A mathematical instrument is a tool or device used in the study or practice of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. In

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, 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 approximation. In

applied mathematics Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a ...

, mathematical instruments were used for measuring angles and distances, in

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

navigation Navigation is a field of study that focuses on the process of monitoring and controlling the motion, movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navig ...

surveying Surveying or land surveying is the technique, profession, art, and science of determining the land, terrestrial Plane (mathematics), two-dimensional or Three-dimensional space#In Euclidean geometry, three-dimensional positions of Point (geom ...

and in the measurement of time.Gerard L'Estrange Turner ''Scientific Instruments, 1500-1900: An Introduction'' ( University of California Press, 1998) page 8

Overview

Instruments such as the

astrolabe An astrolabe (; ; ) is an astronomy, astronomical list of astronomical instruments, instrument dating to ancient times. It serves as a star chart and Model#Physical model, physical model of the visible celestial sphere, half-dome of the sky. It ...

, the quadrant, and others were used to measure and accurately record the relative positions and movements of planets and other celestial objects. The sextant and other related instruments were essential for navigation at sea. Most instruments are used within the field of

, including the

ruler A ruler, sometimes called a rule, scale, line gauge, or metre/meter stick, is an instrument used to make length measurements, whereby a length is read from a series of markings called "rules" along an edge of the device. Usually, the instr ...

, dividers, protractor,

set square A set square or triangle (American English) is an object used in engineering and technical drawing, with the aim of providing a straightedge at a right angle or other particular planar angle to a baseline. Types The simplest form of set s ...

, compass, ellipsograph, T-square and opisometer. Others are used in

arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...

(for example the

abacus An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. A ...

, slide rule and

calculator An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics. The first solid-state electronic calculator was created in the early 1960s. Pocket-si ...

) or in

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

(the integraph). In astronomy, many have said the pyramids (along with Stonehenge) were actually instruments used for tracking the stars over long periods or for the annual planting seasons.

In schools

The Oxford Set of Mathematical Instruments is a set of instruments used by generations of school children in the United Kingdom and around the world in mathematics and geometry lessons. It includes two set squares, a 180° protractor, a 15 cm ruler, a metal compass, a metal divider, a 9 cm pencil, a pencil sharpener, an eraser and a 10mm stencil.

References

External reading

*J. L. Heilbron (ed.), ''The Oxford Companion To the History of Modern Science'' (Oxford University Press, 2003) , ''Instruments and Instrument Making'', pp. 408–411 Mathematical tools Articles containing video clips {{math-stub

Overview

In schools

See also

References

External reading