In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays are also known as plane angles as they lie in the plane that contains the rays. Angles are also formed by the intersection of two planes; these are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection.
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.
In mathematics, the slope or gradient of a line is a number that describes the direction and steepness of the line. Often denoted by the letter m, slope is calculated as the ratio of the vertical change to the horizontal change between two distinct points on the line, giving the same number for any choice of points. A line descending left-to-right has negative rise and negative slope. The line may be physical – as set by a road surveyor, pictorial as in a diagram of a road or roof, or abstract.
The horizon is the apparent curve that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This curve divides all viewing directions based on whether it intersects the relevant body's surface or not.
A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases occur and coexist at equilibrium.
An azeotrope or a constant heating point mixture is a mixture of two or more components in fluidic states whose proportions cannot be altered or changed by simple distillation. This happens because when an azeotrope is boiled, the vapour has the same proportions of constituents as the unboiled mixture. Azeotropic mixture behavior is important for fluid separation processes.
In geometry, two geometric objects are perpendicular if their intersection forms right angles at the point of intersection called a foot. The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂. Perpendicular intersections can happen between two lines, between a line and a plane, and between two planes.
In geology, a fault is a planar fracture or discontinuity in a volume of rock across which there has been significant displacement as a result of rock-mass movements. Large faults within Earth's crust result from the action of plate tectonic forces, with the largest forming the boundaries between the plates, such as the megathrust faults of subduction zones or transform faults. Energy release associated with rapid movement on active faults is the cause of most earthquakes. Faults may also displace slowly, by aseismic creep.
The grade (US) or gradient (UK) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt". Often slope is calculated as a ratio of "rise" to "run", or as a fraction in which run is the horizontal distance and rise is the vertical distance.
The horopter was originally defined in geometric terms as the locus of points in space that make the same angle at each eye with the fixation point, although more recently in studies of binocular vision it is taken to be the locus of points in space that have the same disparity as fixation. This can be defined theoretically as the points in space that project on corresponding points in the two retinas, that is, on anatomically identical points. The horopter can be measured empirically in which it is defined using some criterion.
A transition curve is a spiral-shaped length of highway or railroad track that is used between sections having different profiles and radii, such as between straightaways (tangents) and curves, or between two different curves.
In field hockey, each player carries a stick and cannot take part in the game without it. The stick for an adult is usually in the range 89–95 cm (35–38 in) long. A maximum length of 105 cm (41.3") was stipulated from 2015. The maximum permitted weight is 737 grams. The majority of players use a stick in the range 19 oz to 22 oz. Traditionally hockey sticks were made of hickory, ash or mulberry wood with the head of the sticks being hand carved and therefore required skilled craftsmen to produce. Sticks made of wood continue to be made but the higher grade sticks are now manufactured from composite materials which were first permitted after 1992. These sticks usually contain a combination of fibreglass, aramid fiber and carbon fibre in varying proportions according to the characteristics required.
Strike-slip tectonics or wrench tectonics is a type of tectonics that is dominated by lateral (horizontal) movements within the Earth's crust. Where a zone of strike-slip tectonics forms the boundary between two tectonic plates, this is known as a transform or conservative plate boundary. Areas of strike-slip tectonics are characterised by particular deformation styles including: stepovers, Riedel shears, flower structures and strike-slip duplexes. Where the displacement along a zone of strike-slip deviates from parallelism with the zone itself, the style becomes either transpressional or transtensional depending on the sense of deviation. Strike-slip tectonics is characteristic of several geological environments, including oceanic and continental transform faults, zones of oblique collision and the deforming foreland of zones of continental collision.
Cross slope, cross fall or camber is a geometric feature of pavement surfaces: the transverse slope with respect to the horizon. It is a very important safety factor. Cross slope is provided to provide a drainage gradient so that water will run off the surface to a drainage system such as a street gutter or ditch. Inadequate cross slope will contribute to aquaplaning. On straight sections of normal two-lane roads, the pavement cross section is usually highest in the center and drains to both sides. In horizontal curves, the cross slope is banked into superelevation to reduce steering effort and lateral force required to go around the curve. All water drains to the inside of the curve. If the cross slope magnitude oscillates within 1–25 metres (3–82 ft), the body and payload of high (heavy) vehicles will experience high roll vibration.
An architectural drawing or architect's drawing is a technical drawing of a building that falls within the definition of architecture. Architectural drawings are used by architects and others for a number of purposes: to develop a design idea into a coherent proposal, to communicate ideas and concepts, to convince clients of the merits of a design, to assist a building contractor to construct it based on design intent, as a record of the design and planned development, or to make a record of a building that already exists.
The geometric design of roads is the branch of highway engineering concerned with the positioning of the physical elements of the roadway according to standards and constraints. The basic objectives in geometric design are to optimize efficiency and safety while minimizing cost and environmental damage. Geometric design also affects an emerging fifth objective called "livability", which is defined as designing roads to foster broader community goals, including providing access to employment, schools, businesses and residences, accommodate a range of travel modes such as walking, bicycling, transit, and automobiles, and minimizing fuel use, emissions and environmental damage.
Track geometry is concerned with the properties and relations of points, lines, curves, and surfaces in the three-dimensional positioning of railroad track. The term is also applied to measurements used in design, construction and maintenance of track. Track geometry involves standards, speed limits and other regulations in the areas of track gauge, alignment, elevation, curvature and track surface. Standards are usually separately expressed for horizontal and vertical layouts although track geometry is three-dimensional.
In astronomy, geography, and related sciences and contexts, a direction or plane passing by a given point is said to be vertical if it contains the local gravity direction at that point.
The moment-area theorem is an engineering tool to derive the slope, rotation and deflection of beams and frames. This theorem was developed by Mohr and later stated namely by Charles Ezra Greene in 1873. This method is advantageous when we solve problems involving beams, especially for those subjected to a series of concentrated loadings or having segments with different moments of inertia.
