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A protractor is a measuring instrument, typically made of transparent plastic, for measuring angles. Some protractors are simple half-discs or full circles. More advanced protractors, such as the bevel protractor, have one or two swinging arms, which can be used to help measure the angle. Most protractors measure angles in degrees (°).
This illustration shows how the Imperial Japanese Navy used the measurement of the angle subtended by a ship to estimate the ship's angle on the bow. The target course was the most difficult piece of target data to obtain. In many cases, instead of measuring target course many systems measured a related quantity called angle on the bow. Angle ...
Animation of construction of a pentagon using a compass and straightedge. A mathematical instrument is a tool or device used in the study or practice of mathematics.In geometry, construction of various proofs was done using only a compass and straightedge; arguments in these proofs relied only on idealized properties of these instruments and literal construction was regarded as only an ...
Lux meter for measuring illuminance, i.e. incident luminous flux per unit area; Luminance meter for measuring luminance, i.e. luminous flux per unit area and unit solid angle; Light meter, an instrument used to set photographic exposures. It can be either a lux meter (incident-light meter) or a luminance meter (reflected-light meter), and is ...
Greek astronomers used the dioptra to measure the positions of stars; both Euclid and Geminus refer to the dioptra in their astronomical works. It continued in use as an effective surveying tool. Adapted to surveying, the dioptra is similar to the theodolite , or surveyor's transit, which dates to the sixteenth century.
Angles are measured using a sine bar with the help of gauge blocks and a dial gauge or a spirit level. The aim of a measurement is to measure the surface on which the dial gauge or spirit level is placed horizontally. For example, to measure the angle of a wedge, the wedge is placed on a horizontal table. The sine bar is placed over the ...
These instruments are also used to measure the angular distance between objects: Octant, invented in 1731. The first widely accepted instrument that could measure an angle without being strongly affected by movement. Sextant, derived from the octant in 1757, eventually made all previous instruments used for the same purpose obsolete.
Postulate III: Postulate of angle measure. The set of rays { ℓ, m, n , ...} through any point O can be put into 1:1 correspondence with the real numbers a (mod 2 π ) so that if A and B are points (not equal to O ) of ℓ and m , respectively, the difference a m − a ℓ (mod 2π) of the numbers associated with the lines ℓ and m is ∠ AOB .
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