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Area Codes In Connecticut
Area is the measure of a region's size on a surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). Two different regions may have the same area (as in squaring the circle); by synecdoche, "area" sometimes is used to refer to the region, as in a " polygonal area". The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Disk (mathematics)
In geometry, a disk (Spelling of disc, also spelled disc) is the region in a plane (geometry), plane bounded by a circle. A disk is said to be ''closed'' if it contains the circle that constitutes its boundary, and ''open'' if it does not. For a radius r, an open disk is usually denoted as D_r, and a closed disk is \overline. However in the field of topology the closed disk is usually denoted as D^2, while the open disk is \operatorname D^2. Formulas In Cartesian coordinates, the ''open disk'' with center (a, b) and radius ''R'' is given by the formula D = \, while the ''closed disk'' with the same center and radius is given by \overline = \. The area (geometry), area of a closed or open disk of radius ''R'' is π''R''2 (see area of a disk). Properties The disk has circular symmetry. The open disk and the closed disk are not topologically equivalent (that is, they are not homeomorphism, homeomorphic), as they have different topological properties from each other. For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Squaring The Circle
Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square (geometry), square with the area of a circle, area of a given circle by using only a finite number of steps with a compass and straightedge. The difficulty of the problem raised the question of whether specified axioms of Euclidean geometry concerning the existence of Line (geometry), lines and circles implied the existence of such a square. In 1882, the task was proven to be impossible, as a consequence of the Lindemann–Weierstrass theorem, which proves that pi (\pi) is a transcendental number. That is, \pi is not the zero of a function, root of any polynomial with Rational number, rational coefficients. It had been known for decades that the construction would be impossible if \pi were transcendental, but that fact was not proven until 1882. Approximate constructions with any given non-perfect accuracy exist, and many such constructions have been f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the ''base'', in which case the opposite vertex is called the ''apex''; the shortest segment between the base and apex is the ''height''. The area of a triangle equals one-half the product of height and base length. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formula
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a ''chemical formula''. The informal use of the term ''formula'' in science refers to the general construct of a relationship between given quantities. The plural of ''formula'' can be either ''formulas'' (from the most common English plural noun form) or, under the influence of scientific Latin, ''formulae'' (from the original Latin). In mathematics In mathematics, a formula generally refers to an equation or inequality relating one mathematical expression to another, with the most important ones being mathematical theorems. For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Real Number
In mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and in many other branches of mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers, sometimes called "the reals", is traditionally denoted by a bold , often using blackboard bold, . The adjective ''real'', used in the 17th century by René Descartes, distinguishes real numbers from imaginary numbers such as the square roots of . The real numbers include the rational numbers, such as the integer and the fraction . The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless Quantity
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined Unit of measurement, units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific Unit of volume, units of volume used, such as in milliliters per milliliter (mL/mL). The 1, number one is recognized as a dimensionless Base unit of measurement, base quantity. Radians serve as dimensionless units for Angle, angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference. Dimensionless quantities play a crucial role serving as parameters in differential equations in various technical disciplines. In calculus, concepts like the unitless ratios ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Square
In mathematics, a unit square is a square whose sides have length . Often, ''the'' unit square refers specifically to the square in the Cartesian plane with corners at the four points ), , , and . Cartesian coordinates In a Cartesian coordinate system with coordinates , a unit square is defined as a square consisting of the points where both and lie in a closed unit interval from to . That is, a unit square is the Cartesian product , where denotes the closed unit interval. Complex coordinates The unit square can also be thought of as a subset of the complex plane, the topological space formed by the complex numbers. In this view, the four corners of the unit square are at the four complex numbers , , , and . Rational distance problem It is not known whether any point in the plane is a rational distance from all four vertices of the unit square. See also * Unit circle In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequentl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bureau International Des Poids Et Mesures
The International Bureau of Weights and Measures (, BIPM) is an intergovernmental organisation, through which its 64 member-states act on measurement standards in areas including chemistry, ionising radiation, physical metrology, as well as the International System of Units (SI) and Coordinated Universal Time (UTC). It is headquartered in the Pavillon de Breteuil in Saint-Cloud, near Paris, France. The organisation has been referred to as IBWM (from its name in English) in older literature. Function The BIPM has the mandate to provide the basis for a single, coherent system of measurements throughout the world, traceable to the International System of Units (SI). This task takes many forms, from direct dissemination of units to coordination through international comparisons of national measurement standards (as in electricity and ionising radiation). Following consultation, a draft version of the BIPM Work Programme is presented at each meeting of the General Conference f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metre
The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of a second, where the second is defined by a hyperfine transition frequency of caesium. The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's polar circumference is approximately . In 1799, the metre was redefined in terms of a prototype metre bar. The bar used was changed in 1889, and in 1960 the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of proper length. From 1983 until 2019, the metre was formally defined as the length of the pat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Metre
The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter ( American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square with sides one metre in length. Adding and subtracting SI prefixes creates multiples and submultiples; however, as the unit is exponentiated, the quantities grow exponentially by the corresponding power of 10. For example, 1 kilometre is 103 (one thousand) times the length of 1 metre, but 1 square kilometre is (103)2 (106, one million) times the area of 1 square metre, and 1 cubic kilometre is (103)3 (109, one billion) cubic metres. SI prefixes applied The square metre may be used with all SI prefixes used with the metre. Unicode characters Unicode has several characters used to represent metric area units, but these are for compatibility with East Asian character encodings and are meant to be used in new documents. * * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International System Of Units
The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce. The SI system is coordinated by the International Bureau of Weights and Measures, which is abbreviated BIPM from . The SI comprises a coherent system of units of measurement starting with seven base units, which are the second (symbol s, the unit of time), metre (m, length), kilogram (kg, mass), ampere (A, electric current), kelvin (K, thermodynamic temperature), mole (mol, amount of substance), and candela (cd, luminous intensity). The system can accommodate coherent units for an unlimited number of additional quantities. These are called coherent derived units, which can always be represented as products of powers of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
