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In Riemannian geometry, the filling radius of a Riemannian manifold X is a metric invariant of X. It was originally introduced in 1983 by Mikhail Gromov
Filling_radius
Line segment in a circle or sphere from its center to its perimeter or surface
plane. Bend radius Filling radius in Riemannian geometry Mean radius Radius of convergence Radius of convexity Radius of curvature Radius of gyration
Radius
Inequality in Riemannian geometry
key ideas of the proof is the introduction of filling invariants, namely the filling radius and the filling volume of X. Namely, Gromov proved a sharp inequality
Gromov's systolic inequality for essential manifolds
Gromov's_systolic_inequality_for_essential_manifolds
Form of differential geometry
its fundamental group. The proof involves a new invariant called the filling radius, introduced by Gromov, defined as follows. Denote by A the coefficient
Systolic_geometry
Geometric figure which is "snugly enclosed" by another figure
circumscribed circle or circumcircle. The inradius or filling radius of a given outer figure is the radius of the inscribed circle or sphere, if it exists.
Inscribed_figure
Measure of the size of an atom
atomic radius. Five widely used definitions of atomic radius are covalent radius, Van der Waals radius, charge radius, ionic radius, and metallic radius. Typically
Atomic_radius
volume than the original manifold M. Filling radius Pu's inequality Systolic geometry Gromov, Mikhail (1983). "Filling Riemannian Manifolds". J. Diff. Geom
Filling_area_conjecture
Type of 3D molecular model
In chemistry, a space-filling model, also known as a calotte model, is a type of three-dimensional (3D) molecular model where the atoms are represented
Space-filling_model
systolic inequality for essential manifolds Essential manifold Filling radius Filling area conjecture Bolza surface First Hurwitz triplet Hermite constant
List of differential geometry topics
List_of_differential_geometry_topics
Russian-French mathematician
step in constructing coordinates on the limiting space is an injectivity radius estimate for closed manifolds. Cheeger, Gromov, and Michael Taylor localized
Mikhael Gromov (mathematician)
Mikhael_Gromov_(mathematician)
Pulsar in the constellation Sagittarius
with a radius of 5–6 solar radii. Hessels and collaborators state that the companion may be a "bloated main-sequence star, possibly still filling its Roche
PSR_J1748−2446ad
Principle of atomic physics
measured electron configuration of the copper atom is [Ar] 3d10 4s1. By filling the 3d subshell, copper can be in a lower energy state. A special exception
Aufbau_principle
Natural satellite orbiting Earth
(Earth radius / Radius of Moon's orbit)2 ] relative to the direct solar illumination that occurs for a full moon. (Earth albedo = 0.367; Earth radius = (polar
Moon
Set of points equidistant from a center
mentioned earlier r is the sphere's radius; any line from the center to a point on the sphere is also called a radius. 'Radius' is used in two senses: as a line
Sphere
Dense arrangement of congruent spheres in an infinite, regular arrangement
where r1 is the radius of the first sphere and r2 is the radius of the second. In close packing all of the spheres share a common radius, r. Therefore,
Close-packing of equal spheres
Close-packing_of_equal_spheres
Core of an atom composed of nucleons
of about 27,000 (uranium's atomic radius is about 156 pm (156×10−12 m)) to about 60,000 (hydrogen's atomic radius is about 52.92 pm). The branch of physics
Atomic_nucleus
Molecule interaction model
it is simply the computed surface area of a sphere of radius equal to the van der Waals radius of the gaseous atom: A w = 4 π r w 2 {\displaystyle A_{\rm
Van_der_Waals_surface
Atomic model introduced by Niels Bohr in 1913
to predict a, the radius of the electron orbiting in the ground state of the hydrogen atom. This value is now called the Bohr radius. The first Solvay
Bohr_model
Filling factor, F , {\displaystyle ~F,~} is a quantity measuring the efficiency of absorption of pump in the core of a double-clad fiber. The efficiency
Filling_factor
Region of space
approximately 2,000 galaxies expected for an area of comparable size. With a radius of 62 megaparsecs (nearly 200 million light-years), it is one of the largest
Boötes_Void
Elements with atomic numbers 57-70
but one of the lanthanides are f-block elements, corresponding to the filling of the 4f electron shell. Lutetium is a d-block element (thus also a transition
Lanthanide
American less-lethal pyrotechnic
Length 5.25 inches (133 mm) Diameter 1.73 inches (44 mm) Filling Magnesium/Ammonium Nitrate Filling weight 0.16 ounces (4.5 g) Detonation mechanism M201A1
M84_stun_grenade
Hand grenade
detonation generate a lethal radius of between 6 metres (20 ft) and 20 m (66 ft). The RGO is capable of spreading fragments to a radius of 100 m (330 ft) from
RGO_hand_grenade
Catalan solid with 12 faces
Denoting by a {\displaystyle a} the edge length of a rhombic dodecahedron, the radius of its inscribed sphere (a sphere that is tangent to each of the rhombic
Rhombic_dodecahedron
Hand grenade
soldier) Filling White phosphorus Filling weight 15 oz (430 g) Detonation mechanism Pyrotechnic delay M206A2 fuse—4 seconds Blast yield Burst Radius of 34
M34_grenade
Rotating device used for wastewater treatment
which the pond depth in the bowl can be set. The weir discs determine the filling volume of the bowl. The main application of decanter centrifuges is to
Decanter_centrifuge
Mathematical object
3-manifold. In coordinates, a 3-sphere with center (C0, C1, C2, C3) and radius r is the set of all points (x0, x1, x2, x3) in real, 4-dimensional space
3-sphere
Theoretical matter within neutron stars
nearly pure neutron matter with sparse protons and electrons interspersed, filling a space several thousand times smaller than the progenitor star. At the
Nuclear_pasta
Hand grenade developed and used during the Second World War
adopted into service due to the need for a grenade with smaller destructive radius than the No. 36M "Mills bomb". This allowed the thrower to use a grenade
No._69_grenade
Well-spaced set of points in a metric space
related definitions of well-spaced sets of points, and the packing radius and covering radius of these sets measure how well-spaced they are. These sets have
Delone_set
Tabular arrangement of the chemical elements
increases in magnitude with the charge and radius of the ion. In Mg+, the outermost orbital (which determines ionic radius) is still 3s, so the hydration enthalpy
Periodic_table
Type of solid bitumen, or rock containing solid bitumen
possible mud volcanoes. Layer and vein shungite varieties, and shungite filling cavities and forming the matrix of breccias, are interpreted as migrated
Shungite
Nano-scale semiconductor particles
Bohr radius, three regimes can be defined. In the 'strong confinement regime', the quantum dot's radius is much smaller than the exciton Bohr radius, respectively
Quantum_dot
500 lb unguided aerial bomb
general-purpose bomb, part of the United States Mark 80 series. The explosive filling is usually tritonal, though other compositions have sometimes been used
Mark_82_bomb
Biological system in animals and plants for gas exchange
both the posterior and anterior air sacs expand, the posterior air sacs filling with fresh inhaled air, while the anterior air sacs fill with "spent" (oxygen-poor)
Respiratory_system
Pressure exerted by circulating blood upon the walls of arteries
vessel depends on its radius as described by the Hagen-Poiseuille's equation (resistance∝1/radius4). Hence, the smaller the radius, the higher the resistance
Blood_pressure
German rocket-powered interceptor
650 L) of fuel, which was exhausted in 4 to 7 minutes, limiting its flight radius to 25 miles (40 km). The fuel system was particularly troublesome, as leaks
Messerschmitt_Me_163_Komet
Chinese philosophical symbol representing two opposites combined as one
represents the Taiji as harboring Dualism, yin and yang, represented by filling the circle in a black-and-white pattern. In some diagrams, there is a smaller
Taijitu
Development of the table of chemical elements
1887 cast doubt on the possibility of a luminiferous ether as a space-filling medium, physicists set constraints for its properties. Mendeleev believed
History_of_the_periodic_table
Grenade launcher with repeating fire mechanism
weight 260 g (0.57 lb) 275 g (0.606 lb) — — — Filling — — 47 g (1.7 oz) — 90 g (3.2 oz) — — Kill radius/area 10 m (33 ft) — 90 m2 (970 sq ft) 120 m2 (1
Automatic_grenade_launcher
Mathematical model of the Big Bang
approximately 50% of all baryonic matter is outside dark matter haloes, filling the space between galaxies. Together with the amount of baryons inside
Lambda-CDM_model
Chemical element with atomic number 14 (Si)
single-bond covalent radius of 117.6 pm is intermediate between those of carbon (77.2 pm) and germanium (122.3 pm). The hexacoordinate ionic radius of silicon may
Silicon
Formula to approximate nuclear mass based on nucleon counts
Pauli exclusion principle. Unequal numbers of neutrons and protons imply filling higher energy levels for one type of particle, while leaving lower energy
Semi-empirical_mass_formula
Pre-assembled firearm ammunition
(SWC) identical to the WC with a smaller diameter flap pointed conical or radiused nose added. Has the same advantages for target shooters but is easier to
Cartridge_(firearms)
Tetrahedron whose faces are all congruent
has radius (the circumradius) R = l 2 + m 2 + n 2 8 , {\displaystyle R={\sqrt {\frac {l^{2}+m^{2}+n^{2}}{8}}},} and the inscribed sphere has radius r =
Disphenoid
Empirical study of systems in transformation
is its unit of volume: a tetrahedron defined by four closest-packed unit-radius spheres. This tetrahedron anchors a set of concentrically arranged polyhedra
Synergetics_(Fuller)
Great circle with a characteristic length
distinguished from a metric ball, the subset of a metric space within a given radius from a central point. A metric space is a subspace of a metric circle (or
Metric_circle
the conversion of the BL 15-pounder to BLC 15-pounder. Calibre radius head: the radius of a circle with the curve of the shell's nose on its circumference
Glossary of British ordnance terms
Glossary_of_British_ordnance_terms
Bowed string instrument
painted or stained black (a process called "ebonizing"). The fingerboard is radiused using a curve, for the same reason that the bridge is curved: if the fingerboard
Double_bass
First ironclad of the US Navy, 1861–1862
wreck, and everything around it, a .5-nautical-mile (0.93 km; 0.58 mi) radius was designated as the Monitor National Marine Sanctuary, the first U.S.
USS_Monitor
Alternative to silicon-based photovoltaics
typically below 10–20 nanometers, falling within or near the exciton Bohr radius (the characteristic distance between an electron and hole in a bound state)
Perovskite_solar_cell
Form of matter
while the other radius of curvature is small. As the stem of the bubble grows in length, it becomes more unstable as one of the radius grows and the other
Foam
Reciprocating internal combustion engine
filling with fuel/air mix. The rpm band over which the pressure wave arrives at the open inlet valves and is able to assist in the cylinder filling is
Alfa_Romeo_Twin_Spark_engine
Soviet anti-personnel fragmentation grenade
produces around 350 fragments with a fatality radius of around 3 metres (9.8 ft) and a wounding radius of 25 metres (82 ft). Typically, the RGD-5 uses
RGD-5
Standards and guidelines for designing plastic parts for manufacturing
base radius for ribs: A fillet of a certain minimum radius value should be provided at the base of a rib to reduce stress. However, the radius should
Design_of_plastic_components
1989 video game
the staircase on the other by rotating turnstiles, moving blocks, and filling holes with blocks. The game has three skill levels: Level 1 - Easy, Level
Kwirk
Range 300-3000 GHz of the electromagnetic spectrum
5 June 2021. Williams, G. (2003). "Filling the THz gap" (PDF). jlab.org. CASA Seminar. Cooke, Mike (2007). "Filling the THz gap with new applications"
Terahertz_radiation
on the building's hip roof. Meanwhile, host Steve Thomas learns about filling in a flue channel, which is a structural element of the house before finding
List of This Old House episodes (seasons 21–30)
List_of_This_Old_House_episodes_(seasons_21–30)
Type of fire-resistant electrical cable
cable is made by placing copper rods inside a circular copper tube and filling the spaces with dry magnesium oxide powder. The overall assembly is then
Mineral-insulated copper-clad cable
Mineral-insulated_copper-clad_cable
Geometric figure which has infinite surface area but finite volume
also the area of a circle of radius 2 , {\displaystyle {\sqrt {2}},} and the nested surfaces of the cylinders (filling the volume of the solid) are thus
Gabriel's_horn
Flemish Jesuit missionary (1623–1688)
Altazimuth, six feet in radius, for measuring altitudes or zenith distances of celestial bodies. Sextant, eight feet in radius, used to measure the angle
Ferdinand_Verbiest
120mm mortar cluster bomb
and scattering 650 steel fragments out to a lethal radius of around 6 meters, and an effective radius of 18 meters. Within the impact area, the probability
MAT-120
Hand grenade
Stielhandgranate 15 relied on its blast effect, which had an effective radius of 15 m (16 yd) on open field. The warhead was made of a thin sheet of steel
Stielhandgranate
Large conventional bombs used in World War II by the Royal Air Force
evacuation of 70,000 within a radius of 3 km (1.9 mi), while in 2014 defusing operations required the evacuation of 30,000 within a radius of 2.5 km (1.6 mi). On
Blockbuster_bomb
Polyhedron with four faces
{\tfrac {3}{2}}}} , 1 6 {\displaystyle {\sqrt {\tfrac {1}{6}}}} . A space-filling tetrahedron packs with directly congruent or enantiomorphous (mirror image)
Tetrahedron
Cylindrical container for storing pressurised gas
screwed into the internal neck thread at the top for connecting to the filling or receiving apparatus. Gas cylinders may be grouped by several characteristics
Gas_cylinder
Use of the second law of thermodynamics to distinguish past from future
According to this theory the universe (or, rather, its accessible part, a radius of 46 billion light years around Earth) evolved from a tiny, totally uniform
Entropy_as_an_arrow_of_time
Application of the science of anthropology in a legal setting
In addition to the leg bones, the bones of the arm, humerus, ulna, and radius can be used. The formulas that are used to determine stature rely on various
Forensic_anthropology
Small explosive weapon that typically is thrown by hand
fragmentation grenades, such as the United States M67 grenade, have a wounding radius of 15 m (50 ft) – half that of older style grenades, which can still be
Grenade
Antenna with a fractal shape
volume. Such fractal antennas are also referred to as multilevel and space filling curves, but the key aspect lies in their repetition of a motif over two
Fractal_antenna
Historic migration route in the western United States
On a wagon there was essentially no reverse or brakes and the turning radius was nearly always greater than 125 feet (38 m) so the teamsters had to think
California_Trail
Bounding antipersonnel mine
self-destruct feature initiates the mine in 4 hours plus 0-20%. Height: 3.203 in Radius (max): 2.924 in Thickness: 72° wedge Land mine "TM-43-0001-36 Ammunition
M86 pursuit deterrent munition
M86_pursuit_deterrent_munition
Intersection of a torus and a plane
radius 5 and minor radius 3. That means that the torus is the locus of some vertical circles of radius three whose centers are on a circle of radius five
Villarceau_circles
Overview of notable inventions and discoveries from Scotland or Scottish people
Ambassador: investigations in American culture Eric Mottram Hutchinson Radius, 1989 Raynor, Tauria (2008-10-30). "Boys' Brigade want alumni to return
List of Scottish inventions and discoveries
List_of_Scottish_inventions_and_discoveries
Highest particle energy in a Fermi gas at absolute zero
dwarfs have mass comparable to the Sun, but have about a hundredth of its radius. The high densities mean that the electrons are no longer bound to single
Fermi_energy
American hand grenade
by the grenade body fracturing and have an injury radius of 15 meters (49 ft) and a fatality radius of 5 meters (16 ft), though some fragments can travel
M67_grenade
2023 disaster in Ohio, United States
chloride and phosgene into the air. Residents within a 1-mile (1.6-kilometer) radius were evacuated. Agencies from Ohio, Pennsylvania, West Virginia, and Virginia
East Palestine, Ohio, train derailment
East_Palestine,_Ohio,_train_derailment
Type of rechargeable battery
ionic radius of Na+ (116 pm) is substantially larger than that of Fe2+ and Fe3+ (69–92 pm depending on the spin state), whereas the ionic radius of Li+
Sodium-ion_battery
WWII German strategic bombing campaign
explosion which was capable of destroying buildings within a 300 ft (91 m) radius. The most common types were the Luftmine A, weighing 500 kg (1,100 lb),
Operation_Steinbock
Size of a two-dimensional surface
of least area spanning ("filling") it is a minimal surface. Familiar examples include soap bubbles. The question of the filling area of the Riemannian circle
Area
Standards defined by VESA for mounting flat panel displays to stands or wall mounts
radius of at most 7 mm. The bracket is within a rounded rectangle whose sides extend at most 7.5 mm beyond the hole centres and with a corner radius of
VESA_mount
Smaller and outer moon of Mars
two natural satellites of Mars, the other being Phobos. Deimos has a mean radius of 6.2 km (3.9 mi) and takes 30.3 hours to orbit Mars. Deimos is 23,457
Deimos_(moon)
2004 remix album by Pigface and Defrag
2004 album by Pigface and Defrag. AllMusic said that "dogs within a mile radius will be howling for half the album, and old video game systems will hear
8_Bit_Head
Potential configurations of electrons
ionic radius 62 pm, Co3+ ionic radius 54.5 pm, Ni4+ ionic radius 48 pm. d7 Octahedral high spin: Co2+ ionic radius 74.5 pm, Ni3+ ionic radius 60 pm.
Spin_states_(d_electrons)
Periodic table group
elements tend to increase with increasing atomic number. Carbon's atomic radius is 77 picometers, silicon's is 118 picometers, germanium's is 123 picometers
Carbon_group
Extinct genus of dinosaurs
differs from Kunbarrasaurus by having a curved instead of straight ulna and radius and a process from the maxilla running towards the lacrimal bone that is
Stegouros
Alloy of bismuth, lead, tin and cadmium
fill thin-walled tube so that it can be bent to a radius without kinking or collapsing. The filling is easily melted and run out of the tube after bending
Wood's_metal
Vessel filled with a superheated transparent liquid
chamber, both in application and in basic principle. It is normally made by filling a large cylinder with a liquid heated to just below its boiling point.
Bubble_chamber
Heavily forested area of Southeast Texas, US
forest. That same year, 182 bears were killed within a 10-mile (16 km) radius of Tarkington Prairie, and annual hunting continued until 1900, when the
Big_Thicket
Star in constellation Eridanus
classification of K3/4(III). It has a mass of 1.594 M☉ but has expanded to a radius of 12.6 R☉. It radiates 52.2 times the luminosity of the Sun from its inflated
HD_20722
American White House intern (b. 1943)
not skilled in clerical or stenographic work. In other words, she was filling a chair which could have been filled by somebody else had those skills
Mimi_Alford
French dual-purpose rifle grenade
capacity, the APAV 40 is used in indirect fire. The APAV 40 has a lethal radius of 12 m (13 yd) and its shrapnel is dangerous up to 100 m (110 yd) away
APAV40
Moat and canal around medieval Milan, Italy
flow from the Cerchia dei Navigli into the Vettabbia Canal [it]. With the filling of the Cerchia dei Navigli, the Naviglio della Martesana was entirely diverted
Cerchia_dei_Navigli
Soviet military intermediate rifle cartridge
somewhat stubbier appearance than later 7.62×39 bullets, with its maximal radius being attained after only 13.01 mm from its tip, and it was lacking a boat
7.62×39mm
Feature on some watches for saturation diving
hydrogen. Since helium atoms are the smallest natural gas particles—the atomic radius of a helium atom is 0.49 angstrom and that of a water molecule is about
Helium_release_valve
Hand grenade
detonation. Since its effective throwing range was greater than its burst radius, advancing soldiers could throw them in the open without risk of injury
Stielhandgranate_24
Representation of a molecule's bonds and 3D structure
is often indicated by the sphere's color. In a ball-and-stick model, the radius of the spheres is usually much smaller than the rod lengths, in order to
Ball-and-stick_model
Galaxy in the constellation Cancer
amount of the mass outflow rate of 4C +29.30 is obtained with the ~3 kpc radius. For the mass outflow rate and outflow kinetic power in the southern knot
4C_+29.30
Chemical element with atomic number 18 (Ar)
Space-filling model of argon fluorohydride
Argon
American football player (1935–2021)
death of halfback Willie Galimore prior to the season. "Ron Bull has been filling in adequately," Halas said, "but we needed another man at the position
Jon_Arnett
travel, tourism, insurance
FILLING RADIUS
FILLING RADIUS
FILLING RADIUS
FILLING RADIUS
FILLING RADIUS
FILLING RADIUS
FILLING RADIUS
FILLING RADIUS
FILLING RADIUS
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