Division of circles

A circle division denotes a division of a circle into equal arcs . The term is used in mathematics as well as in metrology .

mathematics

The question of whether, for a given natural number, a circle can be broken down into equal arcs using only a compass and ruler , was already investigated in ancient times . This task is equivalent to the construction task of a regular polygon with corners. Those polygons for which such a construction is possible are called constructible polygons . Finding specific construction regulations quickly turns out to be very time-consuming as the number of corners increases. There are such construction regulations for the 17-corner , the 257-corner and the 65537-corner . ${\displaystyle n}$ ${\displaystyle n}$ ${\displaystyle n}$

Since the answer to the question whether the regular corner can be constructed with a compass and ruler can be traced back to algebraic facts, the term “circle division” gave its name to algebraic objects such as circle division equations , circle division solids and circle division polynomials . ${\displaystyle n}$

Are as additional aids such. B. the Quadratrix of Hippias or the Archimedean spiral , which in addition to the three-way division also allow divisions with equal angles, are thought to be all regular corners such. B. also the elf (exact) constructable . ${\displaystyle n}$ ${\displaystyle n}$

If a solution with an approximate value of the central angle is sufficient , its abbreviated cosine or sine value is constructed using the 3rd theorem on a number line . The desired accuracy of the approximate value depends on the selected number of decimal places of the cosine or sine value.

Metrology

In metrology, the division of a circle denotes the unit of measurement used for angle measurement , e.g. B. degrees , Gon , stroke or radian (radian) .

See also

• Circle dividing machine
• Circle reading

Web links

• Circular division, an approximation construction using the 3rd ray theorem using the heptagon as an example

Individual evidence

1. ↑ Eva Lübbe, Mathematik für Bauberufe , Wiesbaden 2009, ISBN 978-3834805836 , doi : 10.1007 / 978-3-8348-9274-4 , p. 64
2. ↑ Martin Klein, Introduction to the DIN standards . DIN, German Institute for Standardization e. V. (Ed.), 13th edition, Stuttgart 2001, ISBN 978-3519263012 , doi : 10.1007 / 978-3-322-92719-4 , p. 104