Protractor
A protractor (also yardstick , even in older parlance transporter called) is a simple goniometer for angle measurement or for entering a angle . It consists of a circular or semicircular disc with angles. The disc can be made of plastic, strong paper or sheet metal. Diameters of 8 to 15 cm and divisions of 1 ° or 0.5 ° are common, and 0.5 gon (grads) when measuring . The accuracy is about 0.1 to 0.5 °, depending on the diameter of the scale.
Often protractors are integrated into drawing or set triangles . A triangle of nautical cutlery is regularly equipped with a protractor. More precise protractors have a swiveling rail with a rule (length division into millimeters), which can be determined at the desired angle.
With the semicircular feed dog, the mm graduation runs along the diameter. Specimens for geodesy (for mapping measured points) or for cartography have large diameters of around 30 cm. Here the scale can also be numbered in the most commonly used scale (e.g. 1: 500 or 1: 2000, or 1: 1440 or 1: 2880 for the earlier cadastral maps ). In craft, the exact measuring an angle is usually unnecessary here is an angle to a workpiece for transmitting a bevel used.
- Various protractors
360 degree protractor
Typical protractor with a small ruler for school use
Medical protractor
electronic protractor with digital display
Protractors in today's sense emerged in the second half of the 18th century, when scientists like Jesse Ramsden and Georg Friedrich Brander refined the previously rather imperfect devices to such an extent that the individual graduation marks could hardly be distinguished with the naked eye. At that time the preferred materials of manufacture were wood, brass, silver, copper or ivory; tin and celluloid were common in the first half of the 20th century . Today there are also electronic protractors, which usually work with a rotary sensor.
Related measuring devices are the inclinometer , the theodolite , an optical protractor in the construction industry and land surveying, the slope meter as a simple, optical protractor for determining slopes, inclines and for indirect height measurement, as well as the sextant as an optical protractor for navigation . In synthetic geometry , the unrestricted possibility of measuring angles, that is to say that every length of the path uniquely corresponds to a class of angles, is formulated as an axiom, the protractor axiom, see → Euclidean solid .
Web links
Individual evidence
- ↑ a b cf. Hans-Joachim Vollrath , Historical angle measuring devices , online resource of the University of Würzburg, p. 5 (PDF)
- ↑ cf. Johann Heinrich Moritz von Poppe : History of mathematics from the oldest to the most recent. Tübingen 1828, p. 103
- ↑ cf. History, function and construction methods