In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal axes. A hyperboloid is the surface obtained from a hyperboloid of revolution by deforming it by means of directional scalings, or more generally, of an affine transformation.
In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry.
Mathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building; from the Pythagoreans of the sixth century BC onwards, to create forms considered harmonious, and thus to lay out buildings and their surroundings according to mathematical, aesthetic and sometimes religious principles; to decorate buildings with mathematical objects such as tessellations; and to meet environmental goals, such as to minimise wind speeds around the bases of tall buildings.
In geometry, a surface in 3-dimensional Euclidean space S is ruled if through every point of S, there is a straight line that lies on S. Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space.
In structural engineering, a tensile structure is a construction of elements carrying only tension and no compression or bending. The term tensile should not be confused with tensegrity, which is a structural form with both tension and compression elements. Tensile structures are the most common type of thin-shell structures.
The Shukhov Radio Tower, also known as the Shabolovka Tower, is a broadcasting tower deriving from the Russian avant-garde in Moscow designed by Vladimir Shukhov. The 160-metre-high (520 ft) free-standing steel diagrid structure was built between 1920 and 1922, during the Russian Civil War.
In mathematics, a developable surface is a smooth surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion. Conversely, it is a surface which can be made by transforming a plane. In three dimensions all developable surfaces are ruled surfaces. There are developable surfaces in four-dimensional space which are not ruled.
A diagrid is a framework of diagonally intersecting metal, concrete, or wooden beams that is used in the construction of buildings and roofs. It requires less structural steel than a conventional steel frame. Hearst Tower in New York City, designed by Norman Foster, uses 21 percent less steel than a standard design. The diagrid obviates the need for columns and can be used to make large column-free expanses of roofing. Another iconic building designed by Foster, 30 St Mary Axe, in London, UK, known as "The Gherkin", also uses the diagrid system.
Vladimir Grigoryevich Shukhov was a Russian and Soviet engineer-polymath, scientist and architect renowned for his pioneering works on new methods of analysis for structural engineering that led to breakthroughs in industrial design of the world's first hyperboloid structures, diagrid shell structures, tensile structures, gridshell structures, oil reservoirs, pipelines, boilers, ships and barges. He is also the inventor of the first cracking method.
The Church of Colònia Güell is an unfinished work by Antoni Gaudí. It was built as a place of worship for the people on a hillside in a manufacturing area in Santa Coloma de Cervelló, near Barcelona. Colònia Güell was the brainchild of Count Eusebi de Güell; who enlisted the help of architect Antoni Gaudí in 1898. However, work was not started until 1908, 10 years after commission. The plan for the building consisted of constructing two naves, an upper and a lower, two towers, and one forty-meter-high central dome. In 1914, the Güell family halted construction due to the death of Count Güell. At the time, the lower nave was almost complete so between the years of 1915 and 1917, it was completed and readied for use.
The Shukhov Tower on the Oka River is the world’s only diagrid hyperboloid transmission tower. It is located in Russia, in the western suburbs of Nizhny Novgorod, on the left bank of the Oka River near Dzerzhinsk. The tower is one of several structures designed by Russian engineer and scientist Vladimir Shukhov; its power lines, however, were decommissioned in 1989.
A gridshell is a structure which derives its strength from its double curvature, but is constructed of a grid or lattice.
The Shukhov Tower in Polibino, designed in 1896 by Russian engineer and architect Vladimir Shukhov, is the world's first diagrid hyperboloid structure. The tower is today located in the former estate of Yury Nechaev-Maltsov in the selo of Polibino in Lipetsk Oblast in Russia.
A saddle roof is a roof form which follows a convex curve about one axis and a concave curve about the other. The hyperbolic paraboloid form has been used for roofs at various times since it is easily constructed from straight sections of lumber, steel, or other conventional materials. The term is used because the form resembles the shape of a saddle.
Shukhov Rotunda was a round exhibition pavilion built for All-Russia Exhibition 1896 in Nizhny Novgorod, Russia. It was built in 1896 with a diagrid hanging cover and was the world's first Hyperboloid structure. It is named after Vladimir Shukhov, who designed it in 1895.
Antoni Gaudí i Cornet was a Catalan architect and designer, known as the greatest exponent of Catalan Modernism. Gaudí's works have a sui generis style. Most are located in Barcelona, including his main work, the Sagrada Família church.
A shell is a three-dimensional solid structural element whose thickness is very small compared to its other dimensions. It is characterized in structural terms by mid-plane stress which is both coplanar and normal to the surface. A shell can be derived from a plate in two steps: by initially forming the middle surface as a singly or doubly curved surface, then by applying loads which are coplanar to the plate's plane thus generating significant stresses. Materials range from concrete to fabric.
Café Fantasy or the Octopus was a coffeehouse situated in the town of Batumi, on the boulevard by the Black Sea, beside Shota Rustaveli State University. It used to face the old holiday house “Batumi”, recently replaced by Hilton Batumi.
