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Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a protractor
is a circular or semicircular tool for measuring an angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...
or a circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
. The units of measurement utilized are usually degree
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
Some protractors are simple half-discs; these have existed since ancient times. More advanced protractors, such as the bevel protractor, have one or two swinging arms, which can be used to help measure the angle.
A bevel protractor is a graduated circular protractor having a pivoted arm; used for measuring or marking off angles. Sometimes vernier scale
A vernier scale is an additional scale which allows a distance or angle measurement to be read more precisely than directly reading a uniformly-divided straight or circular measurement scale...
s are attached to give more precise readings. It has wide application in architectural and mechanical drawing although with the availability of modern drawing software or CAD the tool is less commonly used in that sphere.
Universal bevel protractors are also used by toolmakers, as they measure angles by mechanical contact they are classed as mechanical protractors.
- Protractor compass
A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry is derived from two Greek words, gōnia, meaning angle, and metron, meaning measure....
- Geometry template
A geometry template is a piece of clear plastic with cut-out shapes for use in mathematics and other subjects in primary school through secondary school. It functions as a stencil, protractor, ruler, French curve and straightedge. It can also be called a mathomat....
An inclinometer or clinometer is an instrument for measuring angles of slope , elevation or depression of an object with respect to gravity...
- Birkhoff's axioms
In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry sometimes referred to as Birkhoff's axioms. These postulates are all based on basic geometry that can be confirmed experimentally with a scale and protractor. Since the postulates build upon the real numbers, the...