An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

In elementary geometry, pertaining to or involving right angles or perpendiculars.
Of a system of real functions, defined so that the integral of the product of any two different functions is zero.
Of a linear transformation, defined so that the length of a vector under the transformation equals the length of the original vector.
Of a square matrix, defined so that its product with its transpose results in the identity matrix.

→ ortho- + gonia "angle," related to gony "knee;" L. genu "knee;" Mod.Pers. zânu "knee;" Av. žnav-, žnu- "knee;" Skt. janu-; PIE base *g(e)neu-, see below, + → -al

Ardâkonj, from ardâ-, → ortho-, + konj "angle, corner, confined place" (variants xong "corner, angle," Tabari kânj, Kurd. kunj, Hamadâni kom), maybe from the PIE base *g(e)neu-, as above, and related to Mod.Pers. zânu "knee" (Av. žnu-), Skt. kona- "angle, corner," Gk. gony, gonia, L. cuneus "a wedge," Albanian (Gheg dialect) kân "angle, corner," Albanian (Toks) kënd "angle, corner."

A set of functions, any two of which, by analogy to orthogonal vectors, vanish if their product is summed by integration over a specified interval.

→ orthogonal; → function.

Perpendicular lines.

→ orthogonal; → line.

Math.: An → isogonal trajectory where the family of curves are cut at right angles.

→ orthogonal; → trajectory.

Two non-zero vectors which are perpendicular, i.e. their → scalar product is zero.

→ orthogonal; → vector.

1) The property of → orthogonal functions.
2) The following conditions satisfied by the → Fourier series:
∫ cos (mx) sin (nx) dx = 0 (summed from -π to +π) for all m, n
∫ cos (mx) cos (nx) dx = 0 (summed from -π to +π) for all m ≠ n, = 2π for m = n = 0, = π for (m = n) > 0
∫ sin (mx) sin (nx) dx = 0 (summed from -π to +π) for m ≠ n, = π for (m = n) > 0.

→ orthogonal; → -ity.