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Architectural glass is glass that is used as a building material. It is most typically used as transparent glazing material in the building envelope, including windows in the external walls. Glass is also used for internal partitions and as an architectural feature | https://huggingface.co/datasets/fmars/wiki_stem |
Cathedral glass is the name given commercially to monochromatic sheet glass. It is thin by comparison with slab glass, may be coloured, and is textured on one side.
The name draws from the fact that windows of stained glass were a feature of medieval European cathedrals from the 10th century onwards | https://huggingface.co/datasets/fmars/wiki_stem |
Float glass is a sheet of glass made by floating molten glass on a bed of molten metal of a low melting point, typically tin, although lead was used for the process in the past. This method gives the sheet uniform thickness and a very flat surface. Modern windows are usually made from float glass | https://huggingface.co/datasets/fmars/wiki_stem |
Glazing, which derives from the Middle English for 'glass', is a part of a wall or window, made of glass. Glazing also describes the work done by a professional "glazier". Glazing is also less commonly used to describe the insertion of ophthalmic lenses into an eyeglass frame | https://huggingface.co/datasets/fmars/wiki_stem |
The Grand Canyon Skywalk is a horseshoe-shaped cantilever bridge with a glass walkway at Eagle Point in Arizona near the Colorado River, on the edge of a side canyon in the Grand Canyon West area of the main canyon. It opened as a tourist attraction in 2007, located outside the boundaries of the Grand Canyon National Park.
USGS topographic maps indicate the Skywalk's elevation as 4,770 ft (1,450 m) above sea level | https://huggingface.co/datasets/fmars/wiki_stem |
Leadlights, leaded lights or leaded windows are decorative windows made of small sections of glass supported in lead cames. The technique of creating windows using glass and lead came to be known as came glasswork. The term 'leadlight' could be used to describe any window in which the glass is supported by lead, but traditionally, a distinction is made between stained glass windows and leadlights; the former is associated with the ornate coloured-glass windows of churches and similar buildings, while the latter is associated with the windows of vernacular architecture and defined by its simplicity | https://huggingface.co/datasets/fmars/wiki_stem |
The stained glass in Liverpool Cathedral all dates from the 20th century. The designs were planned by a committee working in conjunction with the architect of the cathedral, Giles Gilbert Scott, with the intention of forming an integrated scheme throughout the cathedral. A number of stained glass designers were involved in the scheme, but the major contributors came from James Powell and Sons (Whitefriars Glass), in particular J | https://huggingface.co/datasets/fmars/wiki_stem |
Manchester Civil Justice Centre is a governmental building in Manchester, England. Completed in 2007, it houses Manchester's county court and the Manchester District Registry of the High Court, the city's family proceedings court, the district probate registry, and the regional and area offices of the Court Service. The Civil Justice Centre was the first major court complex built in Britain since George Edmund Street's Royal Courts of Justice in London completed in 1882 | https://huggingface.co/datasets/fmars/wiki_stem |
The National Glass Association is the largest trade association for the auto glass, architectural glass, and window and door markets. The NGA was founded in 1948, and currently has close to 3,000 member companies. This international association represents the interests of companies worldwide | https://huggingface.co/datasets/fmars/wiki_stem |
Pavement lights (UK), vault lights (US), floor lights, or sidewalk prisms are flat-topped walk-on skylights, usually set into pavement (sidewalks) or floors to let sunlight into the space below. They often use anidolic lighting prisms to throw the light sideways under the building. They were developed in the 19th century, but declined in popularity with the advent of cheap electric lighting in the early 20th | https://huggingface.co/datasets/fmars/wiki_stem |
Prism lighting is the use of prisms to improve the distribution of light in a space. It is usually used to distribute daylight, and is a form of anidolic lighting.
Prism lighting was popular from its introduction in the 1890s through to the 1930s, when cheap electric lights became commonplace and prism lighting became unfashionable | https://huggingface.co/datasets/fmars/wiki_stem |
Rippled glass refers to textured glass with marked surface waves. Louis Comfort Tiffany made use of such textured glass to represent, for example, water or leaf veins.
The texture is created during the glass sheet-forming process | https://huggingface.co/datasets/fmars/wiki_stem |
Rose window is often used as a generic term applied to a circular window, but is especially used for those found in Gothic cathedrals and churches. The windows are divided into segments by stone mullions and tracery. The term rose window was not used before the 17th century and comes from the English flower name rose | https://huggingface.co/datasets/fmars/wiki_stem |
Labyrinth: The Computer Game is a 1986 graphic adventure game developed by Lucasfilm Games and published by Activision. Based on the fantasy film Labyrinth, it tasks the player with navigating a maze while solving puzzles and evading dangers. The player's goal is to find and defeat the main antagonist, Jareth, within 13 real-time hours | https://huggingface.co/datasets/fmars/wiki_stem |
Phantasie II is the second game in the Phantasie series of role-playing video games.
Gameplay
In 1986, SSI published the next part of the Phantasie series, Phantasie II. Again, the Dark Lord Nikademus was the nemesis | https://huggingface.co/datasets/fmars/wiki_stem |
An articulated hauler, articulated dump truck (ADT), or sometimes a dump hauler, is a very large heavy-duty type of dump truck used to transport loads over rough terrain, and occasionally on public roads. The vehicle usually has all-wheel drive and consists of two basic units: the front section, generally called the tractor, and the rear section that contains the dump body, called the hauler or trailer section. Steering is made by pivoting the front in relation to the back by hydraulic rams | https://huggingface.co/datasets/fmars/wiki_stem |
Sand slinger is the term for two different types of machines. Both of which use a short conveyor belt to direct sand, gravel or similar materials to varying locations.
Stationary mold filling machine
A stationary sand slinger is a type of machine used for filling and uniform ramming of sand in casting molds, and is particularly advantageous with large molds | https://huggingface.co/datasets/fmars/wiki_stem |
A backhoe loader, also called a loader backhoe, loader excavator, digger in layman's terms, or colloquially shortened to backhoe within the industry, is a heavy equipment vehicle that consists of a tractor-like unit fitted with a loader-style shovel/bucket on the front and a backhoe on the back. Due to its (relatively) small size and versatility, backhoe loaders are very common in urban engineering and small construction projects (such as building a small house, fixing urban roads, etc. ) as well as developing countries | https://huggingface.co/datasets/fmars/wiki_stem |
A bucket (also called a scoop to qualify shallower designs of tools) is a specialized container attached to a machine, as compared to a bucket adapted for manual use by a human being. It is a bulk material handling component.
The bucket has an inner volume as compared to other types of machine attachments like blades or shovels | https://huggingface.co/datasets/fmars/wiki_stem |
Heavy Equipment, Heavy Machinery, Earthmovers, Construction Vehicles, or Construction Equipment, refers to heavy-duty vehicles specially designed to execute construction tasks, most frequently involving earthwork operations or other large construction tasks. Heavy equipment usually comprises five equipment systems: the implement, traction, structure, power train, and control/information.
Heavy equipment has been used since at least the 1st century BC when the ancient Roman engineer Vitruvius described a crane in De architectura when it was powered via human or animal labor | https://huggingface.co/datasets/fmars/wiki_stem |
Excavators are heavy construction equipment consisting of a boom, dipper (or stick), bucket and cab on a rotating platform known as the "house". The house sits atop an undercarriage with tracks or wheels. They are a natural progression from the steam shovels and often mistakenly called power shovels, as power shovels may have similar looking buckets | https://huggingface.co/datasets/fmars/wiki_stem |
A roadheader, also called a boom-type roadheader, road header machine, road header or just header machine, is a piece of excavating equipment consisting of a boom-mounted cutting head, a loading device usually involving a conveyor, and a crawler travelling track to move the entire machine forward into the rock face. The cutting head can be a general purpose rotating drum mounted in line or perpendicular to the boom, or can be special function heads such as jackhammer-like spikes, compression fracture micro-wheel heads like those on larger tunnel boring machines, a slicer head like a gigantic chain saw for dicing up rock, or simple jaw-like buckets of traditional excavators.
History
The first roadheader patent was applied for by Dr | https://huggingface.co/datasets/fmars/wiki_stem |
The iRobot R-Gator is an unmanned robotic platform from iRobot Corporation and John Deere. The 1,450 pounds (660 kg) robot is built upon Deere's M-Gator currently in use by the US Military. The R-Gator can operate autonomously, performing perimeter patrol and other missions while keeping personnel out of harm's way | https://huggingface.co/datasets/fmars/wiki_stem |
Timberjack is a manufacturer of forestry machinery for both cut-to-length and whole tree logging, and was a subsidiary of John Deere from 2000 to 2006.
History
Timberjack was founded in Woodstock, Ontario in the 1950s by Wesley Maggill and Robert Simons, who designed an articulated
four-wheel drive tractor with a winch at the back. They produced a prototype and production took off from there | https://huggingface.co/datasets/fmars/wiki_stem |
The Komatsu D575A is a 1,150 horsepower (860 kW) tractor crawler produced in a 'SR' or Super Ripper bulldozer/ripper configuration, or as a dedicated bulldozer in the form of the 'SD' or Super Dozer. Both models can move 90 cubic yards (69 m3) of material per pass using the standard blade. The D575A-3 SD Super Dozer can move 125 cubic yards (96 m3) of material per pass if equipped with an optional blade | https://huggingface.co/datasets/fmars/wiki_stem |
The Komatsu PC200-8 Hybrid is a hydraulic excavator manufactured by Komatsu Limited. It is the world's first hybrid (electro-hydraulic) powered construction equipment. At the time of its launch it was found to consume 25% less fuel than comparable non-hybrid excavators and up to 40% less fuel while carrying out certain functions | https://huggingface.co/datasets/fmars/wiki_stem |
A military engineering vehicle is a vehicle built for construction work or for the transportation of combat engineers on the battlefield. These vehicles may be modified civilian equipment (such as the armoured bulldozers that many nations field) or purpose-built military vehicles (such as the AVRE). The first appearance of such vehicles coincided with the appearance of the first tanks, these vehicles were modified Mark V tanks for bridging and mine clearance | https://huggingface.co/datasets/fmars/wiki_stem |
The armored bulldozer is a basic tool of combat engineering. These combat engineering vehicles combine the earth moving capabilities of the bulldozer with armor which protects the vehicle and its operator in or near combat. Most are civilian bulldozers modified by addition of vehicle armor/military equipment, but some are tanks stripped of armament and fitted with a dozer blade | https://huggingface.co/datasets/fmars/wiki_stem |
The Cheetah MMPV (Medium Mine Protected Vehicle) was a prototype built by the Force Protection, Inc. , division of General Dynamics. It was intended as part of Force Protection's armoured military vehicle line-up, which includes the MRAP-class of Buffalo and Cougar vehicles and the Ocelot light protected patrol vehicle (LPPV) | https://huggingface.co/datasets/fmars/wiki_stem |
A demolition vehicle is a vehicle used to demolish buildings and other structures.
Military forces require such vehicles to clear obstacles, fortifications and rubble so that they can safely advance. Military engineers may use a variety of specialised vehicles including armoured bulldozers and explosive robotic drones | https://huggingface.co/datasets/fmars/wiki_stem |
The JCB HMEE (High Mobility Engineer Excavator) is a military engineering vehicle made by JCB.
Design
The HMEE is an armoured backhoe loader designed for high speeds in order to self-deploy with military convoys. Most backhoes are limited to much lower speeds | https://huggingface.co/datasets/fmars/wiki_stem |
The Terex THS15 Motorscraper was a concept machine scraper displayed for the first time at Minexpo 2000. This machine features some unusual design concepts, including an adjustable cutting edge on the bowl to reduce friction when loading. Other notable features were the rear-mounted drivetrain (there was no engine on the front module) and a hydrostatic transmission, which featured hydraulic wheel motors | https://huggingface.co/datasets/fmars/wiki_stem |
A tractor is an engineering vehicle specifically designed to deliver a high tractive effort (or torque) at slow speeds, for the purposes of hauling a trailer or machinery such as that used in agriculture, mining or construction. Most commonly, the term is used to describe a farm vehicle that provides the power and traction to mechanize agricultural tasks, especially (and originally) tillage, and now many more. Agricultural implements may be towed behind or mounted on the tractor, and the tractor may also provide a source of power if the implement is mechanised | https://huggingface.co/datasets/fmars/wiki_stem |
A steam tractor is a vehicle powered by a steam engine which is used for pulling.
In North America, the term steam tractor usually refers to a type of agricultural tractor powered by a steam engine, used extensively in the late 19th and early 20th centuries.
In Great Britain, the term steam tractor is more usually applied to the smallest models of traction engine - typically those weighing seven tons or less - used for hauling small loads on public roads | https://huggingface.co/datasets/fmars/wiki_stem |
A driverless tractor is an autonomous farm vehicle that delivers a high tractive effort (or torque) at slow speeds for the purposes of tillage and other agricultural tasks. It is considered driverless because it operates without the presence of a human inside the tractor itself. Like other unmanned ground vehicles, they are programmed to independently observe their position, decide speed, and avoid obstacles such as people, animals, or objects in the field while performing their task | https://huggingface.co/datasets/fmars/wiki_stem |
The Allis-Chalmers 190XT, also known as the One-Ninety XT, is a row crop tractor produced by Allis Chalmers from 1964 to 1971. The tractors are powered by diesel fuel, gasoline, or LP gas (though few of the latter two were made). As its model number implies, it was based on the Allis-Chalmers D19 from the D Series, though it featured many alterations and improvements over the D19 | https://huggingface.co/datasets/fmars/wiki_stem |
Belt Pulley was a U. S. -based magazine dedicated to antique farm tractors of all brands and makes | https://huggingface.co/datasets/fmars/wiki_stem |
Cat's cradle is a game involving the creation of various string figures between the fingers, either individually or by passing a loop of string back and forth between two or more players. The true origin of the name is debated, though the first known reference is in The light of nature pursued by Abraham Tucker in 1768. The type of string, the specific figures, their order, and the names of the figures vary | https://huggingface.co/datasets/fmars/wiki_stem |
In category theory, a branch of mathematics, the categorical trace is a generalization of the trace of a matrix.
Definition
The trace is defined in the context of a symmetric monoidal category C, i. e | https://huggingface.co/datasets/fmars/wiki_stem |
In 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 | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows:
2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in line segments of equal length, then the two regions have equal areas.
3-dimensional case: Suppose two regions in three-space (solids) are included between two parallel planes | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, coaxial means that several three-dimensional linear or planar forms share a common axis. The two-dimensional analog is concentric.
Common examples:
A coaxial cable is a three-dimensional linear structure | https://huggingface.co/datasets/fmars/wiki_stem |
The coin rotation paradox is the counter-intuitive observation that, when one coin is rolled around the rim of another coin of equal size, the moving coin completes two full rotations after going all the way around the stationary coin.
Description
Start with two identical coins touching each other on a table, with their "head" sides displayed and parallel. Keeping coin A stationary, rotate coin B around A, keeping a point of contact with no slippage | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a complex reflection group is a finite group acting on a finite-dimensional complex vector space that is generated by complex reflections: non-trivial elements that fix a complex hyperplane pointwise.
Complex reflection groups arise in the study of the invariant theory of polynomial rings. In the mid-20th century, they were completely classified in work of Shephard and Todd | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, a corner-point grid is a tessellation of a Euclidean 3D volume, where the base cell has 6 faces (hexahedron).
A set of straight lines defined by their end points define the pillars of the corner-point grid. The pillars have a lexicographical ordering that determines neighbouring pillars | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, the tests for congruence and similarity involve comparing corresponding sides and corresponding angles of polygons. In these tests, each side and each angle in one polygon is paired with a side or angle in the second polygon, taking care to preserve the order of adjacency. For example, if one polygon has sequential sides a, b, c, d, and e and the other has sequential sides v, w, x, y, and z, and if b and w are corresponding sides, then side a (adjacent to b) must correspond to either v or x (both adjacent to w) | https://huggingface.co/datasets/fmars/wiki_stem |
A Coxeter decomposition of a polygon is a decomposition into a finite number of polygons in which any two sharing a side are reflections of each other along that side. Hyperbolic polygons are the analogues of Euclidean polygons in hyperbolic geometry. A hyperbolic n-gon is an area bounded by n segments, rays, or entire straight lines | https://huggingface.co/datasets/fmars/wiki_stem |
A datum reference or just datum (plural: datums) is some important part of an object—such as a point, line, plane, hole, set of holes, or pair of surfaces—that serves as a reference in defining the geometry of the object and (often) in measuring aspects of the actual geometry to assess how closely they match with the nominal value, which may be an ideal, standard, average, or desired value. For example, on a car's wheel, the lug nut holes define a bolt circle that is a datum from which the location of the rim can be defined and measured. This matters because the hub and rim need to be concentric to within close limits (or else the wheel will not roll smoothly) | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, an equichordal point is a point defined relative to a convex plane curve such that all chords passing through the point are equal in length. Two common figures with equichordal points are the circle and the limaçon. It is impossible for a curve to have more than one equichordal point | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, the exsphere of a face of a regular polyhedron is the sphere outside the polyhedron which touches the face and the planes defined by extending the adjacent faces outwards. It is tangent to the face externally and tangent to the adjacent faces internally.
It is the 3-dimensional equivalent of the excircle | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a finite subdivision rule is a recursive way of dividing a polygon or other two-dimensional shape into smaller and smaller pieces. Subdivision rules in a sense are generalizations of regular geometric fractals. Instead of repeating exactly the same design over and over, they have slight variations in each stage, allowing a richer structure while maintaining the elegant style of fractals | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, the flatness (symbol: ⏥) of a surface is the degree to which it approximates a mathematical plane. The term is often generalized for higher-dimensional manifolds to describe the degree to which they approximate the Euclidean space of the same dimensionality. (See curvature | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a genus g surface (also known as a g-torus or g-holed torus) is a surface formed by the connected sum of g many tori: the interior of a disk is removed from each of g many tori and the boundaries of the g many disks are identified (glued together), forming a g-torus. The genus of such a surface is g.
A genus g surface is a two-dimensional manifold | https://huggingface.co/datasets/fmars/wiki_stem |
Geometric drawing consists of a set of processes for constructing geometric shapes and solving problems with the use of a ruler without graduation and the compass (drawing tool). Modernly, such studies can be done with the aid of software, which simulates the strokes performed by these instruments. For ancient mathematicians, geometry could not do without the methods of geometric constructions, necessary for understanding, theoretical enrichment, and problem-solving | https://huggingface.co/datasets/fmars/wiki_stem |
In discrete geometry, geometric rigidity is a theory for determining if a geometric constraint system (GCS) has finitely many
d
{\displaystyle d}
-dimensional solutions, or frameworks, in some metric space. A framework of a GCS is rigid in
d
{\displaystyle d}
-dimensions, for a given
d
{\displaystyle d}
if it is an isolated solution of the GCS, factoring out the set of trivial motions, or isometric group, of the metric space, e. g | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both
R
2
{\displaystyle \mathbb {R} ^{2}}
or both
R
3
{\displaystyle \mathbb {R} ^{3}}
— such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations | https://huggingface.co/datasets/fmars/wiki_stem |
In physics, geometrothermodynamics (GTD) is a formalism developed in 2007 by Hernando Quevedo to describe the properties of thermodynamic systems in terms of concepts of differential geometry. Consider a thermodynamic system in the framework of classical equilibrium thermodynamics. The states of thermodynamic equilibrium are considered as points of an abstract equilibrium space in which a Riemannian metric can be introduced in several ways | https://huggingface.co/datasets/fmars/wiki_stem |
In computer science, one approach to the dynamic optimality problem on online algorithms for binary search trees involves reformulating the problem geometrically, in terms of augmenting a set of points in the plane with as few additional points as possible in order to avoid rectangles with only two points on their boundary.
Access sequences and competitive ratio
As typically formulated, the online binary search tree problem involves search trees defined over a fixed key set
{
1
,
2
,
.
| https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, the Gram–Euler theorem, Gram-Sommerville, Brianchon-Gram or Gram relation (named after Jørgen Pedersen Gram, Leonhard Euler, Duncan Sommerville and Charles Julien Brianchon) is a generalization of the internal angle sum formula of polygons to higher-dimensional polytopes. The equation constrains the sums of the interior angles of a polytope in a manner analogous to the Euler relation on the number of d-dimensional faces.
Statement
Let
P
{\displaystyle P}
be an
n
{\displaystyle n}
-dimensional convex polytope | https://huggingface.co/datasets/fmars/wiki_stem |
A great ellipse is an ellipse passing through two points on a spheroid and having the same center as that of the spheroid. Equivalently, it is an ellipse on the surface of a spheroid and centered on the origin, or the curve formed by intersecting the spheroid by a plane through its center.
For points that are separated by less than about a quarter of the circumference of the earth, about
10
000
k
m
{\displaystyle 10\,000\,\mathrm {km} }
, the length of the great ellipse connecting the points is close (within one part in 500,000) to the geodesic distance | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, the Hart circle is derived from three given circles that cross pairwise to form eight circular triangles. For any one of these eight triangles, and its three neighboring triangles, there exists a Hart circle, tangent to the inscribed circles of these four circular triangles. Thus, the three given circles have eight Hart circles associated with them | https://huggingface.co/datasets/fmars/wiki_stem |
Hatch marks (also called hash marks or tick marks) are a form of mathematical notation. They are used in three ways as:
Unit and value marks — as on a ruler or number line
Congruence notation in geometry — as on a geometric figure
Graphed points — as on a graphHatch marks are frequently used as an abbreviation of some common units of measurement. In regard to distance, a single hatch mark indicates feet, and two hatch marks indicate inches | https://huggingface.co/datasets/fmars/wiki_stem |
The Huzita–Justin axioms or Huzita–Hatori axioms are a set of rules related to the mathematical principles of origami, describing the operations that can be made when folding a piece of paper. The axioms assume that the operations are completed on a plane (i. e | https://huggingface.co/datasets/fmars/wiki_stem |
In algebraic geometry, an infinitely near point of an algebraic surface S is a point on a surface obtained from S by repeatedly blowing up points. Infinitely near points of algebraic surfaces were introduced by Max Noether (1876). There are some other meanings of "infinitely near point" | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem or the upside down Pythagorean theorem) is as follows:
Let A, B be the endpoints of the hypotenuse of a right triangle △ABC. Let D be the foot of a perpendicular dropped from C, the vertex of the right angle, to the hypotenuse. Then
1
C
D
2
=
1
A
C
2
+
1
B
C
2
| https://huggingface.co/datasets/fmars/wiki_stem |
Lacunarity, from the Latin lacuna, meaning "gap" or "lake", is a specialized term in geometry referring to a measure of how patterns, especially fractals, fill space, where patterns having more or larger gaps generally have higher lacunarity. Beyond being an intuitive measure of gappiness, lacunarity can quantify additional features of patterns such as "rotational invariance" and more generally, heterogeneity. This is illustrated in Figure 1 showing three fractal patterns | https://huggingface.co/datasets/fmars/wiki_stem |
In crystallography, a lattice plane of a given Bravais lattice is any plane containing at least three noncollinear Bravais lattice points. Equivalently, a lattice plane is a plane whose intersections with the lattice (or any crystalline structure of that lattice) are periodic (i. e | https://huggingface.co/datasets/fmars/wiki_stem |
Line moiré is one type of moiré pattern; a pattern that appears when superposing two transparent layers containing correlated opaque patterns. Line moiré is the case when the superposed patterns comprise straight or curved lines. When moving the layer patterns, the moiré patterns transform or move at a faster speed | https://huggingface.co/datasets/fmars/wiki_stem |
The line of sight, also known as visual axis or sightline (also sight line), is an imaginary line between a viewer/observer/spectator's eye(s) and a subject of interest, or their relative direction. The subject may be any definable object taken note of or to be taken note of by the observer, at any distance more than least distance of distinct vision. In optics, refraction of a ray due to use of lenses can cause distortion | https://huggingface.co/datasets/fmars/wiki_stem |
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of points as being colored red. These two sets are linearly separable if there exists at least one line in the plane with all of the blue points on one side of the line and all the red points on the other side | https://huggingface.co/datasets/fmars/wiki_stem |
The link in a simplicial complex is a generalization of the neighborhood of a vertex in a graph. The link of a vertex encodes information about the local structure of the complex at the vertex.
Link of a vertex
Given an abstract simplicial complex X and
v
{\textstyle v}
a vertex in
V
(
X
)
{\textstyle V(X)}
, its link
Lk
(
v
,
X
)
{\textstyle \operatorname {Lk} (v,X)}
is a set containing every face
τ
∈
X
{\textstyle \tau \in X}
such that
v
∉
τ
{\textstyle v\not \in \tau }
and
τ
∪
{
v
}
{\textstyle \tau \cup \{v\}}
is a face of X | https://huggingface.co/datasets/fmars/wiki_stem |
Local coordinates are the ones used in a local coordinate system or a local coordinate space. Simple examples:
Houses. In order to work in a house construction, the measurements are referred to a control arbitrary point that will allow to check it: stick/sticks on the ground, steel bar, nails | https://huggingface.co/datasets/fmars/wiki_stem |
Mathematical phenomena can be understood and explored via visualization. Classically this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century), while today it most frequently consists of using computers to make static two or three dimensional drawings, animations, or interactive programs. Writing programs to visualize mathematics is an aspect of computational geometry | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, the minimum or smallest bounding or enclosing box for a point set S in N dimensions is the box with the smallest measure (area, volume, or hypervolume in higher dimensions) within which all the points lie. When other kinds of measure are used, the minimum box is usually called accordingly, e. g | https://huggingface.co/datasets/fmars/wiki_stem |
The Minkowski content (named after Hermann Minkowski), or the boundary measure, of a set is a basic concept that uses concepts from geometry and measure theory to generalize the notions of length of a smooth curve in the plane, and area of a smooth surface in space, to arbitrary measurable sets.
It is typically applied to fractal boundaries of domains in the Euclidean space, but it can also be used in the context of general metric measure spaces.
It is related to, although different from, the Hausdorff measure | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematical physics, Minkowski space (or Minkowski spacetime) () combines inertial space and time manifolds (x,y) with a non-inertial reference frame of space and time (x',t') into a four-dimensional model relating a position (inertial frame of reference) to the field (physics). A four-vector (x,y,z,t) consists of a coordinate axes such as a Euclidean space plus time. This may be used with the non-inertial frame to illustrate specifics of motion, but should not be confused with the spacetime model generally | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, the Minkowski–Steiner formula is a formula relating the surface area and volume of compact subsets of Euclidean space. More precisely, it defines the surface area as the "derivative" of enclosed volume in an appropriate sense.
The Minkowski–Steiner formula is used, together with the Brunn–Minkowski theorem, to prove the isoperimetric inequality | https://huggingface.co/datasets/fmars/wiki_stem |
The multicover bifiltration is a two-parameter sequence of nested topological spaces derived from the covering of a finite set in a metric space by growing metric balls. It is a multidimensional extension of the offset filtration that captures density information about the underlying data set by filtering the points of the offsets at each index according to how many balls cover each point. The multicover bifiltration has been an object of study within multidimensional persistent homology and topological data analysis | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, the Newton–Gauss line (or Gauss–Newton line) is the line joining the midpoints of the three diagonals of a complete quadrilateral.
The midpoints of the two diagonals of a convex quadrilateral with at most two parallel sides are distinct and thus determine a line, the Newton line. If the sides of such a quadrilateral are extended to form a complete quadrangle, the diagonals of the quadrilateral remain diagonals of the complete quadrangle and the Newton line of the quadrilateral is the Newton–Gauss line of the complete quadrangle | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, for a given dimension, and that geometric transformations are permitted that transform the extra points (called "points at infinity") to Euclidean points, and vice-versa | https://huggingface.co/datasets/fmars/wiki_stem |
A partial linear space (also semilinear or near-linear space) is a basic incidence structure in the field of incidence geometry, that carries slightly less structure than a linear space.
The notion is equivalent to that of a linear hypergraph.
Definition
Let
S
=
(
P
,
L
,
I
)
{\displaystyle S=({\mathcal {P}},{\mathcal {L}},{\textbf {I}})}
an incidence structure, for which the elements of
P
{\displaystyle {\mathcal {P}}}
are called points and the elements of
L
{\displaystyle {\mathcal {L}}}
are called lines | https://huggingface.co/datasets/fmars/wiki_stem |
Geological perspective correlation is a theory in geology describing geometrical regularities in the layering of sediments. Seventy percent of the Earth's surface are occupied by sedimentary basins – volumes consisted of sediments accumulated during million years, and alternated by long interruptions in sedimentation (hiatuses). The most noticeable feature of the rocks, which filled the basins, is layering (stratification) | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely.
A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space.
When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the whole space | https://huggingface.co/datasets/fmars/wiki_stem |
The curved point-normal triangle, in short PN triangle, is an interpolation algorithm to retrieve a cubic Bézier triangle from the vertex coordinates of a regular flat triangle and normal vectors. The PN triangle retains the vertices of the flat triangle as well as the corresponding normals. For computer graphics applications, additionally a linear or quadratic interpolant of the normals is created to represent an incorrect but plausible normal when rendering and so giving the impression of smooth transitions between adjacent PN triangles | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a quasisymmetric homeomorphism between metric spaces is a map that generalizes bi-Lipschitz maps. While bi-Lipschitz maps shrink or expand the diameter of a set by no more than a multiplicative factor, quasisymmetric maps satisfy the weaker geometric property that they preserve the relative sizes of sets: if two sets A and B have diameters t and are no more than distance t apart, then the ratio of their sizes changes by no more than a multiplicative constant. These maps are also related to quasiconformal maps, since in many circumstances they are in fact equivalent | https://huggingface.co/datasets/fmars/wiki_stem |
Rabatment of the rectangle is a compositional technique used as an aid for the placement of objects or the division of space within a rectangular frame, or as an aid for the study of art.
Every rectangle contains two implied squares, each consisting of a short side of the rectangle, an equal length along each longer side, and an imaginary fourth line parallel to the short side. The process of mentally rotating the short sides onto the long ones is called "rabatment", and often the imaginary fourth line is called "the rabatment" | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, real trees (also called
R
{\displaystyle \mathbb {R} }
-trees) are a class of metric spaces generalising simplicial trees. They arise naturally in many mathematical contexts, in particular geometric group theory and probability theory. They are also the simplest examples of Gromov hyperbolic spaces | https://huggingface.co/datasets/fmars/wiki_stem |
In three-dimensional space, a regulus R is a set of skew lines, every point of which is on a transversal which intersects an element of R only once, and such that every point on a transversal lies on a line of R
The set of transversals of R forms an opposite regulus S. In ℝ3 the union R ∪ S is the ruled surface of a hyperboloid of one sheet.
Three skew lines determine a regulus:
The locus of lines meeting three given skew lines is called a regulus | https://huggingface.co/datasets/fmars/wiki_stem |
A right circular cylinder is a cylinder whose generatrices are perpendicular to the bases. Thus, in a right circular cylinder, the generatrix and the height have the same measurements. It is also less often called a cylinder of revolution, because it can be obtained by rotating a rectangle of sides
r
{\displaystyle r}
and
g
{\displaystyle g}
around one of its sides | https://huggingface.co/datasets/fmars/wiki_stem |
The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an
I
{\displaystyle I}
(for an axis that lies in the plane of the area) or with a
J
{\displaystyle J}
(for an axis perpendicular to the plane). In both cases, it is calculated with a multiple integral over the object in question | https://huggingface.co/datasets/fmars/wiki_stem |
Shape moiré is one type of moiré patterns demonstrating the phenomenon of moiré magnification. 1D shape moiré is the particular simplified case of 2D shape moiré. One-dimensional patterns may appear when superimposing an opaque layer containing tiny horizontal transparent lines on top of a layer containing a complex shape which is periodically repeating along the vertical axis | https://huggingface.co/datasets/fmars/wiki_stem |
In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object | https://huggingface.co/datasets/fmars/wiki_stem |
A similarity system of triangles is a specific configuration involving a set of triangles. A set of triangles is considered a configuration when all of the triangles share a minimum of one incidence relation with one of the other triangles present in the set. An incidence relation between triangles refers to when two triangles share a point | https://huggingface.co/datasets/fmars/wiki_stem |
In geometry, a snub is an operation applied to a polyhedron. The term originates from Kepler's names of two Archimedean solids, for the snub cube (cubus simus) and snub dodecahedron (dodecaedron simum). In general, snubs have chiral symmetry with two forms: with clockwise or counterclockwise orientation | https://huggingface.co/datasets/fmars/wiki_stem |
Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime | https://huggingface.co/datasets/fmars/wiki_stem |
A spacetime diagram is a graphical illustration of objects' locations in space at various times, especially in the special theory of relativity. Spacetime diagrams can show the geometry underlying phenomena like time dilation and length contraction without mathematical equations.
The history of an object's location through time traces out a line or curve on a spacetime diagram, referred to as the object's world line | https://huggingface.co/datasets/fmars/wiki_stem |
The spectral dimension is a real-valued quantity that characterizes a spacetime geometry and topology. It characterizes a spread into space over time, e. g | https://huggingface.co/datasets/fmars/wiki_stem |
In mathematics, a subpaving is a set of nonoverlapping boxes of R⁺. A subset X of Rⁿ can be approximated by two subpavings X⁻ and X⁺ such that X⁻ ⊂ X ⊂ X⁺.
In R¹ the boxes are line segments, in R² rectangles and in Rⁿ hyperrectangles | https://huggingface.co/datasets/fmars/wiki_stem |
In a Euclidean space, the sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn).
A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides.
It was unknown for a long time whether other geometries exist, for which this sum is different | https://huggingface.co/datasets/fmars/wiki_stem |
Superspace is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions x, y, z, . | https://huggingface.co/datasets/fmars/wiki_stem |
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