what is a geometric compass?

Answer 1

A geometric compass is a tool/device that allows one to draw a circle.
Such device consists of two legs that are pivoted and can open or close depending on the radius of a circle required. One leg is a sharp point that is placed where a center of the circle is required. The other leg holds a pencil, a chalk, or any writing implement that may leave a mark on the surface where a circle is to be drawn. The user moves the leg, containing the writing implement, in the circle as the other leg remains fixed at the center.

Term drafting compass is more frequently used.

Answer 2

In antiquity, geometric constructions of figures and lengths were restricted to the use of only a straightedge and compass (or in Plato's case, a compass only; a technique now called a Mascheroni construction). Although the term "ruler" is sometimes used instead of "straightedge," the Greek prescription prohibited markings that could be used to make measurements. Furthermore, the "compass" could not even be used to mark off distances by setting it and then "walking" it along, so the compass had to be considered to automatically collapse when not in the process of drawing a circle.

Because of the prominent place Greek geometric constructions held in Euclid's Elements, these constructions are sometimes also known as Euclidean constructions. Such constructions lay at the heart of the geometric problems of antiquity of circle squaring, cube duplication, and angle trisection. The Greeks were unable to solve these problems, but it was not until hundreds of years later that the problems were proved to be actually impossible under the limitations imposed. In 1796, Gauss proved that the number of sides of constructible polygons had to be of a certain form involving Fermat primes, corresponding to the so-called Trigonometry Angles.

Although constructions for the regular triangle, square, pentagon, and their derivatives had been given by Euclid , constructions based on the Fermat primes were unknown to the ancients. The first explicit construction of a heptadecagon (17-gon) was given by Erchinger in about 1800. Richelot and Schwendenwein found constructions for the 257-gon in 1832, and Hermes spent 10 years on the construction of the 65537-gon at Göttingen around 1900 (Coxeter 1969). Constructions for the equilateral triangle and square are trivial (top figures below). Elegant constructions for the pentagon and heptadecagon are due to Richmond (1893) (bottom figures below).


Given a point, a circle may be constructed of any desired radius, and a diameter drawn through the center. Call the center , and the right end of the diameter . The diameter perpendicular to the original diameter may be constructed by finding the perpendicular bisector. Call the upper endpoint of this perpendicular diameter . For the pentagon, find the midpoint of and call it . Draw , and bisect , calling the intersection point with . Draw parallel to , and the first two points of the pentagon are and . The construction for the heptadecagon is more complicated, but can be accomplished in 17 relatively simple steps. The construction problem has now been automated (Bishop 1978).

Simple algebraic operations such as , , (for a rational number), , , and can be performed using geometric constructions (bold 1982, Courant and Robbins 1996). Other more complicated constructions, such as the solution of Apollonius' problem and the construction of inverse points can also accomplished