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Ternary Plot
A ternary plot, ternary graph, triangle plot, simplex plot, or Gibbs triangle is a barycentric plot on three variables which sum to a constant. It graphically depicts the ratios of the three variables as positions in an equilateral triangle. It is used in physical chemistry, petrology, mineralogy, metallurgy, and other physical sciences to show the compositions of systems composed of three species. Ternary plots are tools for analyzing compositional data in the three-dimensional case. In population genetics, a triangle plot of genotype frequencies is called a de Finetti diagram. In game theory and convex optimization,Boyd, S. and Vandenberghe, L., 2004. Convex optimization. Cambridge university press. it is often called a simplex plot. In a ternary plot, the values of the three variables , , and must sum to some constant, . Usually, this constant is represented as 1.0 or 100%. Because for all substances being graphed, any one variable is not independent of the others, so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flammability Diagram Methane
A combustible material is a material that can burn (i.e., sustain a flame) in air under certain conditions. A material is flammable if it ignites easily at ambient temperatures. In other words, a combustible material ignites with some effort and a flammable material catches fire immediately on exposure to flame. The degree of flammability in air depends largely upon the volatility of the material this is related to its composition-specific vapour pressure, which is temperature dependent. The quantity of vapour produced can be enhanced by increasing the surface area of the material forming a mist or dust. Take wood as an example. Finely divided wood dust can undergo explosive flames and produce a blast wave. A piece of paper (made from pulp) catches on fire quite easily. A heavy oak desk is much harder to ignite, even though the wood fibre is the same in all three materials. Common sense (and indeed scientific consensus until the mid-1700s) would seem to suggest that materi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinate System
In geometry, a Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of real numbers called ''coordinates'', which are the positive and negative numbers, signed distances to the point from two fixed perpendicular oriented lines, called ''coordinate lines'', ''coordinate axes'' or just ''axes'' (plural of ''axis'') of the system. The point where the axes meet is called the ''Origin (mathematics), origin'' and has as coordinates. The axes direction (geometry), directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three ''Cartesian coordinates'', which are the signed distances from the point to three mutually perpendicular planes. More generally, Cartesian coordinates specify the point in an -dimensional Euclidean space for any di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectangular Ternary Plot
In Euclidean plane geometry, a rectangle is a rectilinear convex polygon or a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. A rectangle with four sides of equal length is a ''square''. The term "oblong" is used to refer to a non-square rectangle. A rectangle with vertices ''ABCD'' would be denoted as . The word rectangle comes from the Latin ''rectangulus'', which is a combination of ''rectus'' (as an adjective, right, proper) and ''angulus'' (angle). A crossed rectangle is a crossed (self-intersecting) quadrilateral which consists of two opposite sides of a rectangle along with the two diagonals (therefore only two sides are parallel). It is a special case of an antiparallelogram, and its angles are not right angles and not all equal, though opposite angles are equal. Other geometries, such as spherical, el ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance From A Point To A Line
The distance (or perpendicular distance) from a point to a line is the shortest Euclidean distance, distance from a fixed Point (geometry), point to any point on a fixed infinite Line (mathematics), line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways. Knowing the shortest distance from a point to a line can be useful in various situations—for example, finding the shortest distance to reach a road, quantifying the scatter on a graph, etc. In Deming regression, a type of linear curve fitting, if the dependent and independent variables have equal variance this results in orthogonal regression in which the degree of imperfection of the fit is measured for each data point as the perpendicular distance of the point from the regression line. Cartesian coordinates Line defined by an equation In the case of a line in the plane giv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilateral
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties. The equilateral triangle can be found in various tilings, and in polyhedrons such as the deltahedron and antiprism. It appears in real life in popular culture, architecture, and the study of stereochemistry resembling the molecular known as the trigonal planar molecular geometry. Properties An equilateral triangle is a triangle that has three equal sides. It is a special case of an isosceles triangle in the modern definition, stating that an isosceles triangle is defined at least as having two equal sides. Based on the modern definition, this leads to an equilateral triangle in which one of the three sides may be considered its base. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isometric Projection
Isometric projection is a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings. It is an axonometric projection in which the three coordinate axes appear equally foreshortened and the angle between any two of them is 120 degrees. Overview The term "isometric" comes from the Greek for "equal measure", reflecting that the scale along each axis of the projection is the same (unlike some other forms of graphical projection). An isometric view of an object can be obtained by choosing the viewing direction such that the angles between the projections of the ''x'', ''y'', and ''z'' axes are all the same, or 120°. For example, with a cube, this is done by first looking straight towards one face. Next, the cube is rotated ±45° about the vertical axis, followed by a rotation of approximately 35.264° (precisely arcsin or arctan , which is related to the Magic angle) about the horizontal axis. Note that with th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Space
In geometry, a Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called ''coordinates'', which are the signed distances to the point from two fixed perpendicular oriented lines, called '' coordinate lines'', ''coordinate axes'' or just ''axes'' (plural of ''axis'') of the system. The point where the axes meet is called the '' origin'' and has as coordinates. The axes directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three ''Cartesian coordinates'', which are the signed distances from the point to three mutually perpendicular planes. More generally, Cartesian coordinates specify the point in an -dimensional Euclidean space for any dimension . These coordinates are the signed distances from the point to mutually perpendicular fixed h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oblique Projection
Oblique projection is a simple type of technical drawing of graphical projection used for producing two-dimensional (2D) images of three-dimensional (3D) objects. The objects are not in perspective and so do not correspond to any view of an object that can be obtained in practice, but the technique yields somewhat convincing and useful results. Oblique projection is commonly used in technical drawing. The cavalier projection was used by French military artists in the 18th century to depict fortifications. Oblique projection was used almost universally by Chinese artists from the 1st or 2nd centuries to the 18th century, especially to depict rectilinear objects such as houses. Various graphical projection techniques can be used in computer graphics, including in Computer Aided Design (CAD), computer games, computer generated animations, and special effects used in movies. Overview Oblique projection is a type of parallel projection: * it projects an image by inters ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ternary Plot Visualisation
Ternary (from Latin ''ternarius'') or trinary is an adjective meaning "composed of three items". It can refer to: Mathematics and logic * Ternary numeral system, a base-3 counting system ** Balanced ternary, a positional numeral system, useful for comparison logic * Ternary logic, a logic system with the values ''true'', ''false'', and some other value * Ternary plot or ternary graph, a plot that shows the ratios of three proportions * Ternary relation, a finitary relation in which the number of places in the relation is three * Ternary operation, an operation that takes three parameters * Ternary function, a function that takes three arguments Computing * Ternary signal, a signal that can assume three significant values * Ternary computer, a computer using a ternary numeral system * Ternary tree, a tree data structure in computer science ** Ternary search tree, a ternary (three-way) tree data structure of strings * Ternary search, a computer science technique for findin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Altitude (triangle)
In geometry, an altitude of a triangle is a line segment through a given Vertex (geometry), vertex (called ''apex (geometry), apex'') and perpendicular to a line (geometry), line containing the side or edge (geometry), edge opposite the apex. This (finite) edge and (infinite) line extension are called, respectively, the ''base (geometry), base'' and ''extended side, extended base'' of the altitude. The point (geometry), point at the intersection of the extended base and the altitude is called the ''foot'' of the altitude. The length of the altitude, often simply called "the altitude" or "height", symbol , is the distance between the foot and the apex. The process of drawing the altitude from a vertex to the foot is known as ''dropping the altitude'' at that vertex. It is a special case of orthogonal projection. Altitudes can be used in the computation of the area of a triangle: one-half of the product of an altitude's length and its base's length (symbol ) equals the triangle's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
