Helmholtz - Article Index

Encyclopedia - Illusion: Encyclopedia - Illusion
An illusion is a distortion of a sensory perception. Each of the human senses can be deceived by illusions, but visual illusions are the ...   » Read the article

Encyclopedia - Germany: Encyclopedia - Germany
(German: Einigkeit und Recht und Freiheit) 2 Prior to 2002: Deutsche Mark Germany, officially the Federal Republic of Germany (German: De...   » Read the article

Encyclopedia - Wilhelm Wundt: Encyclopedia - Wilhelm Wundt
Wilhelm Maximilian Wundt (August 16, 1832–August 31, 1920) was a German physiologist and psychologist. He is generally acknowledged as ...   » Read the article

Encyclopedia - Georges-pierre Seurat: Encyclopedia Ii - Georges-pierre Seurat - Scientific Background And Influences
During the 19th century, scientist-writers such as Eugène Chevreul, Ogden Rood and David Sutter wrote treatises on color, optical effect...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - History
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 Pru...   » Read the article

Encyclopedia - Electrical Double Layer: Encyclopedia Ii - Electrical Double Layer - Historical Development Of Double Layer Models
The earliest model of the electrical double layer is usually attributed to Helmholtz (1879). Helmholtz treated the double layer mathemati...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - History
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 Pru...   » Read the article

Encyclopedia - Josiah Willard Gibbs: Encyclopedia Ii - Josiah Willard Gibbs - Biography
Gibbs' scientific career can be divided into four phases. Up until 1879, he worked on the theory of thermodynamics. From 1880 to 1884, he...   » Read the article

Encyclopedia - History Of Calculus: Encyclopedia Ii - History Of Calculus - Invention Of Calculus
Many of the results of Newton and Leibniz were known to mathematicians in Kerala, India almost 300 years previously. In 1835, Charles Whi...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - History
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 Pru...   » Read the article

Encyclopedia - Wilhelm Wundt: Encyclopedia Ii - Wilhelm Wundt - Wundt's Life And Works
Wundt was born August 16, 1832 at Neckarau, in Baden - The fourth child to parents Maximilian Wundt (a Lutheran minister), and his wife M...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - The Natural Scale
Human beings distinguish sounds on the basis of their frequency. Actually what really matters is the ratio between their frequencies. The...   » Read the article

Encyclopedia - Timbre: Encyclopedia Ii - Timbre - Spectra
Each note produced by a musical instrument is made of a number of distinct frequencies, measured in hertz (Hz). The lowest frequency is c...   » Read the article

Encyclopedia - Philipp Lenard: Encyclopedia Ii - Philipp Lenard - Photoelectric Investigation
The radiant energy was difficult to study because it was inside sealed glass tubes, difficult to access, and because the rays were in the...   » Read the article

Encyclopedia - Georges-pierre Seurat: Encyclopedia Ii - Georges-pierre Seurat - Seurat's Scientific Background And Influences
During the 19th century, scientist-writers such as Eugene Chevreul, Ogden Rood and David Sutter wrote treatises on color, optical effects...   » Read the article

Encyclopedia - Max Planck: Encyclopedia Ii - Max Planck - Education
Planck was musically gifted: he took voice lessons in addition to playing the piano, organ and cello, and composing songs and operas. Ho...   » Read the article

Encyclopedia - Legendre Transformation: Encyclopedia Ii - Legendre Transformation - Applications
The strategy behind the use of Legendre transforms is to shift the dependence of a function from one independent variable to another by a...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - History
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 Pru...   » Read the article

Encyclopedia - Eigenvalue Eigenvector And Eigenspace: Encyclopedia Ii - Eigenvalue Eigenvector And Eigenspace - Eigenvalues And Eigenvectors Of Matrices
Eigenvalue eigenvector and eigenspace - Computing eigenvalues and eigenvectors of matrices. Suppose that we want to compute the eigenva...   » Read the article

Encyclopedia - Legendre Transformation: Encyclopedia Ii - Legendre Transformation - Applications
The strategy behind the use of Legendre transforms is to shift the dependence of a function from one independent variable to another by t...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - The Natural Scale
Human beings distinguish sounds on the basis of their frequency. Actually what really matters is the ratio between their frequencies. The...   » Read the article

Encyclopedia - Reciprocity Electromagnetism: Encyclopedia Ii - Reciprocity Electromagnetism - Conditions For Reciprocity
The Lorentz reciprocity theorem is simply a reflection of the fact that the linear operator relating and at a fixed frequency (in line...   » Read the article

Encyclopedia - Josiah Willard Gibbs: Encyclopedia Ii - Josiah Willard Gibbs - Biography
Gibbs' scientific career can be divided into four phases: Until 1879: theoretical thermodynamics. 1880-1884: vector analysis. 1882 to 18...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Politics
Germany - Legal system. Main article: Judiciary of Germany Germany has a civil or statute law system based ultimately on Roman law. L...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Geography
Germany - Federal States Länder. Main article: States of Germany Germany is divided into sixteen federal states (in German called LÃ...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Economy
Germany is the largest European economy and the fifth largest economy in the world measured by gross domestic product purchasing power pa...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmonics Partials And Overtones
The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies abov...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmonics And Non-linearities
When a periodic wave is composed of a fundamental and only odd harmonics (f, 3f, 5f, 7f, ...), the summed wave is half-wave symmetric; it...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Society
Germany - Demographics. Main article: Demographics of Germany Due to the country's federal and decentralized structure Germany has a ...   » Read the article

Encyclopedia - Timbre: Encyclopedia Ii - Timbre - Envelope
The timbre of a sound is also greatly effected by the following factors: attack or Interonset interval, decay, sustain, release, and tran...   » Read the article

Encyclopedia - Reciprocity Electromagnetism: Encyclopedia Ii - Reciprocity Electromagnetism - Lorentz Reciprocity
Specifically, suppose that one has a current density that produces an electric field and a magnetic field , where all three are periodi...   » Read the article

Encyclopedia - Reciprocity Electromagnetism: Encyclopedia Ii - Reciprocity Electromagnetism - Reciprocity For Electrical Networks
Above, Lorentz reciprocity was phrased in terms of an externally applied current source and the resulting field. Often, especially for el...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - The Equal Tempered Scale
In the natural scale the ratio of the frequencies of two notes which differ for one tone is not always the same. Consequently a certain m...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Politics
Germany - Legal system. Main articles: Judiciary of Germany, and [[]], and [[]], and [[]], and [[]]   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmony
If two notes are simultaneously played, with frequency ratios that are simple fractions (e.g. 2/1, 3/2 or 5/4), then the composite wave w...   » Read the article

Encyclopedia - Timbre: Encyclopedia Ii - Timbre - In Music
Timbre is often cited as one of the fundamental aspects of music. Formally, timbre and other factors are usually secondary to pitch. "To ...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Economy
Germany is the largest European economy and the fifth largest economy in the world measured by gross domestic product purchasing power pa...   » Read the article

Encyclopedia - Legendre Transformation: Encyclopedia Ii - Legendre Transformation - Examples
The exponential function ex has  x ln x âˆ’ x  as a Legendre transform since the respective first derivativ...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - The Equal Tempered Scale
In the natural scale the ratio of the frequencies of two notes which differ for one tone is not always the same. Consequently a certain m...   » Read the article

Encyclopedia - Eigenvalue Eigenvector And Eigenspace: Encyclopedia Ii - Eigenvalue Eigenvector And Eigenspace - Spectral Theorem
The spectral theorem depicts the importance of the eigenvalues and eigenvectors for characterizing a linear transformation in a unique wa...   » Read the article

Encyclopedia - Georges-pierre Seurat: Encyclopedia Ii - Georges-pierre Seurat - Life
Seurat was born to a well-off family in Paris. His father, a legal official, was a solitary man, and so was his son. Seurat attended the ...   » Read the article

Encyclopedia - Georges-pierre Seurat: Encyclopedia Ii - Georges-pierre Seurat - Challenging The Impressionists
Seurat and his fellow Neoimpressionists rejected contemporary Impressionism, with its emphasis on intuition and spontaneity, for a new "s...   » Read the article

Encyclopedia - Georges-pierre Seurat: Encyclopedia Ii - Georges-pierre Seurat - Seurat's Melding Of Science And Emotion
Seurat took to heart the color theorists' notion of a scientific approach to painting. Sutter predicted that someone could learn the laws...   » Read the article

Encyclopedia - Josiah Willard Gibbs: Encyclopedia Ii - Josiah Willard Gibbs - Scientific Recognition
Recognition was slow in coming, in good part because Gibbs published mainly in the Transactions of the Connecticut Academy of Sciences, a...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Transportation
Due to its central situation in Europe a very high traffic volume exists in Germany. In particular for the goods traffic it represents an...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Society
Germany - Demographics. Main article: Demographics of Germany Due to the country's federal and decentralized structure Germany has a ...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Society
Germany - Demographics. Main articles: Demographics of Germany, and [[]], and [[]], and [[]]   » Read the article

Encyclopedia - Georges-pierre Seurat: Encyclopedia Ii - Georges-pierre Seurat - Endnotes
[1] Seurat, Georges. Letter to Maurice Beaubourg (1890), in Impressionism and Post-Impressionism: Sources and Documents. L. Nochlin (ed.)...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Sound Waves
Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to...   » Read the article

Encyclopedia - Legendre Transformation: Encyclopedia Ii - Legendre Transformation - Geometric Interpretation
For a strictly convex function the Legendre-transformation can be interpreted as a mapping between the graph of the function and the fami...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Politics
Germany - Legal system. Main article: Judiciary of Germany Germany has a civil or statute law system based ultimately on Roman law. L...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Economy
Germany is the largest European economy and the fifth largest economy in the world measured by gross domestic product purchasing power pa...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Geography
Germany - Federal States Länder. Main article: States of Germany Germany is divided into sixteen federal states (in German called LÃ...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Geography
Germany - Federal States Bundesländer. Main articles: States of Germany, and [[]], and [[]], and [[]], and [ ... See also:Germany, Ge...   » Read the article

Encyclopedia - Philipp Lenard: Encyclopedia Ii - Philipp Lenard - Biography
Philipp Lenard was born in Bratislava (then part of the Austro-Hungarian Empire) on July 7, 1862. He studied under the illustrious Bunsen...   » Read the article

Encyclopedia - Georges-pierre Seurat: Encyclopedia Ii - Georges-pierre Seurat - Life
Seurat attended the Ecole des Beaux-Arts in 1878 and 1879. After a year of military service at Brest military academy, he returned to Par...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Society
Germany - Demographics. Due to the country's federal and decentralized structure Germany has a number of larger cities. The most populo...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Economy
Germany is the largest European economy and the fifth largest economy in the world measured by gross domestic product purchasing power pa...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Geography
Germany - States Länder. Germany is divided into sixteen federal states (in German called Länder, singular Land; though more commonly...   » Read the article

Encyclopedia - Georges-pierre Seurat: Encyclopedia Ii - Georges-pierre Seurat - Seurat's Melding Of Science And Emotion
Seurat took to heart the color theorists' notion of a scientific approach to painting. Sutter had predicted that someone could learn the ...   » Read the article

Encyclopedia - Georges-pierre Seurat: Encyclopedia Ii - Georges-pierre Seurat - Endnotes
[1] Hunter, Sam. Georges Seurat, in S. Hunter and J. Jacobus, Modern Art (3rd ed.). New York: Harry N. Abrams, Inc. 1992, p. 26 [2] Seur...   » Read the article

Encyclopedia - Josiah Willard Gibbs: Encyclopedia Ii - Josiah Willard Gibbs - Scientific Recognition
Among the honors given to Gibbs' memory after his death, Yale University created the "J. Willard Gibbs Professorship in Theoretical Chemi...   » Read the article

Encyclopedia - History Of Calculus: Encyclopedia Ii - History Of Calculus - Integrals
Niels Henrik Abel seems to have been the first to consider in a general way the question as to what differential expressions can be integ...   » Read the article

Encyclopedia - History Of Calculus: Encyclopedia Ii - History Of Calculus - Controversy Newton Leibnitz... Or Madhava?
Madhava of Sangamagrama and the Kerala school were the first to come up with the important ideas of calculus in the 14th century and some...   » Read the article

Encyclopedia - Germany: Encyclopedia Ii - Germany - Politics
Germany - Legal system. Germany has a civil or statute law system based ultimately on Roman law. Legislative power is divided between t...   » Read the article

Encyclopedia - Eigenvalue Eigenvector And Eigenspace: Encyclopedia Ii - Eigenvalue Eigenvector And Eigenspace - Applications
An example of an eigenvalue equation where the transformation is represented in terms of a differential operator is the time-independent...   » Read the article

Encyclopedia - Eigenvalue Eigenvector And Eigenspace: Encyclopedia Ii - Eigenvalue Eigenvector And Eigenspace - Definitions
Transformations of space—such as translation (or shifting the origin), rotation, reflection, stretching, compression, or any combinatio...   » Read the article

Encyclopedia - Eigenvalue Eigenvector And Eigenspace: Encyclopedia Ii - Eigenvalue Eigenvector And Eigenspace - Examples
As the Earth rotates, every arrow pointing outward from the center of the Earth also rotates, except those arrows that lie on the axis of...   » Read the article

Encyclopedia - Eigenvalue Eigenvector And Eigenspace: Encyclopedia Ii - Eigenvalue Eigenvector And Eigenspace - Infinite-dimensional Spaces
If the vector space is infinite dimensional, it may be advantageous to define the concept of spectral values. The spectral values are the...   » Read the article

Encyclopedia - Eigenvalue Eigenvector And Eigenspace: Encyclopedia Ii - Eigenvalue Eigenvector And Eigenspace - Spectral Theorem
The spectral theorem depicts the whole importance of the eigenvalues and eigenvectors for characterizing a linear transformation in a uni...   » Read the article

Encyclopedia - Eigenvalue Eigenvector And Eigenspace: Encyclopedia Ii - Eigenvalue Eigenvector And Eigenspace - Eigenvalue Equation
Mathematically, vλ is an eigenvector and λ the corresponding eigenvalue of a transformation if the equation: is true, where is the...   » Read the article

Encyclopedia - Legendre Transformation: Encyclopedia Ii - Legendre Transformation - Examples
The exponential function ex has x ln x − x as a Legendre transform since the respective first derivatives ex and ln x are inverse ...   » Read the article

Encyclopedia - Legendre Transformation: Encyclopedia Ii - Legendre Transformation - Legendre Transformation In One Dimension
In one dimension, a Legendre transform to a function f : R â†’ R with an invertible first derivative may be found usi...   » Read the article

Encyclopedia - Max Planck: Encyclopedia Ii - Max Planck - Einstein And The Theory Of Relativity
In 1905 the three epochal papers of hitherto completely unknown Albert Einstein were published in the journal Annalen der Physik; Planck ...   » Read the article

Encyclopedia - Max Planck: Encyclopedia Ii - Max Planck - Black-body Radiation
In 1894 Planck turned his attention to the problem of black-body radiation. He had been commissioned by electric companies to discover h...   » Read the article

Encyclopedia - Max Planck: Encyclopedia Ii - Max Planck - Family
In March 1887 Planck married Marie Merck (1861-1909), sister of a school fellow, and moved with her into a sublet apartment in Kiel. Four...   » Read the article

Encyclopedia - Max Planck: Encyclopedia Ii - Max Planck - Academic Career
With the completion of his habilitation thesis, Planck became an unpaid private lecturer in Munich, waiting until he would be offered an ...   » Read the article

Encyclopedia - Max Planck: Encyclopedia Ii - Max Planck - Nazi Dictatorship And Second World War
When the Nazis seized power in 1933, Planck had already reached the age of 74; he had to witness how many Jewish friends and colleagues w...   » Read the article

Encyclopedia - Max Planck: Encyclopedia Ii - Max Planck - Final Years
After the war, a number of German physicists assembled in Göttingen in order to reestablish the Kaiser-Wilhelm-Gesellschaft. In July of...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmonics And Non-linearities
When a periodic wave is composed of a fundamental and only odd harmonics (f, 3f, 5f, 7f, ...), the summed wave is symmetrical; it can be ...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmonics Partials And Overtones
The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies abov...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Sound Waves
Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to...   » Read the article

Encyclopedia - Max Planck: Encyclopedia Ii - Max Planck - Origin And Youth
Planck came from a traditional, intellectual family. His paternal great-grandfather and grandfather were both theology professors in Göt...   » Read the article

Encyclopedia - Legendre Transformation: Encyclopedia Ii - Legendre Transformation - Legendre Transformation In More Than One Dimension
For a differentiable real-valued function on an open subset U of Rn the Legendre conjugate of the pair (U, f) is defined to be the pair (...   » Read the article

Encyclopedia - Legendre Transformation: Encyclopedia Ii - Legendre Transformation - Geometric Interpretation
For a strictly convex function the Legendre-transformation can be interpreted as a mapping between the graph of the function and the fami...   » Read the article

Encyclopedia - Max Planck: Encyclopedia Ii - Max Planck - World War And Weimar Republic
At the onset of the First World War Planck was not immune to the general excitement of the public: "... besides of much horrible also muc...   » Read the article

Encyclopedia - Max Planck: Encyclopedia Ii - Max Planck - Professor At Berlin University
In Berlin Planck joined the local Physical Society: later he wrote about this time: "In those days I was essentially the only Theoretical...   » Read the article

Encyclopedia - Musical Acoustics: Encyclopedia Ii - Musical Acoustics - Harmony
If two notes are simultaneously played, with frequency ratios that are simple fractions (e.g. 2/1, 3/2 or 5/4), then the composite wave w...   » Read the article