# Translations of Encyclopedia about Mathematics

## Other Polygons

Besides triangles and quadrangles, we have other forms of polygons, such as the pentagon or the hexagon. But, besides the octagon we see in the shape of the standard stop sign, we rarely see this shape.

Circumference of Polygons

Circumference is the combined length of all sides which border a particular shape. In other words, it is the distance of the path one must take to travel the periphery of a particular shape to come back to the same point from which they started.

It is the summation of lengths of all abscissae which make up the sides of a polygon. For example, a triangle has three sides and its circumference is equal to the sum of the length of these three sides.

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## Circles

Mathematically, a circle may be perceived as a normal n-square with an infinite number of cusps or vertexes. If we can imagine normal polygons and start to continually add to them vertexes, their sides become increasingly shorter and the polygon approaches the shape of a circle.

A ring is a curve defined as the set of all points which have the same distance from a point S and which lie on a single plain.

A circle is a flat shape defined as the set of all points which have the same or less distance from a point S, where this distance can be defined as an abscissa r lying on a single plain. The point S is the centre of the circle and the distance between it and its perimeter ring is r, called the radius. A circle is therefore a flat surface limited within some ring.

Every connecting line between a point on the ring and the centre of the circle is therefore a radius because, according to its definition, the length of all points on a ring from the centre is always the same. A connecting line between two points on a ring which also passes through the centre of a circle is called the diameter d, its length being twice that of the radius.

Circles are something we also often run into in our daily lives, such as with transport signs depicting the maximum speed on a highway, or a ban of entry. There are also other round shapes in our daily lives, such as the wheel, the coffee cup coaster, the horizontal cross-section of a glass, and a CD rom.

The following relations may be derived from circles.

The circumference of a Circle Equals the Length of a Ring

The circumference of a circle is as well defined as with polygons, although it is not possible to measure the length of its individual sides. However, it is possible to estimate that larger circles have longer circumferences. Larger circles also have larger diameters.

The relation between the radius and circumference of a circle is the following:

O = 2 . p . r

The number p is an irrational number and is equal to 3,141592…

Surface Area of a Circle

As with a circle’s circumference, its surface area depends on the length of its diameter. The following applies:

P = p . r2

A circle with a diameter of 1 is called a unitary circle. A particular characteristic of this type of circle is that its circumference is 2p and its surface area equals to p .

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