Abbe sine condition
butâr-e sinus-e Abbe
Fr.: condition des sinus d'Abbe
In → geometric optics, a condition for eliminating → spherical aberration and → coma in an → optical system. It is expressed by the relationship: sin u'/U' = sin u/U, where u and U are the angles, relative to the → optical axis, of any two rays as they leave the object, and u' and U' are the angles of the same rays where they reach the image plane. A system which satisfies the sine condition is called → aplanatic.
Named after Ernst Karl Abbe (1840-1905), a German physicist; → sine; → condition.
Fr.: Tables alfonsines
A set of tables created in Toledo, under Alfonso X, el sabio, king of Castile and Léon (1252 to 1284) to correct the anomalies in the → Toledan Tables. The starting point of the Alfonsine Tables is January 1, 1252, the year of king's coronation (1 June). The original Spanish version of the tables is lost, but a set of canons (introductory instructions) for planetary tables are extant. They are written by Isaac ben Sid and Judah ben Moses ha-Cohen, two of the most active collaborators of Alfonso X. The Alfonsine Tables were the most widely used astronomical tables in the Middle Ages and had an enormous impact on the development of European astronomy from the 13th to 16th century. They were replaced by Erasmus Reinhold's → Prutenic Tables, based on Copernican models, that were first published in 1551.The Latin version of the Alfonsine Tables first appeared in Paris around 1320, where a revision was undertaken by John of Lignères and John of Murs, accompanied by a number of canons for their use written by John of Saxony. There is a controversy as to the exact relationship of these tables with the work commissioned by the Spanish king.
After the Spanish monarch Alfonso X (1221-1284); → table.
Fr.: approximation de Boussinesq
A simplification in the equations of → hydrodynamics that treats the density as constant except in the → buoyancy term. This approximation is motivated by the fact that when pressure and temperature differences in a flow are small, then it follows from the thermodynamic → equation of state that a change in the density is also small.
Named after Joseph Valentin Boussinesq (1842-1929), a French physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat; → approximation.
A trigonometric function giving the ratio of the side adjacent to a given angle to the hypotenuse.
Fr.: cosinus hyperbolique
A function, denoted cosh x, defined for all real values of x, by the relation: cosh x = (1/2) (ex + e-x).
→ hyperbolic; → cosine.
Fr.: sinus hyperbolique
A function, denoted cosh x, defined for all real values of x, by the relation: cosh x = (1/2) (ex - e-x).
→ hyperbolic; → sine.
Lambert's cosine law
qânun-e cosinus-e Lambert
Fr.: loi en cosinus de Lambert
The intensity of the light emanating in any given direction from a perfectly diffusing surface is proportional to the cosine of the angle between the direction and the normal to the surface. Also called → Lambert's law.
law of cosines
Fr.: loi des cosinus
An expression that for any triangle relates the length of a side to the cosine of the opposite angle and the lengths of the two other sides. If a, b, and c are the sides and A, B, and C are the corresponding opposites angles: a2 = b2 + c2 - 2bc cos A; b2 = c2 + a2 - 2ca cos B; c2 = a2 + b2 - 2ab cos C.
law of sines
Fr.: loi des sinus
In any triangle the sides are proportional to the sines of the opposite angles: a/sin A = b/sin B = c/sin C, where A, B, and C are the three vertices and a, b, and c are the corresponding sides.
In trigonometry, the function of an acute angle of a right triangle represented by the ratio of the opposite side to the hypotenuse.
Greek mathematicians were not aware of the advantages of sine and instead used chord.
The invention of this function is a great Indian contribution. It seems that Aryabhata (c. AD 500)
was the first who coined a term in Skt. for this concept: árdha-jiyā-
"half chord," which was later shortened to
jiyā- "chord." This Skt. word was subsequently loaned in Ar. and corrupted to
Sinus loanword from Fr., as above.
mowj-e sinusi (#)
Fr.: onde sinusoïdale
A periodic oscillation that is defined by the function y = sin x.