Helmholtz

An illusion is a distortion of a sensory perception. Each of the human senses can be deceived by illusions, but visual illusions are the most well known. Some illusions are subjective; different people may experience an illusion differently, or not at all. Optical illusions, such the use of false perspective, exploit assumptions made by the human visual system. Mirages are optical distortions through the atmosphere that may be photographed. While the perceived reality (such as water in the desert) is illusory, th ...

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(German: Einigkeit und Recht und Freiheit) 2 Prior to 2002: Deutsche Mark Germany, officially the Federal Republic of Germany (German: Deutschland or Bundesrepublik Deutschland listen ▶ (help·info)) is one of the world's leading industrialised countries, located in Europe. It is bordered to the north by the North Sea, Denmark, and the Baltic Sea, to the east by Poland and the Czech Republic, to the south by Austria and Switzerland, and to the west by Fr ...

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• Germany - History
• Germany - Early history of the Germanic tribes 100 BC-300 AD
• Germany - The Holy Roman Empire of the German Nation 843–1806
• Germany - Restoration and revolution 1814–1871
• Germany - German Empire 1871–1918
• Germany - Weimar Republic 1919–1933
• Germany - Third Reich 1933–1945
• Germany - Division and reunification 1945–1990
• Germany - Politics
• Germany - Legal system
• Germany - Foreign Relations
• Germany - Armed Forces
• Germany - Energy policy
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• Germany - States Länder
• Germany - Territory
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• Germany - Economy
• Germany - Exports
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Wilhelm Maximilian Wundt (August 16, 1832–August 31, 1920) was a German physiologist and psychologist. He is generally acknowledged as the founder of experimental psychology and cognitive psychology. Wundt combined philosophical introspection with techniques and laboratory apparatuses brought over from his physiological studies with Helmholtz, as well as many of his own design. This experimental introspection was in contrast to what had been called psychology until then, a branch of philosophy where people introspected themse ...

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• Wilhelm Wundt - Wundt's life and works
• Wilhelm Wundt - Wundt's Impact

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During the 19th century, scientist-writers such as Eugène Chevreul, Ogden Rood and David Sutter wrote treatises on color, optical effects and perception. They were able to translate the scientific research of Helmholtz and Newton into a written form that was understandable by non-scientists. Chevreul was perhaps the most important influence on artists at the time. His most important contribution was producing the color wheel of primary and intermediary hues. Chevreul was a French chemist who restored old tapestries. During his restor ...

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Georges-Pierre Seurat, Georges-Pierre Seurat - Life, Georges-Pierre Seurat - Challenging the Impressionists, Georges-Pierre Seurat - Scientific background and influences, Georges-Pierre Seurat - Seurat's melding of science and emotion, Georges-Pierre Seurat - The crowning achievement, Georges-Pierre Seurat - Endnotes

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The state now known as Germany was unified as a modern nation-state only in 1871, when the German Empire, dominated by the Kingdom of Prussia, was forged. This was the second German Reich, usually translated as "empire", but also meaning "kingdom", "domain" or "realm." (Königreich means "kingdom", and Reich- as in Reichskanzler was analogous to Royal- or calling the State the Crown in Commonwealth countries. Today the analogous entity is called der Bund, as in Bundeskanzler, the Federal Chancellor.)See also:

Germany, Germany - History, Germany - Early history of the Germanic tribes 100 BC-300 AD, Germany - Migration Period and Franks 300-843, Germany - The Holy Roman Empire 843–1806, Germany - Restoration and revolution 1814–1871, Germany - German Empire 1871–1918, Germany - Weimar Republic 1919–1933, Germany - Third Reich 1933–1945, Germany - Division and reunification 1945–1990, Germany - Politics, Germany - Legal system, Germany - Foreign Relations, Germany - Armed Forces, Germany - Energy policy, Germany - Geography, Germany - Federal States Länder, Germany - Territory, Germany - Climate, Germany - Economy, Germany - Exports, Germany - Imports, Germany - Agriculture, Germany - Industrial sector, Germany - Service sector, Germany - Natural resources, Germany - Society, Germany - Demographics, Germany - Religion, Germany - Education, Germany - Transportation, Germany - Social issues, Germany - Culture, Germany - Miscellaneous topics

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The earliest model of the electrical double layer is usually attributed to Helmholtz (1879). Helmholtz treated the double layer mathematically as a simple capacitor, based on a physical model in which a single layer of ions is adsorbed at the surface. Later Gouy and Chapman (1910-1913) made significant improvements by introducing a diffuse model of the electrical double layer, in which the poten ...

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Electrical double layer, Electrical double layer - Historical development of double layer models

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The state now known as Germany was unified as a modern nation-state only in 1871, when the German Empire, dominated by the Kingdom of Prussia, was forged. This was the second German Reich, usually translated as "empire", but also meaning "kingdom", "domain" or "realm." (Königreich means "kingdom", and Reich- as in Reichskanzler was analogous to Royal- or calling the State the Crown in Commonwealth countries. Today the analogous entity is called der Bund, as in Bundeskanzler (Fed ...

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Germany, Germany - History, Germany - Early history of the Germanic tribes 100 BC-300 AD, Germany - Migration Period and Franks 300-843, Germany - The Holy Roman Empire 843–1806, Germany - Restoration and revolution 1814–1871, Germany - German Empire 1871–1918, Germany - Weimar Republic 1919–1933, Germany - Third Reich 1933–1945, Germany - Division and reunification 1945–1990, Germany - Politics, Germany - Legal system, Germany - Foreign Relations, Germany - Armed Forces, Germany - Energy policy, Germany - Geography, Germany - Federal States Bundesländer, Germany - Territory, Germany - Climate, Germany - Economy, Germany - Exports, Germany - Imports, Germany - Agriculture, Germany - Industrial sector, Germany - Service sector, Germany - Natural resources, Germany - Society, Germany - Demographics, Germany - Religion, Germany - Education, Germany - Social issues, Germany - Culture, Germany - Miscellaneous topics

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Gibbs' scientific career can be divided into four phases. Up until 1879, he worked on the theory of thermodynamics. From 1880 to 1884, he worked on the field of vector analysis. From 1882 to 1889, he worked on optics and the electromagnetic theory of light. After 1889, he worked on statistical mechanics, laying a foundation and "providing a mathematical framework for quantum theory and for Maxwell's theories" [1]; he also produced classic textbooks on the matter. See also:

Josiah Willard Gibbs, Josiah Willard Gibbs - Biography, Josiah Willard Gibbs - Early years, Josiah Willard Gibbs - Middle years, Josiah Willard Gibbs - Later years, Josiah Willard Gibbs - Death and afterwards, Josiah Willard Gibbs - Scientific recognition, Josiah Willard Gibbs - External articles and references, Josiah Willard Gibbs - Citations, Josiah Willard Gibbs - General

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Many of the results of Newton and Leibniz were known to mathematicians in Kerala, India almost 300 years previously. In 1835, Charles Whish published an article in the Transactions of the Royal Asiatic Society of Great Britain and Ireland, in which he claimed that the work of the Kerala school "laid the foundation for a complete system of fluxions." It was not until the 1940s however, that historians of mathematics verified Whish's claims, but their work is still underplayed in modern accounts of history ...

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History of calculus, History of calculus - Invention of Calculus, History of calculus - Controversy Newton Leibnitz... or Madhava?, History of calculus - Rigorous foundations, History of calculus - Integrals, History of calculus - Symbolic methods, History of calculus - Calculus of variations, History of calculus - Applications

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The state now known as Germany was unified as a modern nation-state only in 1871, when the German Empire, dominated by the Kingdom of Prussia, was forged. This was the second German Reich, usually translated as "empire", but also meaning "kingdom", "domain" or "realm." (Königreich means "kingdom", and Reich- as in Reichskanzler was analogous to Royal- or calling the State the Crown in Commonwealth countries. Today the analogous entity is called der Bund, as in Bundeskanzler (Federal Chancellor).)See also:

Germany, Germany - History, Germany - Early history of the Germanic tribes 100 BC-300 AD, Germany - Migration Period and Franks 300-843, Germany - The Holy Roman Empire 843–1806, Germany - Restoration and revolution 1814–1871, Germany - German Empire 1871–1918, Germany - Weimar Republic 1919–1933, Germany - Third Reich 1933–1945, Germany - Division and reunification 1945–1990, Germany - Politics, Germany - Legal system, Germany - Foreign Relations, Germany - Armed Forces, Germany - Energy policy, Germany - Geography, Germany - Federal States Länder, Germany - Territory, Germany - Climate, Germany - Economy, Germany - Exports, Germany - Imports, Germany - Agriculture, Germany - Industrial sector, Germany - Service sector, Germany - Natural resources, Germany - Society, Germany - Demographics, Germany - Religion, Germany - Education, Germany - Social issues, Germany - Culture, Germany - Miscellaneous topics

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Wundt was born August 16, 1832 at Neckarau, in Baden - The fourth child to parents Maximilian Wundt (a Lutheran minister), and his wife Marie Frederike. He studied from 1851 to 1856 at Tübingen, Heidelberg, and Berlin. After graduating in medicine from the University of Heidelberg in 1856, Wundt studied briefly with Johannes Müller before joining the University of Heidelberg, where he became an assistant to the physicist and physiologist Hermann von Helmholtz in 1858. There he wrote Contri ...

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Wilhelm Wundt, Wilhelm Wundt - Wundt's life and works, Wilhelm Wundt - Wundt's Impact

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Human beings distinguish sounds on the basis of their frequency. Actually what really matters is the ratio between their frequencies. The natural scale is attributed to the Grecian philosopher Aristoxenus Tarentinus and consists in a succession of notes with increasing frequencies. After fixing the frequency of the first note - the C of the scale - the frequencies of the other notes are determined from the ratios indicated in the following table. On the last C the fol ...

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Musical acoustics, Musical acoustics - Methods and fields of study, Musical acoustics - Sound waves, Musical acoustics - Harmonics partials and overtones, Musical acoustics - Harmonics and non-linearities, Musical acoustics - Harmony, Musical acoustics - The natural scale, Musical acoustics - The equal tempered scale, Musical acoustics - Cent values of equal temperament

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Each note produced by a musical instrument is made of a number of distinct frequencies, measured in hertz (Hz). The lowest frequency is called the fundamental and the pitch produced by this frequency is used to name the note. For example, in western music, instruments are normally tuned to A = 440 Hz. However, the richness of the sound is produced by the combination of this fundamental with a series of harmonics and/or partials (also collectively called overtones). Most western instruments produce harmonic sounds, and these can ...

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Timbre, Timbre - Terms, Timbre - American Standards Association definition, Timbre - Attributes, Timbre - Spectra, Timbre - Envelope, Timbre - In music, Timbre - Sources

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The radiant energy was difficult to study because it was inside sealed glass tubes, difficult to access, and because the rays were in the presence of air molecules (fully evacuated tubes didn't produce rays). Lenard overcame these problems by devising a method of making small metallic windows in the glass that were thick enough to be able to withstand the pressure differences, but thin enough to allow passage of the rays. Having made a window for the rays, he could pass them out into the laboratory, or, alternatively, into another chamber th ...

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Philipp Lenard, Philipp Lenard - Biography, Philipp Lenard - Photoelectric investigation, Philipp Lenard - Books by Philipp Lenard

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During the 19th century, scientist-writers such as Eugene Chevreul, Ogden Rood and David Sutter wrote treatises on color, optical effects and perception. They were able to translate the scientific research of Helmholtz and Newton into a written form that was accessible enough as to be understood by non-scientists. Chevreul was perhaps the most important influence on artists at the time. His most important contribution was producing the color wheel of primary and intermediary hues. Chevreul was a French chemist who used to restore ...

See also:

Georges-Pierre Seurat, Georges-Pierre Seurat - Life, Georges-Pierre Seurat - Seurat's Scientific Background and Influences, Georges-Pierre Seurat - Seurat Challenging of the Impressionists, Georges-Pierre Seurat - Seurat's Melding of Science and Emotion, Georges-Pierre Seurat - The Crowning Achievement, Georges-Pierre Seurat - Endnotes

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Planck was musically gifted: he took voice lessons in addition to playing the piano, organ and cello, and composing songs and operas. However, instead of music he chose to study physics. The Munich physics professor Philipp von Jolly advised him against going into physics, saying, "in this field, almost everything is already discovered, and all that remains is to fill a few holes." Planck replied that he didn't wish to discover new things, only to understand the known fundamentals of the field and began his studies in 1874 in Munic ...

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Max Planck, Max Planck - Origin and youth, Max Planck - Education, Max Planck - Academic career, Max Planck - Family, Max Planck - Professor at Berlin University, Max Planck - Black-body radiation, Max Planck - Einstein and the Theory of Relativity, Max Planck - World War and Weimar Republic, Max Planck - Quantum Mechanics, Max Planck - Nazi dictatorship and Second World War, Max Planck - Final years, Max Planck - Honours and medals

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The strategy behind the use of Legendre transforms is to shift the dependence of a function from one independent variable to another by adding (or subtracting) their product. They are used in thermodynamics to transform among the various thermodynamic potentials. For example, while the internal energy is an explicit function of entropy, volume and chemical composition the enthalpy, the Legendre ...

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Legendre transformation, Legendre transformation - Applications, Legendre transformation - Examples, Legendre transformation - Legendre transformation in one dimension, Legendre transformation - Geometric interpretation, Legendre transformation - Legendre transformation in more than one dimension, Legendre transformation - Further properties, Legendre transformation - Scaling properties, Legendre transformation - Behavior under translation, Legendre transformation - Behavior under inversion, Legendre transformation - Behavior under linear transformations, Legendre transformation - Infimal convolution

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The state now known as Germany was unified as a modern nation-state only in 1871, when the German Empire, dominated by the Kingdom of Prussia, was forged. This was the second German Reich, usually translated as "empire", but also meaning "kingdom", "domain" or "realm." (Königreich means "kingdom", and Reich- as in Reichskanzler was analogous to Royal- or calling the State the Crown in Commonwealth countries. Today the analogous entity is called der Bund, as in Bundeskanzler (Federal Chancellor).) Germany - Early history of the Ge ...

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Germany, Germany - History, Germany - Early history of the Germanic tribes 100 BC-300 AD, Germany - Migration Period and Franks 300-843, Germany - The Holy Roman Empire of the German Nation 843–1806, Germany - Restoration and revolution 1814–1871, Germany - German Empire 1871–1918, Germany - Weimar Republic 1919–1933, Germany - Third Reich 1933–1945, Germany - Division and reunification 1945–1990, Germany - Politics, Germany - Legal system, Germany - Foreign Relations, Germany - Armed Forces, Germany - Energy policy, Germany - Geography, Germany - States Länder, Germany - Territory, Germany - Climate, Germany - Economy, Germany - Exports, Germany - Imports, Germany - Agriculture, Germany - Industrial sector, Germany - Service sector, Germany - Natural resources, Germany - Society, Germany - Demographics, Germany - Religion, Germany - Education, Germany - Social issues, Germany - Culture, Germany - Miscellaneous topics

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Eigenvalue eigenvector and eigenspace - Computing eigenvalues and eigenvectors of matrices. Suppose that we want to compute the eigenvalues of a given matrix. If the matrix is small, we can compute them symbolically using the characteristic polynomial. However, this is often impossible for larger matrices, in which case we must use a numerical method. For more details on this topic, ...

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Eigenvalue eigenvector and eigenspace, Eigenvalue eigenvector and eigenspace - Definitions, Eigenvalue eigenvector and eigenspace - Examples, Eigenvalue eigenvector and eigenspace - Eigenvalue equation, Eigenvalue eigenvector and eigenspace - Spectral theorem, Eigenvalue eigenvector and eigenspace - Eigenvalues and eigenvectors of matrices, Eigenvalue eigenvector and eigenspace - Computing eigenvalues and eigenvectors of matrices, Eigenvalue eigenvector and eigenspace - Properties, Eigenvalue eigenvector and eigenspace - Conjugate eigenvector, Eigenvalue eigenvector and eigenspace - Generalized eigenvalue problem, Eigenvalue eigenvector and eigenspace - Entries from a ring, Eigenvalue eigenvector and eigenspace - Infinite-dimensional spaces, Eigenvalue eigenvector and eigenspace - Applications, Eigenvalue eigenvector and eigenspace - Notes

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The strategy behind the use of Legendre transforms is to shift the dependence of a function from one independent variable to another by taking the difference between the original function and their product. They are used to transform among the various thermodynamic potentials. For example, while the internal energy is an explicit function of the extensive variables, entropy, volume (and chemical composition) the enthalpy, the Legendre transform of USee also:

Legendre transformation, Legendre transformation - Applications, Legendre transformation - Examples, Legendre transformation - Legendre transformation in one dimension, Legendre transformation - Geometric interpretation, Legendre transformation - Legendre transformation in more than one dimension, Legendre transformation - Further properties, Legendre transformation - Scaling properties, Legendre transformation - Behavior under translation, Legendre transformation - Behavior under inversion, Legendre transformation - Behavior under linear transformations, Legendre transformation - Infimal convolution

Read more here: » Legendre transformation: Encyclopedia II - Legendre transformation - Applications