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Mathematics includes the study of such topics as quantity, structure, space, and change. Mathematicians seek and use patterns to formulate new conjectures; they resolve the truth or falsity of conjectures by mathematical proof. 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 approximation. Most instruments are used within the field of geometry, including the ruler, dividers, protractor, set square, compass, ellipsograph, T-square and opisometer.

Others are used in arithmetic (for example the abacus, slide rule and calculator) or in algebra (the integraph).

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