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Nomogram
A nomogram (from Greek , "law" and , "line"), also called a nomograph, alignment chart, or abac, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function. The field of nomography was invented in 1884 by the French engineer Philbert Maurice d'Ocagne (1862–1938) and used extensively for many years to provide engineers with fast graphical calculations of complicated formulas to a practical precision. Nomograms use a parallel coordinate system invented by d'Ocagne rather than standard Cartesian coordinates. A nomogram consists of a set of n scales, one for each variable in an equation. Knowing the values of n-1 variables, the value of the unknown variable can be found, or by fixing the values of some variables, the relationship between the unfixed ones can be studied. The result is obtained by laying a straightedge across the known values on the scales and reading the unknown value from w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lawrence Henderson
Lawrence Joseph Henderson (June 3, 1878, Lynn, Massachusetts – February 10, 1942, Cambridge, Massachusetts) was a physiologist, chemist, biologist, philosopher, and sociologist. He became one of the leading biochemists of the early 20th century. His work contributed to the Henderson–Hasselbalch equation, used to calculate pH as a measure of acidity. Early life Lawrence Henderson was born in Lynn, Massachusetts the son of a business man Joseph Henderson and his wife. He entered Harvard at the age of 16 in 1894. His father was a ship chandler whose principal business was located in nearby Salem, but who also conducted business in Saint Pierre and Miquelon, a French Overseas collectivity off the coast of Canada. Career Lawrence Henderson graduated from Harvard College in 1898 and from Harvard Medical School in 1902, receiving the M.D. (Medical Doctor) degree cum laude. Then followed two years in chemical research at the University of Strasbourg with advanced scientific tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slide Rule
The slide rule is a mechanical analog computer which is used primarily for multiplication and division, and for functions such as exponents, roots, logarithms, and trigonometry. It is not typically designed for addition or subtraction, which is usually performed using other methods. Maximum accuracy for standard linear slide rules is about three decimal significant digits, while scientific notation is used to keep track of the order of magnitude of results. Slide rules exist in a diverse range of styles and generally appear in a linear, circular or cylindrical form, with slide rule scales inscribed with standardized graduated markings. Slide rules manufactured for specialized fields such as aviation or finance typically feature additional scales that aid in specialized calculations particular to those fields. The slide rule is closely related to nomograms used for application-specific computations. Though similar in name and appearance to a standard ruler, the slide rule is not ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analog Computer
An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude ( digital signals). Analog computers can have a very wide range of complexity. Slide rules and nomograms are the simplest, while naval gunfire control computers and large hybrid digital/analog computers were among the most complicated. Complex mechanisms for process control and protective relays used analog computation to perform control and protective functions. Analog computers were widely used in scientific and industrial applications even after the advent of digital computers, because at the time they were typically much faster, but they started to become obsolete as early as the 1950s and 1960s, although they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson's Chi-squared Test
Pearson's chi-squared test (\chi^2) is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates, likelihood ratio, portmanteau test in time series, etc.) – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900. In contexts where it is important to improve a distinction between the test statistic and its distribution, names similar to ''Pearson χ-squared'' test or statistic are used. It tests a null hypothesis stating that the frequency distribution of certain events observed in a sample is consistent with a particular theoretical distribution. The events considered must be mutually exclusive and have total probability 1. A common case for this is where the events each cover an outcome of a categorical variable. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philbert Maurice D'Ocagne
Philbert Maurice d'Ocagne (25 March 1862 – 23 September 1938) was a French engineer and mathematician. He founded the field of nomography, the graphic computation of algebraic equations, on charts which he called nomogram. Biography Philbert-Maurice Ocagne was born in Paris on 25 March 1862. He attended high school at the Lycée Fontanges school in Paris, and studied at Chaptal college. In 1877, he published his first mathematical work. In 1880, he entered the École Polytechnique. He published many articles on math. Starting in 1885, he served for six years as engineer, supporting waterworks projects in Rochefort and Cherbourg, then worked at Seine-et-Oise, at the residence of Pontoise. From 1882, he continued to published articles on mathematics in the French Academy of Sciences and major journals including ''Journal of the École Polytechnique'', '' Bulletin de la Société Mathématique de France'', ''Acta Mathematica'', ''Archiv der Mathematik und Physik'', and ''America ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithmic Scale
A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a scale is nonlinear: the numbers 10 and 20, and 60 and 70, are not the same distance apart on a log scale. Rather, the numbers 10 and 100, and 60 and 600 are equally spaced. Thus moving a unit of distance along the scale means the number has been ''multiplied'' by 10 (or some other fixed factor). Often exponential growth curves are displayed on a log scale, otherwise they would increase too quickly to fit within a small graph. Another way to think about it is that the ''number of digits'' of the data grows at a constant rate. For example, the numbers 10, 100, 1000, and 10000 are equally spaced on a log scale, because their numbers of digits is going up by 1 each time: 2, 3, 4, and 5 digits. In this way, adding two digits ''multiplies'' the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parallel Scale Nomogram
Parallel is a geometric term of location which may refer to: Computing * Parallel algorithm * Parallel computing * Parallel metaheuristic * Parallel (software), a UNIX utility for running programs in parallel * Parallel Sysplex, a cluster of IBM mainframes * Parallel communication * Parallel port * Parallel ATA * Parallel Computers, Inc., an American computer manufacturer of the 1980s Mathematics and science * Parallel circuits, as opposed to series * Parallel (geometry) * Parallel (operator), mathematical function used in electrical engineering * Parallel postulate * Parallel evolution * Parallel transport *Parallel manipulator Navigation * Parallel (latitude), an imaginary east–west line circling a globe * Parallel of declination, used in astronomy Music and entertainment * ''Parallel'' (manga) * ''Parallel'' (2018 film), a Canadian science fiction thriller film * Parallel (2023 film) an upcoming American science fiction thriller film * Parallel key, the minor (or m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification and rectification, which distinguishes it from classical electrical engineering, which only uses passive effects such as resistance, capacitance and inductance to control electric current flow. Electronics has hugely influenced the development of modern society. The central driving force behind the entire electronics industry is the semiconductor industry sector, which has annual sales of over $481 billion as of 2018. The largest industry sector is e-commerce, which generated over $29 trillion in 2017. History and development Electronics has hugely influenced the development of modern society. The identification of the electron in 1897, along with the subsequent invention of the vacuum tube which could amplify and rectify small ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Mean
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is : \left(\frac\right)^ = \frac = \frac = 2\,. Definition The harmonic mean ''H'' of the positive real numbers x_1, x_2, \ldots, x_n is defined to be :H = \frac = \frac = \left(\frac\right)^. The third formula in the above equation expresses the harmonic mean as the reciprocal of the arithmetic mean of the reciprocals. From the following formula: :H = \frac. it is more apparent that the harmonic mean is related to the arithmetic and geometric means. It is the reciprocal dual of the arithmetic mean for positive inputs: :1/H(1/x_1 \ldots 1/x_n) = A(x_1 \ldots x_n) The harmonic mean is a Schur-conca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Series And Parallel Circuits
Two-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology. Whether a two-terminal "object" is an electrical component (e.g. a resistor) or an electrical network (e.g. resistors in series) is a matter of perspective. This article will use "component" to refer to a two-terminal "object" that participate in the series/parallel networks. Components connected in series are connected along a single "electrical path", and each component has the same current through it, equal to the current through the network. The voltage across the network is equal to the sum of the voltages across each component. Components connected in parallel are connected along multiple paths, and each component has the same voltage across it, equal to the voltage across the network. The current through the network is equal to the sum of the currents through each c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lens (optics)
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), usually arranged along a common axis. Lenses are made from materials such as glass or plastic, and are ground and polished or molded to a desired shape. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called lenses, such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses. Lenses are used in various imaging devices like telescopes, binoculars and cameras. They are also used as visual aids in glasses to correct defects of vision such as myopia and hypermetropia. History The word '' lens'' comes from '' lēns'', the Latin name of the lentil (a seed of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thin Lens
In optics, a thin lens is a lens with a thickness (distance along the optical axis between the two surfaces of the lens) that is negligible compared to the radii of curvature of the lens surfaces. Lenses whose thickness is not negligible are sometimes called ''thick lenses''. The thin lens approximation ignores optical effects due to the thickness of lenses and simplifies ray tracing calculations. It is often combined with the paraxial approximation in techniques such as ray transfer matrix analysis. Focal length The focal length, ''f'', of a lens in air is given by the lensmaker's equation: :\frac = (n-1) \left \frac - \frac + \frac \right where ''n'' is the index of refraction of the lens material, and ''R''1 and ''R''2 are the radii of curvature of the two surfaces. For a thin lens, ''d'' is much smaller than one of the radii of curvature (either ''R''1 or ''R''2). In these conditions, the last term of the Lensmaker's equation becomes negligible, and the focal length of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
