An Etymological Dictionary of Astronomy and Astrophysics
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Put in modern notation, if α and β are acute angles and if β <α, then sin α / sin β <α / β < tan α / tan β. Aristarchus probably used this inequality to show that the Sun is between 18 and 20 times as far from the Earth as the Moon is.

Aristarchus of Samos (c.310-c.230 BC); → inequality.

Any of a large number of inequality relations developed to study the → hidden variable hypothesis suggested in the → EPR paradox. Using Bell's inequalities, the → Aspect experiment showed that no local hidden variable theory can make predictions in agreement with those of quantum mechanics. If, in a measurement, the inequality is violated, the measurement is in agreement with the predictions of the quantum theory. If the equality is satisfied, it suggests that a classical, causal, and local model is adequate to explain the outcome of the measurements. See also → quantum entanglement.

John Stewart Bell (1928-1990); → inequality.

1) A statement of the form a ≠ b, a > b, or a < b, asserting one quantity is greater than or less than another quantity. → equality.
2) An irregularity in the movement of a celestial object in its orbit about another which cannot be explained by their mutual gravitational attraction. Irregularities are often due to perturbation by other neighboring objects.

→ in-; → equality.

An irregularity in the Moon's motion caused by the Sun's gravitational attraction, which sets the Moon ahead or behind its normal orbital position. The Moon is about 2 arcminutes ahead of its expected position at first quarter, and a similar amount behind at last quarter.

→ parallactic; → inequality.

1) A theorem according to which any side of a triangle is always shorter than the sum of the other two sides.
2) The third requirement for a → distance function describing a → metric space.

→ triangle; → inequality.