set of points in a plane that are equidistant from a given point, called the centre of the circle. The circle is one of the four conic sections, formed by cutting a cone parallel to the base. Here are some interesting facts about circles:

• Every point on the circumference of the circle is the same distance from the centre.
• Every diameter of the circle is an axis of rotational symmetry. While an equilateral triangle has three axes of symmetry and a square has four axes of symmetry, the circle has an infinite number of axes of symmetry.
• A circle has rotational symmetry around its centre for every angle. The order of rotational symmetry for a circle is infinite, as you can rotate a circle any number of degrees and it will still look the same.
• Every line tangent to a circle is perpendicular to the radius drawn from the centre to the point where the tangent line meets the circle.
• The curvature of a circle is constant at every point. The only other curve like this is a straight line.
• Out of all of the curves that enclose the same area, the circle has the smallest perimeter.