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##### The Collaborative International Dictionary
Orthogonal

Orthogonal \Or*thog"o*nal\, a. [Cf. F. orthogonal.] Right-angled; rectangular; as, an orthogonal intersection of one curve with another.

Orthogonal projection. See under Orthographic.

##### Douglas Harper's Etymology Dictionary
orthogonal

1570s, from French orthogonal, from orthogone, from Late Latin orthogonius, from Greek orthogonios "right-angled," from ortho- "straight" (see ortho-) + gonia "angle," related to gony "knee" (see knee (n.)). Related: Orthogonally.

##### Wiktionary
orthogonal

a. 1 (context geometry English) Of two objects, at right angles; perpendicular to each other. 2 (context mathematics English) 3 # Of a pair of vectors: having a zero inner product; perpendicular. 4 # Of a square matrix: such that its transpose is equal to its inverse. 5 # Of a linear transformation: preserve its angles. 6 # Of grid graphs, board games and polyominoes: vertical or horizontal but not diagonal. 7 (context statistics English) Statistically independent, with reference to variates. 8 (context software engineering English) Of two or more aspects of a problem, able to be treated separately. 9 Of two or more problems or subjects, independent of or irrelevant to each other.

##### WordNet
orthogonal
1. adj. not pertinent to the matter under consideration; "an issue extraneous to the debate"; "the price was immaterial"; "mentioned several impertinent facts before finally coming to the point" [syn: extraneous, immaterial, impertinent]

2. statistically unrelated

3. having a set of mutually perpendicular axes; meeting at right angles; "wind and sea may displace the ship's center of gravity along three orthogonal axes"; "a rectangular Cartesian coordinate system" [syn: rectangular]

##### Wikipedia
Orthogonal (series)

Orthogonal is a science fiction trilogy by Australian author Greg Egan taking place in a universe where, rather than three dimensions of space and one of time, there are four fundamentally identical dimensions.

Technically, the space-time of the universe portrayed in the novels has a positive-definite Riemannian metric, rather than a pseudo-Riemannian metric, which is the kind that describes our own universe.

The first novel of the trilogy, The Clockwork Rocket, was published in 2011, the second, The Eternal Flame, in 2012, and the third, The Arrows of Time, in 2013.

#### Usage examples of "orthogonal".

The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out, fuming factorially, and fell upon the King and hurt him passing sore.

Like the determinant of a linear system under orthogonal rotation, or the Newtonian equations of motion with a Galilean transformation, or Maxwell's equations with a Lorentz transformation.

She had been trained as an orthogonist at art school, and using orthogonal projection she could create figures on the walkways that would appear to be erect - amusing figures, dancing, walking, holding hands.

Therefore it is in the process of self-repair, which includes: rebuilding our subcircuit (world) via linear and orthogonal time changes (sequences of events), as well as continual signaling to us both en masse and individually (to us received subliminally by the right brain hemisphere, which gestalts the constituents of the messages into meaningful entities), to stimulate blocked neural (memory) banks within us to fire and hence retrieve what is there.