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Unbounded quadric surface
In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal
Hyperboloid
Type of unbounded quadratic surface-shaped building or work
Hyperboloid structures are architectural structures designed using a hyperboloid in one sheet. Often these are tall structures, such as towers, where the
Hyperboloid_structure
Device which rejects waste heat to the atmosphere through the cooling of a water stream
Cooling towers vary in size from small roof-top units to very large hyperboloid structures that can be up to 200 metres (660 ft) tall and 100 metres
Cooling_tower
This page is a list of hyperboloid structures. These were first applied in architecture by Russian engineer Vladimir Shukhov (1853–1939). Shukhov built
List of hyperboloid structures
List_of_hyperboloid_structures
Model of n-dimensional hyperbolic geometry
In geometry, the hyperboloid model, also known as the Minkowski model after Hermann Minkowski, is a model of n-dimensional hyperbolic geometry in which
Hyperboloid_model
1926–1927 novel by Aleksey Nikolayevich Tolstoy
The Garin Death Ray, also known as The Death Box and The Hyperboloid of Engineer Garin (Russian: Гиперболоид инженера Гарина), is a science-fiction novel
The_Garin_Death_Ray
Type of non-Euclidean geometry
some regions, where they locally resemble the hyperbolic plane. The hyperboloid model of hyperbolic geometry provides a representation of events one
Hyperbolic_geometry
circular section is a circle on a quadric surface (such as an ellipsoid or hyperboloid). It is a special plane section of the quadric, as this circle is the
Circular_section
Model of hyperbolic geometry
projection of the hyperboloid model (Hy) with as center the center of the hyperboloid (O) and the projection plane tangent to the hyperboloid. Given two distinct
Beltrami–Klein_model
Device used to join electrical conductors
form the hyperboloid structure are usually anchored at each end by bending the tip into a groove or notch in the housing. Whilst hyperboloid contacts
Electrical_connector
Geometric surface
the hyperboloid model of the hyperbolic plane, the hyperboloid is referred to as a pseudosphere. This usage of the word is because the hyperboloid can
Pseudosphere
Basilica under construction since 1882 in Barcelona, Spain
central columns of porphyry supporting a great hyperboloid surrounded by two rings of twelve hyperboloids (currently under construction). The central vault
Sagrada_Família
1965 Soviet Union film
The Hyperboloid of Engineer Garin (Russian: Гиперболоид инженера Гарина, translit. Giperboloid inzhenera Garina) also abbreviated as Engineer Garin is
The Hyperboloid of Engineer Garin (film)
The_Hyperboloid_of_Engineer_Garin_(film)
as "Garin i Giperboloidy" (Garin & The Hyperboloids), after Aleksey Nikolayevich Tolstoy's novel The Hyperboloid of Engineer Garin, was formed in 1981
Kino_discography
Four-dimensional associative algebra over the reals
norm contains exactly two opposite points on this hyperboloid, one on each sheet; and the hyperboloid does not contain any other point. The algebra generated
Split-quaternion
Model of hyperbolic geometry
related to the hyperboloid model projectively. If we have a point [t, x1, ..., xn] on the upper sheet of the hyperboloid of the hyperboloid model, thereby
Poincaré_disk_model
Non-Euclidean geometry
hyperboloid model is immediate through the action of the connected component of S O ( n , 1 ) {\displaystyle \mathrm {SO} (n,1)} on the hyperboloid.
Hyperbolic_space
Locus of the zeros of a polynomial of degree two
three-dimensional space, quadrics include ellipsoids, paraboloids, and hyperboloids. More generally, a quadric hypersurface (of dimension D) embedded in
Quadric
Catalan architect (1852–1926)
helicoid form to movement and the hyperboloid to light. Concerning ruled surfaces, he said: Paraboloids, hyperboloids and helicoids, constantly varying
Antoni_Gaudí
Russian polymath, engineer, scientist and architect (1853–1939)
geometry, are known today as hyperboloids of revolution. Shukhov developed not only many varieties of light-weight hyperboloid towers and roof systems, but
Vladimir_Shukhov
Product of the principal curvatures of a surface
everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus. Gaussian curvature is an intrinsic measure
Gaussian_curvature
Communications and observation tower in Guangzhou (Canton), China
official opening in December 2011. The Canton Tower's twisted shape or hyperboloid structure corresponds to the Russian Empire patent No. 1896, dated 12
Canton_Tower
Lines not in the same plane
the surface of revolution swept out by L is a hyperboloid of one sheet. For instance, the three hyperboloids visible in the illustration can be formed in
Skew_lines
Surface containing a line through every point
distinct lines that lie on the surface. The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces. The plane is the only surface
Ruled_surface
Three-dimensional orthogonal coordinate system
when the boundary conditions are defined on an oblate spheroid or a hyperboloid of revolution. For example, they played an important role in the calculation
Oblate_spheroidal_coordinates
Constructivist broadcasting tower in Moscow, Russia
during the Russian Civil War. Vladimir Shukhov invented the world's first hyperboloid structure in the year 1890. Later he wrote a book, Rafters, in which
Shukhov_Tower
Configurations of a system that do or do not satisfy classical equations of motion
another on-shell theorem. Mass shell is a synonym for mass hyperboloid, meaning the hyperboloid in energy–momentum space describing the solutions to the
On_shell_and_off_shell
build a new concrete cooling tower. This led to his work producing the hyperboloid design of cooling towers at the Staatsmijn Emma in 1918; the towers were
Frederik_van_Iterson
Maximal and minimal curvature at a point of a surface
Concave ellipsoid Concave cylinder Hyperboloid surface = 0 Concave cylinder Plane Convex cylinder > 0 Hyperboloid surface Convex cylinder Convex ellipsoid
Principal_curvature
Water tower in Polibino, Lipetsk Oblast, Russia
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
Shukhov_Tower_in_Polibino
Tall structure for long-distance viewing
with bird observation towers to assist with viewing. Hyperboloid structures have a hyperboloid shape that is usually lattice framework and an observation
Observation_tower
Czechoslovak aircraft detection system
target on a hyperboloid. A second side site provides a second TDOA and hence a second hyperboloid. The intersection of these two hyperboloids places the
Tamara_passive_sensor
Russian actress (1938–2026)
for her roles in Soviet cinema, including Comrade Arseny (1964), The Hyperboloid of Engineer Garin (1965), and The Snow Queen (1967). Klimova died in
Natalya_Klimova_(actress)
Roman Catholic cathedral in Brazil
and was completed and dedicated on May 31, 1970. The cathedral is a hyperboloid structure constructed from 16 concrete columns weighing 90 tons each
Cathedral_of_Brasília
Plane curve: conic section
paraboloid Hyperboloid of one sheet Hyperboloid of two sheets Elliptic cone Hyperbolic cylinder Hyperbolic paraboloid Hyperboloid of one sheet Hyperboloid of
Hyperbola
First-level administrative division of Russia
world's first hyperboloid structure—a steel open-work lattice tower—is located in Polibino, Dankovsky District of Lipetsk Oblast. The hyperboloid tower was
Lipetsk_Oblast
American satellite-based radio navigation service
its extensions) forms the axis of the hyperboloid. The receiver is located at the point where three hyperboloids intersect. It is sometimes incorrectly
Global_Positioning_System
sections with one (blue) and two (purple) sheeted hyperboloids. The red points are umbilic points. Hyperboloid of one sheet (see diagram) Semi-axes: a = 0.67
Dupin's_theorem
Radar detection system
target on a hyperboloid. A second side site provides a second TDOA and hence a second hyperboloid. The intersection of these two hyperboloids places the
VERA_passive_sensor
Structural design which uses diagonal members instead of columns
mathematician during the late 19th and early 20th century he created hyperboloid, thin shell and tensile structures of extraordinary refinement and elegance
Diagrid
Greek mathematician and physicist (c. 287 – 212 BC)
segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral. Archimedes' other mathematical
Archimedes
Algebraic curve in mathematics
\mathbb {H} ^{2}} . Specifically, the intersections of the Minkowski hyperboloid with quadric surfaces characterized by a certain constant-angle property
Elliptic_curve
From Within My One and Only 25 Natalya Klimova 87 Russia Actress The Hyperboloid of Engineer Garin The Snow Queen 26 Ahmed Nimal 62 Maldive Islands Actor
2026_in_film
Oblate spheroid Prolate spheroid Ellipsoid Cone (geometry) Hyperboloid of one sheet Hyperboloid of two sheets Hyperbolic paraboloid (a ruled surface) Paraboloid
List_of_surfaces
Surname list
in Aleksey Tolstoy's novel The Garin Death Ray (also in the films The Hyperboloid of Engineer Garin and Failure of Engineer Garin) Seth Garin, character
Garin_(surname)
Group of unitary complex matrices with determinant of 1
that any point p on this hyperboloid can be used as a pole of a sinusoidal wave according to Euler's formula. The hyperboloid is stable under SU(1, 1)
Special_unitary_group
Critical point on a surface graph which is not a local extremum
to as "the saddle surface" or "the standard saddle surface") and the hyperboloid of one sheet. The Pringles potato chip or crisp is an everyday example
Saddle_point
Power plant in Michigan City, Indiana, US
approximately 1 mile of Lake Michigan lakefront space. The use of a hyperboloid cooling tower at the station has been mistaken as evidence for a nuclear
Michigan City Generating Station
Michigan_City_Generating_Station
Spacetime manifold
conditions. (In turn, the leading symbol of the wave operator is that of a hyperboloid.) This is relevant to Albert Einstein's theory of general relativity
Globally_hyperbolic_spacetime
Field of mathematics dealing with three-dimensional Euclidean spaces
cylinders the sphere other quadrics: spheroid, ellipsoid, paraboloid and hyperboloids. Advanced topics include: projective geometry of three dimensions (leading
Solid_geometry
Point at infinity in hyperbolic geometry
model (but rays parallel to the positive y-axis approach it). In the hyperboloid model there are no ideal points. Ideal triangle Ideal polyhedron Points
Ideal_point
Shaped charge used in nuclear weapons
spherically diverging front into a flat one, the boundary shape must be a hyperboloid, and so on. Several boundaries can be used to reduce aberrations (deviations
Explosive_lens
Bridge in Manchester, England
in the 1996 Manchester bombing. The bridge is shaped in the form of a hyperboloid and links the Marks & Spencer/Selfridges building to the Manchester Arndale
Corporation_Street_Bridge
Freestanding framework tower
Eurasia. A lattice towers is often designed as either a space frame or a hyperboloid structure. Before 1940, they were used as radio transmission towers especially
Lattice_tower
Federal capital of Brazil
Cathedral of Brasília is based in the hyperboloid of revolution which sections are asymmetric. The hyperboloid structure itself is a result of 16 identical
Brasília
Geometric shape
section Cylinder (geometry) Democritus Elliptic cone Generalized conic Hyperboloid List of shapes Pyrometric cone Quadric Rotation of axes Ruled surface
Cone
Shukhov in Russia and Antoni Gaudí in Barcelona pioneered the use of hyperboloid structures; in the Sagrada Família, Gaudí also incorporated hyperbolic
Mathematics_and_architecture
Quadric surface with one axis of symmetry and no center of symmetry
paraboloid opens upward. A hyperbolic paraboloid (not to be confused with a hyperboloid) is a doubly ruled surface shaped like a saddle. In a suitable coordinate
Paraboloid
Soviet musician and actor (1962–1990)
Гиперболоиды, lit. 'Garin and the hyperboloids'). The name was an homage to the classic Russian novel The Hyperboloid of Engineer Garin by Aleksey Tolstoy
Viktor_Tsoi
Former observation tower in northern England
New Brighton Tower was a steel lattice hyperboloid observation tower at New Brighton in the town of Wallasey, Cheshire (now in the Borough of Wirral,
New_Brighton_Tower
Rural locality (selo) in Lipetsk Oblast, Russia
palace, English park, regular gardens, ponds, and more. The world's first hyperboloid structure by Vladimir Shukhov is located on the grounds of the estate
Polibino, Dankovsky District, Lipetsk Oblast
Polibino,_Dankovsky_District,_Lipetsk_Oblast
Fictional weapon
G. Wells The Garin Death Ray, title weapon in The Hyperboloid of Engineer Garin (1927): "hyperboloid", a highly concentrated collimated light beam weapon
Raygun
Study of angle-preserving transformations
A hyperboloid of one sheet, which is a surface of revolution contains a pencil of circles which is mapped onto a pencil of circles. A hyperboloid of
Inversive_geometry
Maximally symmetric Lorentzian manifold with a negative cosmological constant
manifold in the hyperboloid model of p-dimensional hyperbolic space, while the metric also takes on the equation of the metric in the hyperboloid model, except
Anti-de_Sitter_space
Curve whose normals converge asymptotically
cases of Apollonius' problem. In the hyperboloid model horocycles are represented by intersections of the hyperboloid with planes that generate parabolas
Horocycle
Lie group of Lorentz transformations
intersection of a null plane, t = z + c2, with a hyperboloid, t2 − x2 − z2 = c3. The case c3 = 0 has the hyperboloid degenerate to a light cone with the orbits
Lorentz_group
possible surfaces can be reduced to. Starting from the foreground: the Hyperboloid (negative), the Cylinder (null), and the Sphere (positive Gaussian curvature)
Curved_structures
City in Krasnodar Krai, Russia
Scientific Library, founded in 1900. Krasnodar is home to the steel lattice hyperboloid tower built by the Russian engineer and scientist Vladimir Grigorievich
Krasnodar
Television transmitter and hotel near Liberec, Czech Republic
Measuring 94 m (308 ft), it is made of reinforced concrete shaped in a "hyperboloid" form. The tower was designed by architect Karel Hubáček, who was assisted
Ještěd_Tower
Limit of the tangent line at a point that tends to infinity
{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=0.} Similarly, the hyperboloid x 2 a 2 − y 2 b 2 − z 2 c 2 = 1 {\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac
Asymptote
Estonian musical group
covered Vennaskond's hit song Insener Garini Hüperboloid (Engineer Garin's Hyperboloid) in Estonia in front of a 60 000 strong crowd during their gig in Tartu
Vennaskond
Capital and most populous city of Russia
architect was Vladimir Shukhov, famous for Shukhov Tower, just one of many hyperboloid towers designed by Shukhov. It was built between 1919 and 1922 as a transmission
Moscow
Upper-half plane model of hyperbolic non-Euclidean geometry
to the flat Euclidean plane. From the hyperboloid model (a representation of the hyperbolic plane on a hyperboloid of two sheets embedded in 3-dimensional
Poincaré_half-plane_model
Moveable linkage with zero mobility
rulings of a hyperboloid of one sheet. As the linkage moves, the associated hyperboloid changes continuously, but remains a hyperboloid of one sheet.
Overconstrained_mechanism
Polynomial with all terms of degree two
eigenvalues of A are non-zero, then the solution set is an ellipsoid or a hyperboloid.[citation needed] If all the eigenvalues are positive, then it is an
Quadratic_form
Type of roof structure
Mary of the Assumption and St. Mary's Cathedral, Tokyo. Hyperboloid structure List of hyperboloid structures Metro San Lázaro Xavier University A Dictionary
Saddle_roof
German mathematician and physicist (1864–1909)
The mathematical basis of Minkowski space can also be found in the hyperboloid model of hyperbolic space already known in the 19th century, because
Hermann_Minkowski
Device that cools air through the evaporation of water
Large hyperboloid cooling towers made of structural steel for a power plant in Kharkiv (Ukraine)
Evaporative_cooler
other being the Shukhov Tower built between 1920-1922 in Moscow) diagrid hyperboloid transmission tower. It is located in Russia, in the western suburbs of
Shukhov Tower on the Oka River
Shukhov_Tower_on_the_Oka_River
1954 U.S. thermonuclear weapon test in the Marshall Islands
of shock wave emergence was considerably higher compared to previous hyperboloid lenses, enabling better and more accurate compression (LA-1632, table
Castle_Bravo
Geodesic dome greenhouse in St. Louis, MO
Center, a museum whose original 1963 planetarium building has a unique hyperboloid structure Mitchell Park Horticultural Conservatory List of botanical
Climatron
(Red Dwarf). Natalya Klimova, 87, Russian actress (Comrade Arseny, The Hyperboloid of Engineer Garin, The Snow Queen). Roman Kofman, 89, Ukrainian conductor
Deaths_in_February_2026
By Vladimir Shukhov 1896 Tensile structure By Vladimir Shukhov 1896 Hyperboloid structure By Vladimir Shukhov, see also Shukhov Tower 1897 Gridshell
Timeline of Russian innovation
Timeline_of_Russian_innovation
Maximally symmetric Lorentzian manifold with a positive cosmological constant
The n-dimensional de Sitter space is the submanifold described by the hyperboloid of one sheet − x 0 2 + ∑ i = 1 n x i 2 = α 2 , {\displaystyle -x_{0}^{2}+\sum
De_Sitter_space
stations. The list includes both wooden and reinforced concrete (RC) hyperboloid cooling towers. Spray ponds and finned tube cooling arrays are not included
List of cooling towers at UK power stations
List_of_cooling_towers_at_UK_power_stations
Soviet rock band
(Russian: Гарин и гиперболоиды, lit. 'Garin and the Hyperboloids') after Aleksei Tolstoi's novel The Hyperboloid of Engineer Garin. The group consisted of Viktor
Kino_(band)
Building in Spain, Spain
pagoda, with each floor rotated 45º from the lower one and joined with a hyperboloid ruled surface. It was controversially demolished in 1999, despite being
La_Pagoda
Venue at the Massachusetts Institute of Technology
42°21′29″N 71°05′42″W / 42.35812°N 71.09507°W / 42.35812; -71.09507 Kresge Auditorium (MIT Building W16) is an auditorium structure at the Massachusetts
Kresge_Auditorium
NASA space telescope launched in 1999
use a Wolter telescope consisting of nested cylindrical paraboloid and hyperboloid surfaces coated with iridium or gold. X-ray photons would be absorbed
Chandra_X-ray_Observatory
Commercial precinct in Perth, Western Australia
completed in 2024, and is 36 stories high with a distinctive narrow hyperboloid shape. The building was required to be narrow to ensure the view from
Mia_Yellagonga
Structure whose members are only in tension
surface and is often used in both in lightweight shell structures (see hyperboloid structures). True ruled surfaces are rarely found in tensile structures
Tensile_structure
could be produced using a combination of a paraboloid with either a hyperboloid or ellipsoid secondary. The three simplest designs are outlined and are
Hans_Wolter
Observation tower in Pennsylvania, United States
The Gettysburg National Tower was a 307-foot (94 m) hyperboloid observation tower that overlooked the Gettysburg National Military Park and Gettysburg
Gettysburg_National_Tower
Conic sections with the same foci
confocal quadrics come in two types: triaxial ellipsoids, hyperboloids of one sheet, and hyperboloids of two sheets; and elliptic paraboloids, hyperbolic paraboloids
Confocal_conic_sections
was open to staff and students at the university. Aspire is a type of hyperboloid structure, designed by Ken Shuttleworth and Make Architects. It consists
Aspire_(sculpture)
the water Typically, natural draft cooling towers are constructed as hyperboloid lattice steel and concrete. The shape is for structure not airflow. Mechanical
Glossary_of_power_generation
Place in Masovian Voivodeship, Poland
brewery, founded in the 18th century, and the science park with the unique hyperboloid water tower. The city has experienced several foreign invasions and was
Ciechanów
Type of parabolic antenna with a convex secondary reflector
at the far focus of the hyperboloid, while the focus of the primary reflector coincides with the near focus of the hyperboloid. Usually the secondary reflector
Cassegrain_antenna
Geometric model of the physical space
six types of non-degenerate quadric surfaces: Ellipsoid Hyperboloid of one sheet Hyperboloid of two sheets Elliptic cone Elliptic paraboloid Hyperbolic
Three-dimensional_space
Thin-walled structural element
called gridshell structures, often in the form of a geodesic dome or a hyperboloid structure Membrane structures, which include fabric structures and other
Shell_(structure)
HYPERBOLOID
HYPERBOLOID
HYPERBOLOID
HYPERBOLOID
Boy/Male
Tamil
Love
Girl/Female
Hindu
Little one
Boy/Male
American, British, Christian, English, German, Hindu, Indian
Wealthy Wolf
Girl/Female
Indian
Flute, Instrument played by Lord Krishna
Surname or Lastname
English
English : variant of Seagrave.
Boy/Male
Hindu
Confined
Girl/Female
Arabic, Muslim
Silver
Girl/Female
Celtic, Christian, French, Gaelic, German, Irish, Scottish
Of the White Shoulders; Form of Finola
Boy/Male
Hindu, Indian, Telugu
Good Natured Person; Gift of Heart
Surname or Lastname
English (Cheshire)
English (Cheshire) : probably a habitational name from a lost or minor place.Americanized spelling of German Äckerle or Ackerlein, or Swiss Aecherli, all diminutives of Acker.
HYPERBOLOID
HYPERBOLOID
HYPERBOLOID
HYPERBOLOID
HYPERBOLOID
n.
Sheet; surface; all that portion of a surface that is continuous in such a way that it is possible to pass from any one point of the portion to any other point of the portion without leaving the surface. Thus, some hyperboloids have one nappe, and some have two.
a.
Having some property that belongs to an hyperboloid or hyperbola.
n.
A surface whose equation in three variables is of the second degree. Spheres, spheroids, ellipsoids, paraboloids, hyperboloids, also cones and cylinders with circular bases, are quadrics.
n.
A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface.