- acute: Composed only of acute angles.
- acute angle: An angle less than 90 degrees.
- altitude: The angular elevation of a celestial body above the horizon. 2. The perpendicular distance from the base of a geometric figure to the opposite vertex, parallel side, or parallel surface.
- angle: The figure made by two lines that meet. 2. The difference in direction of such intersecting lines, or the space within them. 3. A projecting or sharp corner. 4. A secluded area resembling a corner; a nook. 5. A hot-rolled structural steel section having an L-shape, designated by the prefix L followed by the length of each leg and their thickness. Also called angle iron. 6. The space between two lines diverging from a common point, or within two planes diverging from a common line: the figure so formed. 7. The amount of rotation needed to bring one line or plane into coincidence with another, measured in radians or in degrees, minutes, and seconds.
- angle of repose: The maximum slope, measured in degrees from the horizontal, at which loose solid material will remain in place without sliding.
- angle of slide: The minimum slope, measured in degrees from the horizontal, at which loose solid material will begin to slide or flow.
- batter: The slight inward slope sometimes given to a wall, tower, or pier.
- cant: To set at a slant from horizontal or vertical. 2. An oblique line or surface, as one formed by cutting off the corner of a square or cube.
- double angle: A structural member consisting of a pair of angles joined back to back. The parallel legs may be in contact or slightly separated.
- equal leg angle: An angle iron having legs of equal length.
- equiangular: Having all angles equal.
- exterior angle: The angle formed between any side of a polygon and an extended adjacent side.
- external angle: When two lines meet at an angle an internal (re-entrant) angle and an external angle (salient) are formed.
- inclination: Slope of any kind; especially in building that which has to do with decorative effect as contrasted with Batter, which is the slope of walls made thicker at the base for strength, or in a fortification for defense…
- inflection: A bend, angle, or similar change in the shape of a configuration, by means of which a change of relationship to some context or condition is indicated. 2. A change of curvature from convex to concave or vice versa.
- interior angle: The angle formed inside a polygon between any two adjacent sides.
- obtuse: Having an obtuse angle.
- obtuse angle: An angle greater than 90 degrees, but less than 180 degrees.
- polar angle: The angle formed by the polar axis and a radius vector in a polar coordinate system.
- radian: A unit of angular measure equal to the central angle subtending an arc equal in length to the radius: 360/2pie or approx. 57.3 degrees.
- reentrant: Reentering or pointing inward, as an interior angle of a polygon that is greater than 180 degrees.
- right angle: An angle of 90 degrees formed by the perpendicular intersection of two straight lines. 2. A triangle having a right angle.
- salient: Describing any projecting part or member, as a salient corner. 2. Prominent or conspicuous. 3. An outward projecting angle or part.
- seat angle: A short angle for supporting a beam in a shear-resisting connection.
- second: The 60th part of a minute of angular measure.
- shielding angle: The angle below which something can be seen when viewed through a louver. 2. The angle below which a light source can be seen.
- skew back: A sloping surface that serves as a support for the end of an arch.
- solid angle: An angle formed by three or more planes intersecting at a common point.
- squint corner: Angle of a building not ninety degrees.
- talus: The slope or inclination of any work, as a talus wall.
- toe: The forward, lower tip of the base of a footing or retaining wall, extended to give broader bearing and greater stability.
- unequal leg angle: An angle iron having legs of unequal length.
- visual angle: The angle that an object or detail subtends at the point of observation, usually measured in minutes of arc.
- shoulder angle: The angle of a bastion included between the face and the flank of a fortification.
- abscissa: A coordinate determined by measuring parallel to the x-axis. Also called x-coordinate.
- align: The faces of objects that are in line with each other, or when their center-lines lie on the same axis.
- axe: Axis.
- axial: Having an axis.
- axis of abscissas: The axis along which abscissas or x-values are measured in a Cartesian coordinate system.
- axis of ordinates: The axis along which ordinates or y-values are measured in a Cartesian coordinate system.
- center of vision: A point representing the intersection of the central axis of vision and the picture plane in linear perspective.
- central axis of vision: The sightline indicating the direction in which the viewer is looking in linear perspective, perpendicular to the picture plane.
- centre: When used familiarly, a center line, a middle line, an axis, whether of a surface or of a solid. Most common in these phrases: Between centers, from centers, from center to center, on centers, denoting the giving or taking measurements from such a line to the next corresponding similar line. 2. Same as centring.
- cone of vision: The field of vision radiating outward from the eye of the viewer in linear perspective, defined by sightlines forming a 15 degree to 30 degree angle with the central axis of vision. The cone of vision serves as a guide in determining what can be drawn in linear perspective without the appearance of distortion.
- crapaudine: Pivoted on a vertical axis.
- eccentricity: The amount by which an axis deviated from another parallel axis.
- en axe: French for on axis.
- 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.
- ordinate: Of a figure, having all its sides and angles equal (e.g. equilateral triangle). 2. Any one of a series of parallel chords of a conic section, in relation to the diameter that bisects each. It may be used to form an ellipse, so can be applied to the design of vaults. 3. A coordinate determined by measuring parallel to the y-axis. Also called y-coordinate.
- polar axis: The reference axis from which the polar angle is measured in a polar coordinate system.
- terminal: An end feature, as the tip of a building, or a figure terminating a vista or an axis. 2. One end of an electrical conductor.
- x-axis: The axis along which abscissas or x-values are measured in a Cartesian coordinate system. Also called axis of abscissas.
- y-axis: The axis along which ordinates or y-values are measured in a Cartesian coordinate system. Also called axis of ordinates.
- z-axis: The axis along which z-values are measured in a three-dimensional Cartesian coordinate system.
- base: The lowermost portion of a wall, column, pier, or other structure, usually distinctively treated and considered as an architectural unit. 2. The level at which earthquake motions are assumed to be imparted to a structure. 3. The line or surface forming the part of a geometric figure that is most nearly horizontal or on which it is supposed to stand, from which an altitude can be constructed.
- circle: A closed plane curve every point of which is equidistant from a fixed point within the curve.
- circumference: The boundary line of a closed curvilinear figure, especially the perimeter of a circle.
- concentric: Having a common center, as circles or spheres.
- diameter: The distance across a circle through its center.
- pi: A symbol denoting the ratio between the circumference of a circle and its diameter, a constant equal to 3.14159+.
- quadrant: Fourth part of a circle, hence an object or a street with a plan-form based on a fourth of the circumference of a circle… 2. Medieval term for a quadrangle or quad. 3. Octagonal part of a spire. 4. Quarter-round.
- radius: A straight line extending from the center of a circle or sphere to the circumference or bounding surface.
- round: Anything circular, or almost circular, such as a round (i.e. semicircular) arch, round-arched style (Rundbogenstil), round (As opposed to prismatic) billet, round church (i.e. circular on plan), round molding (e.g. torus), round pediment (i.e. segmental or semicircular), round ridge (i.e. with a half-cylindrical crest or ridge-tile), round tower (as in Irish exemplars with conical caps and certain other bell-towers in England and Italy), and round window (as in a Catherine-wheel or rose-window).
- coincident: Occupying the same place in space or time.
- right circular cone: A cone generated by rotating a right triangle about one of its legs.
- congruent: Coinciding at all points when superimposed.
- 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.
- polar coordinate system: A system for locating a point on a plane by its radius vector and polar angle.
- radius vector: A straight line segment that joins a variable point to the fixed origin of a polar coordinate system.
- rectangular coordinate system: A Cartesian coordinate system in which the axes or coordinate planes are perpendicular.
- x-coordinate: A coordinate determined by measuring parallel to the x-axis.
- y-coordinate: A coordinate determined by measuring parallel to the y-axis.
- z-coordinate: A coordinate determined by measuring parallel to the z-axis.
- concave: Curved inward like the interior of a circular arc or hollow sphere.
- convex: Curved or rounded outward like the exterior of a circle or sphere.
- curve: A continuously bending line, without angles.
- cycloid: A curve generated by a point in the plane of a circle when the circle is rolled along a straight line, keeping always in the same plane.
- evolute: The locus of the centers of curvature of, or the envelope of the normals to, another curve.
- French curve: A drafting aid in template form, enabling the draftsman to draw various curves or arcs thereof by guiding his pencil or drawing pen along an edge.
- involute: A curve traced by a point at the end of a string as the string is unwound from a stationary cylinder. 2. Curved spirally.
- isacoustic curve: Equal in acoustic correction.
- three-centred: Drawn from three centers; constructed on three centers.
- vertical curve: A smooth parabolic curve in the vertical plane for connecting two grades of different slope in order to avoid an abrupt transition.
- oblique: A paraline drawing of an oblique projection, having all lines and faces parallel to the picture plane drawn to exact scale, and all receding lines perpendicular to the picture plane shown at any convenient angle other than 90 degrees, sometimes at a reduced scale to offset the appearance of distortion. 2. Neither parallel nor perpendicular to a given line or surface.
- eccentric: Not having the same center or center line.
- geometric: Of or pertaining to shapes and forms which resemble or employ the simple rectilinear or curvilinear elements of geometry.
- geometry: A branch of mathematics that deals with the properties, measurement, and relationships of points, lines, angles, and solids, deduced from their defining conditions by means of certain assumed properties of space.
- height: Distance on a perpendicular line between two points. 2. Extent or distance upward from a given level to a fixed point.
- hexagon: A polygon having six sides and six angles.
- honeycomb: Any hexagonal structure or pattern, or one resembling such a structure or pattern. 2. Voids on a formed concrete surface, caused by segregation during placement or by insufficient consolidation.
- apothem: A perpendicular from the center of a regular polygon to one of its sides.
- 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.
- center line: A line representing an axis of symmetry; usually shown on drawings as a broken line.
- centerline: A broken line consisting of relatively long segments separated by single dashes or dots, used to represent the axis of a symmetrical element or composition. 2. An imaginary line that bisects a plane figure.
- diagonal: An inclined web member joining the top and bottom chords of a truss. 2. A straight line connecting two nonadjacent angles of a rectangle, used in subdividing a whole into proportionate parts or multiplying a basic unit of measurement or space.
- horizontal: Parallel to or operating in a plane parallel to the horizon.
- line: A thin, continuous mark made on a surface with a pencil, pen, or brush, as distinguished from shading or color. 2. The edge or contour of a shape. 3. A geometric element generated by a moving point and having extension without breadth or thickness.
- meridian: Line running north-south, i.e. where the great circle passing through the poles reaches the earth’s surface. Some meridians have been marked on church floors, complete with signs of the zodiac and graduations.
- parallel: Extending in the same direction, equidistant at all points, and never converging or diverging. 2. An arrangement of components in an electric circuit in which all positive terminals are connected to one conductor and all negative terminals are connected to a second conductor, the same voltage being applied to each component.
- parralel: An arrangement of components in an electric circuit in which all positive terminals are connected to one conductor and all negative terminals are connected to a second conductor, the same voltage being applied to each component. 2. Extending in the same direction, equidistant at all points, and never converging or diverging.
- plumb line: The line which supports a plumb or plumb bob.
- plummet: Same as plumb.
- shed line: The summit line of high ground, as being that at which the watershed begins; hence the ridge of a roof.
- skew lines: Any lines in space that are neither parallel nor intersecting.
- sky line: The upper outline or silhouette of a building as seen against the sky.
- vertical: Perpendicular to the plane of the horizon.
- vista: A long-range view from a point.
- octagon: An eight-sided building usually with a hipped roof popularized by Orson Squire Fowler in the 1850s. 2. A polygon having eight sides and eight angles.
- center: A point or place upon which interest, activity, or emotion focuses. Also see centerpiece. 2. The point within a ricle or sphere equally distant from all points of the circumference or surface, or the point within a regular polygon equally distant from the vertices.
- off-center: Not centered or at the center point.
- pentagon: A polygon having five sides and five angles.
- plane: A carpenter’s tool with an adjustable blade for smoothing, leveling and shaping wood. 2. 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.
- plane geometry: The branch of geometry that deals with plane figures.
- polygon method: A graphic technique for finding the vector sum of a coplanar system of several concurrent forces by drawing to scale each force vector in succession, with the tail of each at the head of the one preceding it, and completing the polygon with a vector that represents the resultant force, extending from the tail of the first to the head of the last vector.
- sector: A plane figure bounded by two radii and the included arc of a circle.
- segment: Plane figure contained by a straight line and part of the circumference of a circle: a segmental arch is therefore the shape of a segment, formed by its center far below the springing-line.
- cardinal points: North, south, east, and west, so elevations facing these points are cardinal fronts.
- vertices: The points opposite to and furthest from the base of a triangle, pyramid, or other figure having a base.
- aspect ratio: In any rectangular configuration, the ratio of the longer dimension to the shorter.
- golden rectangle: The basis of standardized sizes of components, in which the ratio of width to length is the same as that of length to the sum of the width and length.
- rectangle: A parallelogram having four right angles, especially one with sides of unequal lengths.
- rectangular: Having edges, surfaces, or faces that meet at right angles.
- rectilinear: Forming, formed by, or characterized by straight lines.
- parallelogram: A quadrilateral having both pairs of opposite sides parallel to each other.
- quadrilateral: A polygon having four sides and four angles.
- similar: Having corresponding sides proportional and corresponding angles equal.
- trapezium: A quadrilateral having no two sides parallel.
- cone: Cone-shaped building enclosing a tile-kiln, glass-furnace, etc. 2. Conical structure (e.g. the brick cone supporting the lantern in St. Paul’s Cathedral, London). 3. A small truncated cone of wood, steel, or plastic attached to a form tie to space and spread wall forms, leaving a neatly finished depression in the concrete surface to be filled or left exposed. 4. A solid whose surface is generated by a straight line, the generator, passing through a fixed point, the vertex, and moving along the intersection with a closed plane curve, the directrix.
- conic section: A plane curve formed by the intersection of a right circular cone with a plane.
- cube: A solid bounded by six equal square sides, the angle between any two adjacent faces being a right angle.
- cylinder: A cylindrical device for retaining the bolt of a lock until the tumblers have been pushed out of its way. 2. A solid bounded by two parallel planes and a surface generated by a straight line moving parallel to a fixed straight line and intersecting a closed plane curve in one of the planes.
- directrix: A fixed line used in the description of a curve or surface.
- dodecahedron: A regular polyhedron having 12 faces.
- edge: A line or narrow part where an area begins or ends. 2. Eave or eaves, or the line in which two surfaces join, or a border or verge… 3. A line at which a surface terminates or at which two surfaces of a solid meet.
- ellipse: The conic section resulting from cutting a cone obliquely through its curved surface. The adjective is elliptical.
- ellipsoid: A solid figure all plane sections of which are ellipses.
- frustum: A drum of a column or pier, or a stump that remains after demolition or after ages of weathering. 2. The portion of a conical solid left after cutting off the top with a plane parallel to the base.
- generator: A machine that converts mechanical energy into electrical energy. 2. The component of an absorption-refrigeration system that uses a heat source to remove excess water vapor from a saline solution. 3. An element that generates a geometric figure, especially a straight line that generates a surface by moving in a specified fashion. Also called generatrix.
- generatrix: An element that generates a geometric figure, especially a straight line that generates a surface by moving in a specified fashion.
- hexahedron: A regular polyhedron having six faces.
- hyperbola: Conic section formed by the intersection of a plane with both branches of a double cone (two identical cones on either side of the same vertex or pointed top). Hyperboloid is therefore a solid figure, some of the plane sections of which are hyperbolas. 2. A plane curve generated by a point so moving that the difference of the distances from two fixed points in the plane remains constant.
- icosahedron: A solid having twenty faces of an equilateral triangular shape. 2. A regular polyhedron having 20 faces.
- oblate: Flattened at the poles.
- oblate spheroid: A spheroid generated by rotating an ellipse about its minor axis.
- octahedron: A regular polyhedron having eight faces.
- parabola: Curve based on a conic section, that is the intersection of a cone with a plane parallel to its side. It resembles a three-centred arch, vertically emphasized. 2. 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. 3. A conic section formed by the intersection of a right circular cone with a plane parallel to a generator of the cone.
- Platonic solid: One of the five regular polyhedrons: tetrahedron, hexahedron, octahedron, dodecahedron, or icosahedron.
- polyhedron: A solid geometric figure bounded by plane faces.
- prism: A polyhedron having ends that are parallel, congruent polygons and sides that are parallelograms.
- prolate: Elongated along the polar diameter.
- prolate spheroid: A spheroid generated by rotating an ellipse about its major axis.
- regular: Uniformly or evenly formed or arranged. 2. Having all sides equal (equilateral) and all angles equal (equilangular). 3. Having all faces congruent regular polygons and all solid angles congruent.
- right circular cylinder: A cylinder generated by a rectangle about one of its sides.
- solid: Matter having relative firmness, coherence of particles, or persistence of form. 2. A geometric figure having the three dimensions of length, breadth, and thickness. Also called body.
- solid geometry: The branch of geometry that deals with solid figures and three-dimensional space.
- sphere: A solid generated by the revolution of a semicircle about its diameter, whose surface is at all points equidistant from the center.
- spheroid: A solid geometrical figure similar in shape to a sphere, as an ellipsoid.
- surface: Any figure having only two dimensions, as a plane or curved two-dimensional locus of points defining the boundary of a solid.
- tetrahedron: A regular polyhedron bounded by four plane faces.
- truncated: Having the apex, vertex, or end cut off by a plane, especially by one parallel to the base.
- vertex: The point at which the sides of an angle intersect. 2. The point opposite to and farthest from the base of a plane figure. 3. A point in a geometric solid common to three or more sides.
- volume: From Latin volvere, “to roll.” In architecture, the amount of space contained within a three-dimensional enclosure. 2. The extent a three-dimensional object or the amount of space that it occupies, measured in cubic units.
- polygon: A closed plane figure having three or more straight sides.
- polygonal: Having more than three angles and three sides.
- strain polygon: Also see strain polygon.
- helix: Any spiral, particularly a small volute or twist under the abacus of the Corinthian capital. 2. The volute of an Ionic capital.
- logarithmic spiral: A spiral which intersects all of its radiants at the same angle.
- slide rule: An instrument for making certain calculations or computations logarithmically.
- spiral: A plane curve generated by a point moving around a fixed point while constantly receding from or approaching it.
- square: A plane figure having four equal sides and four interior right angles. 2. An area of flooring, roofing, or the like, 10 feet square. 3. An open or parked rectangular space in a community. 4. An instrument, sometimes combined with measure, for determining right-angledness. 5. Adjective, descriptive of lines or planes at right angles to each other. 6. A unit for measuring roofing materials, equal to 100 square feet (9.3 square meters) of coverage.
- Euclidian geometry: Geometry based upon the postulates of Euclid, especially the postulate that only one line may be drawn through a given point parallel to a given line.
- trigonometry: The branch of mathematics that deals with the properties of triangles and trigonometric functions, and of their applications.
- 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.
- trapezoid: A quadrilateral having only two sides parallel.
- Egyptian triangle: The 3-4-5 triangle, fundamental to architecture and surveying because it enables a right angle to be constructed.
- hypotenuse: The side of a right triangle that is opposite the right angle.
- isosceles: Having two sides of equal length.
- relieving triangle: Approximate triangle above a lintel where masonry courses in a wall are corbelled over each other so avoiding any loading on the lintel (e.g. in Mycenaean work).
- right triangle: A triangle having a right angle.
- scalene: Having three unequal sides.
- triangle: A drawing instrument in the form of a mathematical right-angled triangle cut from a flat thin piece of wood, hard rubber, celluloid, or metal, or framed of three strips; used for drawing parallel lines at any given angle by sliding it along the fixed blade of a T-square, straight edge, or the like…
- triangle method: A graphic technique for finding the vector sum of two concurrent forces by displacing one force vector parallel to itself until its tail coincides with the head of the other and completing the triangle with a vector that represents the resultant force.
- cosecant: The trigonometric function defined as the ratio of the side opposite a given angle to the side adjacent to the angle.
- cosine: The trigonometric function defined as the ratio of the side adjacent to a given angle to the hypotenuse.
- cotangent: The trigonometric function defined as the ratio of the side 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.
- sine: The trigonometric function defined as the ratio of the side adjacent to a given angle to the hypotenuse.
- tangent: The trigonometric function defined as the ratio of the side opposite a given angle to the side adjacent to the angle. 2. Touching at a single point, as a straight line in relation to a curve, or in contact along a single line, as a plane with a cylinder.
- trignometric function: A function of an angle, as sine or cosine, expressed as the ratio of the sides of a right triangle.
Also see Architecture index.