Visual Dictionary of Architecture: Geometry

Geometry

A branch of mathematics that deals with the properties, measurement, and relationships of points,lines, angles, and solids, deduced from their defining and conditions by means of certain assumed properties of space.

Abscissa

A coordinate determined by measuring parallel to the x-axis. Also called x-coordinate.

Euclidean Geometry

Geometry based upon the postulates of Euclid, esp. the postulate that only one line may be drawn through a given point parallel to a given line.

Point

A dimensionless geometric element that has no property but location, as the intersection of two lines.

Y-Axis

The axis along which ordinates or y-values are measured in a Cartesian coordinate system. Also called axis of ordinates.

Z-Coordinate

A coordinate determined by measuring parallel to the z-axis.

Z-Axis

The axis along which z-values are measured in a three-dimensional Cartesian coordinate system.

Rectangular Coordinate System

A Cartesian coordinate system in which the axes or coordinate planes are perpendicular.

Line

A geometric element generated by a moving point and having extension without breadth or thickness.

Angle

The space between two lines diverging from a common point, or within two planes diverging from a common line: the figure so formed.

Right Angle

An angle of 90° formed by the perpendicular intersection of two straight lines.

Acute Angle

An angels less that 90°.

Obtuse Angle

An angle greater that 90°, but less than 180°.

Vertex

The point at which the sides of an angle intersect.

Horizontal

Parallel to or operating in a plane parallel to the horizon.

Oblique

Neither parallel nor perpendicular to a given line or surface.

Vertical

Perpendicular to the plane of the horizon.

X-Axis

The axis along which abscissas or x-values are measured in a Cartesian coordinate system. Also called axis of abscissas.

Ordinate

A coordinate determined by measuring parallel to the y-axis. Also called y-coordinate.

Cartesian Coordinate

Any of the coordinates for locating a point on a plane by its distance from each of two intersecting lines, or in space by its distance from each of three planes intersecting at a point.

Coordinate

Any of a set of numbers that serve to specify the location of a point on a line, surface, or in space by reference to a fixed figure or system of lines.

Radius Vector

A straight line segment that joins a variable point to the fixed origin of a polar coordinate system.

Polar Angle

The angle formed by the polar axis and a radius vector in a polar coordinate system.

Polar Axis

The reference axis from which the polar angle is measured in a polar coordinate system.

Polar Coordinate System

A system for locating a point on a plane by its radius vector and polar angle.

Parallel

Extending in the same direction, equidistant at all points, and never converging or diverging.

Skew Lines

Any lines in space that are neither parallel nor intersecting.

Angle

The amount of rotation needed to bring one line or plane into coincidence with another, measured in radians or in degrees, minutes, and seconds.

Radian

A unit of angular measure equal to the central angle subtending an are equal in length to the radius:; 360/2x or approx. 57.3°.

Degree

A unit of angular measure, equal to 1/360th of a complete angle or turn, or of the circumference of a circle.

Minute

The 60th part of a degree of angular measure.

Second

The 60th part of a minute of angular measure.

height

Extent or distance of upward from a given level to a fixed point.

base

The line or surface forming the ppart of a geometric figure that is most nearly horizontal or on which it is supposed to stand, from which an altitude can be constructed.

isosceles

Having two sides of equal length.

acute

Composed only of acute angles.

obtuse

having an obtuse angle.

scalene

Having three unequal sides.

coincident

occupying the same place in space or time.

congruent

coinciding at all points when superimposed.

similar

having corresponding sides proportional and corresponding angles equal.

trigonometry

the branch of mathematics that deals with the properties of triangles and trigonometric functions, and of their applications.

trigonometric functions

a function of an angle, as some or cosine, expressed as the ratio of the sides of a right triangle.

sine

the trigonometric function defined as the ratio of the sides opposite a given angle to the hypotenuse.

cosine

the trigonometric function defined as the ratio of the sides adjacent to a given angle to the hypotenuse.

tangent

the trigonometric function defined as the ratio of the sides opposite a given angle to the side adjacent to the angle.

secant

the trigonometric function defined as ratio of the hypotenuse to the side adjacent to a given angle.

cotangent

the trigonometric function defined as the ratio of the sides adjacent to the angle.

vertex

the point opposite to and farthest from the base of a plane figure.

altitude

the perpendicular distance from the base of a geometric figure to the opposite vertex, parallel side, or parallel surface.

reentrant

reentering or pointing inward, as an interior angle of a polygon that is greater than 180°.

triangle

a polygon having three sides and three angles.

salient

an outward projecting angle or part.

exterior angle

the angle formed between any side of a polygon and an extended adjacent side.

interior angle

the angle formed inside a polygon between any two adjacent sides.

cant

an oblique line or surface, as one formed by cutting off the corner of a square or cube.

right triangle

a triangle having a right angle.

hypotenuse

the side of a right triangle that is opposite the right angle.

Pythagorean Theorem

the theorem that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.

regular

having all sides equal (equilateral) and all angles equal (equlangular).

plane geometry

the branch of geometry that deals with plane figures.

plane

a surface generated by a straight line moving at a constant velocity with respect to a fixed point, such that a straight line joining any two of its points lies wholly in the surface.

figure

A combination of geometric elements disposed in a particular form or shape

polygon

a closed plane figure having three or more straight sides.

rectilinear

forming, formed by, or characterized by straight lines.

aspect ratio

In any rectangular configuration ,the ratio of the longer dimension to the shorter.

diagonal

a line connecting two nonadjacent angles or vertices of a polygon or polyhedron.

square

A regular polygon with four equal sides and four right angles.

Parallelogram

a quadrilateral having both pairs of opposite sides parallel to each other.

Trapezoid

a quadrilateral having only two sides parallel

Trapezium

A quadrilateral having no two sides parallel.

Pentagon

A polygon with five sides and five angles

hexagon

a polygon with six sides and six angles

octagon

a polygon with eight sides and eight angles.

apothem

A perpendicular from the center to the regular polygon to one of its sides.

Cosecant

the trigonometric function defined as the ratio of the hypotenuse to the side opposite a given angle.

circle

a closed plane curve every point of which is equidistant from a fixed point within the curve.

arc

any part of the circumference of a circle.

Radius

a straight line extending from the center of a circle or sphere to the circumference or bounding surface

sector

a plane figure bounded by two radii and the included arc of a circle

diameter

a straight line extending through the center of a circle or sphere and meeting the circumference or bounding surface at each end.

center

The point within a circle or sphere equally distant from all points of the circumference or surface, or the point within a regular polygon equal distance from the vertices

circumference

The boundary lines of a closed curvilinear figure esp the perimeter of a circle.

pi

the symbol π denoting the ratio of the circumference of a circle to its diameter, constant equal to 3.14159+.

chord

the straight line segment between two points on a given curve.

major axis

The axis passing through the two foci of an ellipse.

minor axis

the axis of an ellipse that is perpendicular to the major axis at a point equidistant from the foci.

ellipse

a closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points, the foci, is a constant.

spiral

a plane curve generated by a point moving around a fixed point while constantly receding from or approaching it.

Parabola

a plane curve generated by a point so moving that it remains equidistant from a fixed line and a fixed point not on the line.

Asymptote

a straight line limiting a curve such that the perpendicular distance from the curve to the line approaches zero as the curve is extended to infinity.

hyperbola

a plane curve generated by a point so moving that the difference of the distances from two fixed points in the plane remains constant.

eccentric

not having the same center or center line.

off-center

not centered or at the center point.

concentric

having a common center, as circles, or spheres.

Centerline

An imaginary line that bisects a plane figure.

quadrant

an art of 90°, or any of the four quarters into which a plane figure is divided by two perpendicular lines, numbered counterclockwise from the upper right.

curve

a continuously bending line, without angles

concave

curved inward like the interior of a circular arc or hollow sphere

inflection

a change or curvature from convex to concave or vice versa.