|
Dyadic Fraction
In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number. The sum, difference, or product of any two dyadic rational numbers is another dyadic rational number, given by a simple formula. However, division of one dyadic rational number by another does not always produce a dyadic rational result. Mathematically, this means that the dyadic rational numbers form a ring, lying between the ring of integers and the field of rational numbers. This ring may be denoted \Z tfrac12/math>. In advanced mathematics, the dyadic rational numbers are central to the cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dyadic Rational
In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number. The sum, difference, or product of any two dyadic rational numbers is another dyadic rational number, given by a simple formula. However, division of one dyadic rational number by another does not always produce a dyadic rational result. Mathematically, this means that the dyadic rational numbers form a ring, lying between the ring of integers and the field of rational numbers. This ring may be denoted \Z tfrac12/math>. In advanced mathematics, the dyadic rational numbers are central to the con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fusible Number
In recreational mathematics, rope-burning puzzles are a class of mathematical puzzle in which one is given lengths of rope, fuse cord, or shoelace that each burn for a given amount of time, and matches to set them on fire, and must use them to measure a non-unit amount of time. The fusible numbers are defined as the amounts of time that can be measured in this way. As well as being of recreational interest, these puzzles are sometimes posed at job interviews as a test of candidates' problem-solving ability, and have been suggested as an activity for middle school mathematics students. Example A common and simple version of this problem asks to measure a time of 45 seconds using only two fuses that each burn for a minute. The assumptions of the problem are usually specified in a way that prevents measuring out 3/4 of the length of one fuse and burning it end-to-end, for instance by stating that the fuses burn unevenly along their length. One solution to this problem is to perf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floating-point Arithmetic
In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be represented as a base-ten floating-point number: 12.345 = \underbrace_\text \times \underbrace_\text\!\!\!\!\!\!^ In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common. The term ''floating point'' refers to the fact that the number's radix point can "float" anywhere to the left, right, or between the significant digits of the number. This position is indicated by the exponent, so floating point can be considered a form of scientific notation. A floating-point system can be used to represent, with a fixed number of digits, numbers of very different orders of magnitude — such as the number of meters between galaxies or between protons in an atom. For this reason, floating-poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indus Valley Civilisation
The Indus Valley Civilisation (IVC), also known as the Indus Civilisation was a Bronze Age civilisation in the northwestern regions of South Asia, lasting from 3300 BCE to 1300 BCE, and in its mature form 2600 BCE to 1900 BCE. Together with ancient Egypt and Mesopotamia, it was one of three early civilisations of the Near East and South Asia, and of the three, the most widespread. Its sites spanned an area from much of Pakistan, to northeast Afghanistan, and northwestern India. The civilisation flourished both in the alluvial plain of the Indus River, which flows through the length of Pakistan, and along a system of perennial monsoon-fed rivers that once coursed in the vicinity of the Ghaggar-Hakra River, Ghaggar-Hakra, a seasonal river in northwest India and eastern Pakistan. The term ''Harappan'' is sometimes applied to the Indus civilisation after its type site Harappa, the first to be excavated early in the 20th century in what was then the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cup (unit)
The cup is a cooking measure of volume, commonly associated with cooking and serving sizes. In the US, it is traditionally equal to . Because actual drinking cups may differ greatly from the size of this unit, standard measuring cups may be used, with a metric cup being 250 millilitres. United States Customary cup In the United States, the customary cup is half of a liquid pint. Legal cup The cup currently used in the United States for nutrition labelling is defined in United States law as 240 ml. Conversion table to US Legal cup The following information is describing that how to measure US Legal Cup in different ways. Coffee cup A "cup" of coffee in the US is usually 4 fluid ounces (118 ml), brewed using 5 fluid ounces (148 ml) of water. Coffee carafes used with drip coffee makers, e.g. Black and Decker models, have markings for both water and brewed coffee as the carafe is also used for measuring water prior to brewing. A 12-cup carafe, for example, has mar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pint
The pint (, ; symbol pt, sometimes abbreviated as ''p'') is a unit of volume or capacity in both the imperial unit, imperial and United States customary units, United States customary measurement systems. In both of those systems it is traditionally one eighth of a gallon. The British imperial pint is about 20% larger than the American pint because Comparison of the imperial and US customary measurement systems, the two systems are defined differently. Almost all other countries have standardized on the metric system, so although some of them still also have traditional units called pints (such as for beverages), the volume varies by regional custom. The imperial pint (≈) is used in the United Kingdom and Ireland and to a limited extent in Commonwealth of Nations, Commonwealth nations. In the United States, two kinds of pint are used: a liquid pint (≈) and a less-common dry pint (≈). Other Dominion , former British colonies, such as Canada, Australia, South Africa and New Z ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quart
The quart (symbol: qt) is an English unit of volume equal to a quarter gallon. Three kinds of quarts are currently used: the liquid quart and dry quart of the US customary system and the of the British imperial system. All are roughly equal to one liter. It is divided into two pints or (in the US) four cups. Historically, the exact size of the quart has varied with the different values of gallons over time and in reference to different commodities. Name The term comes from the Latin '' quartus'' (meaning one-quarter) via the French ''quart''. However, although the French word ''quart'' has the same root, it frequently means something entirely different. In Canadian French in particular, the quart is called '' pinte'', whilst the pint is called ''chopine''. History Since gallons of various sizes have historically been in use, the corresponding quarts have also existed with various sizes. Definitions and equivalencies US liquid quart In the United States, all tradition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gallon
The gallon is a unit of volume in imperial units and United States customary units. Three different versions are in current use: *the imperial gallon (imp gal), defined as , which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand, and some Caribbean countries; *the US gallon (US gal), defined as , (231 cubic inches) which is used in the US and some Latin American and Caribbean countries; and *the US dry gallon ("usdrygal"), defined as US bushel (exactly ). There are two pints in a quart and four quarts in a gallon. Different sizes of pints account for the different sizes of the imperial and US gallons. The IEEE standard symbol for both US (liquid) and imperial gallon is gal, not to be confused with the gal (symbol: Gal), a CGS unit of acceleration. Definitions The gallon currently has one definition in the imperial system, and two definitions (liquid and dry) in the US customary system. Historically, there were many definitions and redefiniti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inch
Measuring tape with inches The inch (symbol: in or ″) is a unit of length in the British imperial and the United States customary systems of measurement. It is equal to yard or of a foot. Derived from the Roman uncia ("twelfth"), the word ''inch'' is also sometimes used to translate similar units in other measurement systems, usually understood as deriving from the width of the human thumb. Standards for the exact length of an inch have varied in the past, but since the adoption of the international yard during the 1950s and 1960s the inch has been based on the metric system and defined as exactly 25.4 mm. Name The English word "inch" ( ang, ynce) was an early borrowing from Latin ' ("one-twelfth; Roman inch; Roman ounce"). The vowel change from Latin to Old English (which became Modern English ) is known as umlaut. The consonant change from the Latin (spelled ''c'') to English is palatalisation. Both were features of Old English phonology; see and fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pound (mass)
The pound or pound-mass is a unit of mass used in British imperial and United States customary systems of measurement. Various definitions have been used; the most common today is the international avoirdupois pound, which is legally defined as exactly , and which is divided into 16 avoirdupois ounces. The international standard symbol for the avoirdupois pound is lb; an alternative symbol is lbm (for most pound definitions), # ( chiefly in the U.S.), and or ″̶ (specifically for the apothecaries' pound). The unit is descended from the Roman (hence the abbreviation "lb"). The English word ''pound'' is cognate with, among others, German , Dutch , and Swedish . These units are historic and are no longer used (replaced by the metric system). Usage of the unqualified term ''pound'' reflects the historical conflation of mass and weight. This accounts for the modern distinguishing terms ''pound-mass'' and '' pound-force''. Etymology The word 'pound' and its cognates ultim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reverse Mathematics
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast to the ordinary mathematical practice of deriving theorems from axioms. It can be conceptualized as sculpting out necessary conditions from sufficient ones. The reverse mathematics program was foreshadowed by results in set theory such as the classical theorem that the axiom of choice and Zorn's lemma are equivalent over ZF set theory. The goal of reverse mathematics, however, is to study possible axioms of ordinary theorems of mathematics rather than possible axioms for set theory. Reverse mathematics is usually carried out using subsystems of second-order arithmetic,Simpson, Stephen G. (2009), Subsystems of second-order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, doi:10.1017/CBO9780511581007, ISBN 978 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Analysis
Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (mathematics), series, and analytic functions. These theories are usually studied in the context of Real number, real and Complex number, complex numbers and Function (mathematics), functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any Space (mathematics), space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space). History Ancient Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
_cans_in_the_UK.jpg "Click for more on -> Pint")
