Catenary archA catenary arch is a type of architectural arch that follows an inverted catenary curve. The catenary curve has been employed in buildings since ancient times. It is not a parabolic arch, although the non-circumferential curves used in arch designs (parabola, catenary, and weighted catenary) look similar, and match at shallow profiles, so a catenary is often misclassified as a parabola (per Galileo, "the [hanging] chain fits its parabola almost perfectly").
CurveIn mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point.
ParabolaIn mathematics, a parabola ( pə-RA-bə-lə) 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. One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from the directrix and the focus.
CatenoidIn geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. It was formally described in 1744 by the mathematician Leonhard Euler. Soap film attached to twin circular rings will take the shape of a catenoid.
ChainSeries of connected links which are typically made of metal A common metal short-link chain Roller chains A chain is a serial assembly of connected links typically made of metal, with an overall character similar to that of a rope in that it is flexible and curved in compression, but linear, rigid, and load-bearing in tension. A chain may consist of two or more links.
WeightIn science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition. Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar quantity, the magnitude of the gravitational force.
Wire ropeWire rope is composed of as few as two solid metal wires twisted into a helix that forms a composite rope, in a pattern known as laid rope. Larger diameter wire rope consists of multiple strands of such laid rope in a pattern known as cable laid. Manufactured using an industrial machine known as a strander, the wires are fed through a series of barrels and spun into their final composite orientation.
GeometryBranch of mathematics GeometryProjecting a sphere to a plane Branches Euclidean Non-Euclidean Elliptic Spherical Hyperbolic Non-Archimedean geometry Projective Affine Synthetic Analytic Algebraic Arithmetic Diophantine Differential Riemannian Symplectic Discrete differential Complex Finite Discrete/Combinatorial Digital Convex Computational Fractal Incidence Noncommutative geometry Noncommutative algebraic geometry ConceptsFeaturesDimension Straightedge and compass constructions Angle Polytope Centroid Diagonal Orthogonality (Perpendicular) Parallel Vertex Congruence Similarity Symmetry Zero-dimensional Point One-dimensional Line Line segment Ray Curve Geodesic Length Two-dimensional Surface Plane Area Polygon Simple Convex Concave Star Regular Reuleaux Triangle Centers Altitude Hypotenuse Pythagorean theorem Circular Reuleaux Hyperbolic Ideal Spherical Quadrilateral Parallelogram Rectangle Square Rhombus Rhomboid Trapezoid Kite Circle Radius Diameter Circumference Disk Area Three-dimensional Surface area Volume Polyhedron Platonic Solid Tetrahedron Reuleaux cuboid Cube Octahedron Dodecahedron Icosahedron Pyramid Star Toroidal Ideal Solid of revolution Sphere Great circle Cylinder Cone Four - other-dimensional 4-polytope Simplex 5-cell Hypercube Tesseract n-sphere Geometers by name Aida Aryabhata Ahmes Alhazen Apollonius Archimedes Atiyah Baudhayana Bolyai Brahmagupta Cartan Chern Coxeter Descartes Euclid Euler Gauss Gromov Hilbert Huygens Jyeṣṭhadeva Kātyāyana Khayyám Klein Lobachevsky Manava Minkowski Minggatu Pascal Pythagoras Parameshvara Poincaré Riemann Sakabe Sijzi al-Tusi Veblen Virasena Yang Hui al-Yasamin Zhang List of geometers by period BCE Ahmes Baudhayana Manava Pythagoras Euclid Archimedes Apollonius 1–1400s Zhang Kātyāyana Aryabhata Brahmagupta Virasena Alhazen Sijzi Khayyám al-Yasamin al-Tusi Yang Hui Parameshvara 1400s–1700s Jyeṣṭhadeva Descartes Pascal Huygens Minggatu Euler Sakabe Aida 1700s–1900s Gauss Lobachevsky Bolyai Riemann Klein Poincaré Hilbert Minkowski Cartan Veblen Coxeter Chern Present day Atiyah Gromov vte Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
Gravitational fieldIn physics, a gravitational field or gravitational acceleration field is a vectorfield used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain gravitational phenomena, such as the gravitational force field exerted on another massive body. It has dimension of acceleration (L/T) and it is measured in units of newtons per kilogram (N/kg) or, equivalently, in meters per second squared (m/s).PhysicsPhysics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. It is one of the most fundamental scientific disciplines. A scientist who specializes in the field of physics is called a physicist. Physics is one of the oldest academic disciplines.
American EnglishAmerican English, sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States. English is the most widely spoken language in the U.S., as well as the common language used in government, education, and commerce in all 50 states, the District of Columbia, and in all U.S. territories except Puerto Rico. Since the late 20th century, American English has become the most influential form of English worldwide.British EnglishBritish English is the set of varieties of the English language native to the United Kingdom, especially Great Britain. More narrowly, it can refer specifically to the English language in England, or, more broadly, to the collective dialects of English throughout the United Kingdom taken as a single umbrella variety, for instance additionally incorporating Scottish English, Welsh English, and Northern Irish English.*As an Amazon Associate I earn from qualifying purchases.