VS.

# Perpendicular vs. Orthogonal

Published:
Views: 27,091 (geometry) At or forming a right angle (to something).

‘In most houses, the walls are perpendicular to the floor.’;

(geometry) Of two objects, at right angles; perpendicular to each other.

‘A chord and the radius that bisects it are orthogonal.’;

Exactly upright; extending in a straight line toward the centre of the earth, etc.

(mathematics)

Perpendicularnoun

(geometry) A line or plane that is perpendicular to another.

Of a pair of vectors: having a zero inner product; perpendicular.

‘The normal vector and tangent vector at a given point are orthogonal.’;

Perpendicularnoun

A device such as a plumb line that is used in making or marking a perpendicular line.

Of a square matrix: such that its transpose is equal to its inverse.

Exactly upright or vertical; pointing to the zenith; at right angles to the plane of the horizon; extending in a right line from any point toward the center of the earth.

Of a linear transformation: preserving its angles.

At right angles to a given line or surface; as, the line ad is perpendicular to the line bc.

Of grid graphs, board games and polyominoes: vertical or horizontal but not diagonal.

Perpendicularnoun

A line at right angles to the plane of the horizon; a vertical line or direction.

(statistics) Statistically independent, with reference to variates.

Perpendicularnoun

A line or plane falling at right angles on another line or surface, or making equal angles with it on each side.

(software engineering) Of two or more aspects of a problem, able to be treated separately.

‘The content of the message should be orthogonal to the means of its delivery.’;

Perpendicularnoun

a straight line at right angles to another line

Of two or more problems or subjects, independent of or irrelevant to each other.

Perpendicularnoun

a Gothic style in 14th and 15th century England; characterized by vertical lines and a four-centered (Tudor) arch and fan vaulting

Right-angled; rectangular; as, an orthogonal intersection of one curve with another.

Perpendicularnoun

a cord from which a metal weight is suspended pointing directly to the earth's center of gravity; used to determine the vertical from a given point

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’;

Perpendicularnoun

an extremely steep face

statistically unrelated

intersecting at or forming right angles;

‘the axes are perpendicular to each other’; ‘parallel lines never converge’; ‘concentric circles are parallel’; ‘dancers in two parallel rows’;

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’;

at right angles to the plane of the horizon or a base line;

‘a vertical camera angle’; ‘the monument consists of two vertical pillars supporting a horizontal slab’; ‘measure the perpendicular height’;

of or involving right angles; at right angles.

extremely steep;

‘the great perpendicular face of the cliff’;

(of variates) statistically independent.

at an angle of 90° to a given line, plane, or surface or to the ground

‘dormers and gables that extend perpendicular to the main roofline’;

(of an experiment) having variates which can be treated as statistically independent.

at an angle of 90° to the ground; vertical

‘the perpendicular cliff’;

so steep as to be almost vertical

‘houses seem to cling by blind faith to the perpendicular hillside’;

denoting the latest stage of English Gothic church architecture, prevalent from the late 14th to mid 16th centuries and characterized by broad arches, elaborate fan vaulting, and large windows with vertical tracery

‘the Perpendicular style’; ‘the handsome Perpendicular church of St Andrew’;

Perpendicularnoun

a straight line at an angle of 90° to a given line, plane, or surface

‘at each division draw a perpendicular representing the surface line’;

Perpendicularnoun

perpendicular position or direction

‘the wall declines from the perpendicular a little inward’;

Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects.