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Encyclopedia > William Rowan Hamilton
William Hamilton

William Rowan Hamilton
Born August 4, 1805(1805-08-04)
Dublin, Ireland
Died September 2, 1865 (aged 60)
Dublin, Ireland
Residence Ireland
Nationality Irish, of Scottish descent
Field Mathematician, physicist, and astronomer
Institutions Trinity College Dublin
Alma mater Trinity College Dublin
Academic advisor   John Brinkley
Known for Quaternions and Hamiltonians
Religion Anglican
Note that although Hamilton never had a doctoral advisor, scientific genealogy authorities regard the Reverend John Brinkley as Hamilton's equivalent mentor.

Sir William Rowan Hamilton (August 4, 1805September 2, 1865) was an Irish mathematician, physicist, and astronomer who made important contributions to the development of optics, dynamics, and algebra. His discovery of quaternions is perhaps his best known investigation. Hamilton's work was later significant in the development of quantum mechanics. Hamilton is said to have showed immense talent at a very early age, prompting astronomer Bishop Dr. John Brinkley to remark in 1823 of Hamilton at the age of eighteen: “This young man, I do not say will be, but is, the first mathematician of his age.” William Hamilton (and shortened forms) may refer to: William Hamilton, 2nd Duke of Hamilton (1616-1651), Scottish nobleman William Hamilton (surgeon) (died 1717), Surgeon of the British East India Company William Hamilton (educator) (?-1730?), Principal of the University of Edinburgh William Hamilton (poet) (1665-1751), Scottish poet William Hamilton (Jacobite... Hamilton College Enthnic Diversity Chart File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... is the 216th day of the year (217th in leap years) in the Gregorian calendar. ... 1805 was a common year starting on Tuesday (see link for calendar). ... Dublin city centre at night WGS-84 (GPS) Coordinates: , Statistics Province: Leinster County: Dáil Éireann: Dublin Central, Dublin North Central, Dublin North East, Dublin North West, Dublin South Central, Dublin South East European Parliament: Dublin Dialling Code: +353 1 Postal District(s): D1-24, D6W Area: 114. ... is the 245th day of the year (246th in leap years) in the Gregorian calendar. ... 1865 (MDCCCLXV) is a common year starting on Sunday. ... Dublin city centre at night WGS-84 (GPS) Coordinates: , Statistics Province: Leinster County: Dáil Éireann: Dublin Central, Dublin North Central, Dublin North East, Dublin North West, Dublin South Central, Dublin South East European Parliament: Dublin Dialling Code: +353 1 Postal District(s): D1-24, D6W Area: 114. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Not to be confused with physician, a person who practices medicine. ... An astronomer or astrophysicist is a person whose area of interest is astronomy or astrophysics. ... The College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin or more commonly Trinity College, Dublin (TCD) was founded in 1592 by Queen Elizabeth I, is the only constituent college of the University of Dublin, Irelands oldest university. ... The College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin or more commonly Trinity College, Dublin (TCD) was founded in 1592 by Queen Elizabeth I, is the only constituent college of the University of Dublin, Irelands oldest university. ... John Brinkley (1763–September 14, 1835) was the first Royal Astronomer of Ireland and later the Bishop of Cloyne. ... In mathematics, the quaternions are a non-commutative extension of the complex numbers. ... In physics, Hamiltonian has distinct but closely related meanings. ... The term Anglican describes those people and churches following the religious traditions of the Church of England, especially following the Reformation. ... An academic, or scientific, genealogy, is an attempt to organise a family tree of scientists and scholars according to dissertation supervision relationships. ... John Brinkley (1763–September 14, 1835) was the first Royal Astronomer of Ireland and later the Bishop of Cloyne. ... is the 216th day of the year (217th in leap years) in the Gregorian calendar. ... 1805 was a common year starting on Tuesday (see link for calendar). ... is the 245th day of the year (246th in leap years) in the Gregorian calendar. ... 1865 (MDCCCLXV) is a common year starting on Sunday. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Not to be confused with physician, a person who practices medicine. ... An astronomer or astrophysicist is a person whose area of interest is astronomy or astrophysics. ... For the book by Sir Isaac Newton, see Opticks. ... In physics, dynamics is the branch of classical mechanics that is concerned with the effects of forces on the motion of objects. ... This article is about the branch of mathematics. ... In mathematics, the quaternions are a non-commutative extension of the complex numbers. ... In physics, Hamiltonian has distinct but closely related meanings. ... The quantum Hamiltonian is the physical state of a system, which may be characterized as a ray in an abstract Hilbert space (or, in the case of ensembles, as a trace class operator with trace 1). ... John Brinkley (1763–September 14, 1835) was the first Royal Astronomer of Ireland and later the Bishop of Cloyne. ...

Contents

Biography

William Rowan Hamilton's mathematical career included the study of geometrical optics, adaptation of dynamic methods in optical systems, applying quaternion and vector methods to problems in mechanics and in geometry, development of theories of conjugate algebraic couple functions (in which complex numbers are constructed as ordered pairs of real numbers), solvability of polynomial equations and general quintic polynomial solvable by radicals, the analysis on Fluctuating Functions (and the ideas from Fourier analysis), linear operators on quaternions and proving a result for linear operators on the space of quaternions (which is a special case of the general theorem which today is known as the Cayley-Hamilton Theorem). Hamilton also invented "Icosian Calculus", which he used to investigate closed edge paths on a dodecahedron that visit each vertex exactly once. See also list of optical topics. ... Fourier analysis, named after Joseph Fouriers introduction of the Fourier series, is the decomposition of a function in terms of a sum of sinusoidal basis functions (vs. ... In linear algebra, the Cayley-Hamilton theorem (named after the mathematicians Arthur Cayley and William Hamilton) states that every square matrix over the real or complex field, satisfies its own characteristic equation. ... In the mathematical field of graph theory, a Hamiltonian path is a path in a undirected graph which visits each vertex exactly once. ...


Early life

A child prodigy, Hamilton was born the son of Archibald Hamilton, a solicitor, in Dublin at 36 Dominick Street, but was later put up for adoption. His father Archibald Hamilton was from Dunboyne, Co. Meath. Hamilton's genius first displayed itself in the form of a power of acquiring languages. Note: Hamilton's ability to actually speak these languages is disputed by some historians, who claim he had only a very basic understanding of them. At the age of seven he had already made very considerable progress in Hebrew, and before he was thirteen he had acquired, under the care of his uncle (a linguist), almost as many languages as he had years of age. Among these, besides the classical European languages and the modern European languages, were included Persian, Arabic, Hindustani, Sanskrit, and even Malay. But though to the very end of his life he retained much of the singular learning of his childhood and youth, often reading Persian and Arabic in the intervals of sterner pursuits, he had long abandoned them as a study, and employed them merely as a relaxation. A child prodigy is someone who is a master of one or more skills or arts at an early age. ... Dublin city centre at night WGS-84 (GPS) Coordinates: , Statistics Province: Leinster County: Dáil Éireann: Dublin Central, Dublin North Central, Dublin North East, Dublin North West, Dublin South Central, Dublin South East European Parliament: Dublin Dialling Code: +353 1 Postal District(s): D1-24, D6W Area: 114. ... “Hebrew” redirects here. ... “Farsi” redirects here. ... “Arabic” redirects here. ... The word Hindustani is an adjective used to denote a connection to India, or, more precisely, the historical region that encompasses Northern India, Pakistan, and nearby areas. ... Sanskrit ( , for short ) is a classical language of India, a liturgical language of Hinduism, Buddhism, Sikhism, and Jainism, and one of the 23 official languages of India. ... Not to be confused with the Malayalam language, spoken in India. ...


Hamilton later attended Westminster School with Zerah Colburn. He was part of a small but well-regarded school of mathematicians associated with Trinity College, Dublin, where he spent his life. He studied both classics and science, and was appointed Professor of Astronomy in 1827, prior to his graduation. For other uses, see Westminster School (disambiguation). ... Zerah Colburn (1804-1840) was a famous child prodigy of the 19th century. ... Trinity College, Dublin TCD, corporately designated as the Provost, Fellows and Scholars of the College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin, was founded in 1592 by Elizabeth I, and is the only constituent college of the University of Dublin, Irelands oldest university. ... For other uses, see Astronomy (disambiguation). ...


Mathematical studies

Hamilton's mathematical studies seem to have been undertaken and carried to their full development without any assistance whatsoever, and the result is that his writings belong to no particular "school", unless indeed we consider them to form, as they are well entitled to do, a school by themselves. As an arithmetical calculator Hamilton was not only an expert, but he seems to have occasionally found a positive experience in working out to an enormous number of places of decimals the result of some irksome calculation. At the age of twelve Hamilton engaged Zerah Colburn, the American "calculating boy", who was then being exhibited as a curiosity in Dublin, and he had not always the worst of the encounter. But, two years before, he had accidentally fallen in with a Latin copy of Euclid, which he eagerly devoured; and at twelve Hamilton studied Newton’s Arithmetica Universalis. This was his introduction to modern analysis. Hamilton soon commenced to read the Principia, and at sixteen Hamilton had mastered a great part of that work, besides some more modern works on analytical geometry and the differential calculus. Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... Arithmetic tables for children, Lausanne, 1835 Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. ... Zerah Colburn (1804-1840) was a famous child prodigy of the 19th century. ... This article does not cite any references or sources. ... For other uses, see Latin (disambiguation). ... For other uses, see Euclid (disambiguation). ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Title page of the Arithmetica, published 1707 The English translation by Raphson was published in 1720 The Arithmetica Universalis was a mathematics text written by Isaac Newton. ... Analysis has its beginnings in the rigorous formulation of calculus. ... Newtons own copy of his Principia, with handwritten corrections for the second edition. ... Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. ... Differential calculus is the theory of and computations with differentials; see also derivative and calculus. ...


About this period Hamilton was also engaged in preparation for entrance at Trinity College, Dublin, and had therefore to devote a portion of time to classics. In the summer of 1822, in his seventeenth year, he began a systematic study of Laplace's Mécanique Céleste. Nothing could be better fitted to call forth such mathematical powers as those of Hamilton; for Laplace's great work, rich to profusion in analytical processes alike novel and powerful, demands from the student careful and often laborious study. Trinity College, Dublin TCD, corporately designated as the Provost, Fellows and Scholars of the College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin, was founded in 1592 by Elizabeth I, and is the only constituent college of the University of Dublin, Irelands oldest university. ... Pierre-Simon Laplace Pierre-Simon Laplace (March 23, 1749 – March 5, 1827) was a French mathematician and astronomer, the discoverer of the Laplace transform and Laplaces equation. ... Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. ...


It was in the successful effort to open this treasure-house that Hamilton’s mind received its final temper, "Dês-lors il commença à marcher seul" (from that time it began to go alone), to use the words of the biographer of another great mathematician. From that time Hamilton appears to have devoted himself almost wholly to the mathematics investigation, though he ever kept himself well acquainted with the progress of science both in Britain and abroad. Hamilton detected an important defect in one of Laplace’s demonstrations, and he was induced by a friend to write out his remarks, that they might be shown to Dr John Brinkley, then the first Astronomer Royal for Ireland, and an accomplished mathematician. Brinkley seems at once to have perceived the vast talents of young Hamilton, and to have encouraged him in the kindest manner. The history of science and technology (HST) is a field of history which examines how humanitys understanding of science and technology has changed over the millennia. ... John Brinkley (1763–September 14, 1835) was the first Royal Astronomer of Ireland and later the Bishop of Cloyne. ... An office attached to the directorship of an astronomical observatory at Dunsink, near Dublin. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ...


Hamilton’s career at College was perhaps unexampled. Amongst a number of competitors of more than ordinary merit, he was first in every subject and at every examination. He achieved the rare distinction of obtaining an optime for both Greek and for physics. The amount of many more such honours Hamilton might have attained it is impossible to say; but Hamilton was expected to win both the gold medals at the degree examination, had his career as a student not been cut short by an unprecedented event. This was Hamilton’s appointment to the Andrews Professorship of Astronomy in the University of Dublin, vacated by Dr Brinkley in 1827. The chair was not exactly offered to him, as has been sometimes asserted, but the electors, having met and talked over the subject, authorized one of their number, who was Hamilton's personal friend, to urge Hamilton to become a candidate, a step which Hamilton's modesty had prevented him from taking. Thus, when barely twenty-two, Hamilton was established at the Dunsink Observatory, near Dublin. At the University of Cambridge in England, an optime makes you lose The Game and is a student who graduates with a second-class (Senior Optime) or third-class (Junior Optime) honours mathematics degree. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Gold Medal is an album by American band The Donnas, released in 2004. ... The University of Dublin, corporately designated the Chancellor, Doctors and Masters of the University of Dublin located in Dublin, Ireland, was founded in 1592 by Queen Elizabeth I, making it Irelands oldest university. ... The Dunsink Observatory is an astronomical observatory established in approximately 1785 near the city of Dublin, Ireland. ...


Hamilton was not specially fitted for the post, for although he had a profound acquaintance with theoretical astronomy, he had paid but little attention to the regular work of the practical astronomer. And it must be said that Hamilton’s time was better employed in original investigations than it would have been had he spent it in observations made even with the best of instruments. Hamilton was intended by the university authorities who elected him to the professorship of astronomy to spend his time as Hamilton best could for the advancement of science, without being tied down to any particular branch. If Hamilton devoted himself to practical astronomy, the University of Dublin would assuredly have furnished him with instruments and an adequate staff of assistants. Theoretical astrophysics is the discipline that seeks to explain the phenomena observed by astronomers in physical terms with a theoretic approach. ... An astronomer or astrophysicist is a person whose area of interest is astronomy or astrophysics. ... Part of a scientific laboratory at the University of Cologne. ...


In 1835, being secretary to the meeting of the British Association which was held that year in Dublin, he was knighted by the lord-lieutenant. Other honours rapidly succeeded, among which his election in 1837 to the president’s chair in the Royal Irish Academy, and the rare distinction of being made corresponding member of the Academy of St Petersburg. These are the few salient points (other, of course, than the epochs of Hamilton's more important discoveries and inventions presently to be considered) in the uneventful life of Hamilton. The British Association or the British Association for the Advancement of Science or the BA is a learned society with the object of promoting science, directing general attention to scientific matters, and facilitating intercourse between scientific workers. ... The silver Anglia knight, commissioned as a trophy in 1850, intended to represent the Black Prince. ... Official standard of the Lord Lieutenant of Ireland The Lord Lieutenant of Ireland (plural: Lords Lieutenant), also known as the Judiciar in the early mediaeval period and as the Lord Deputy as late as the 17th century, was the Kings representative and head of the Irish executive during the... President is a title held by many leaders of nothing, companies, trade unions, universities, and countries. ... The Royal Irish Academy (RIA) is one of Irelands premier learned societies and cultural institutions. ... For other uses, see Academy (disambiguation). ... Saint Petersburg (Russian: Санкт-Петербу́рг, English transliteration: Sankt-Peterburg), colloquially known as Питер (transliterated Piter), formerly known as Leningrad (Ленингра́д, 1924–1991) and...


Optics and dynamics

He made important contributions to optics and to dynamics. Hamilton's papers on optics and dynamics demonstrated theoretical dynamics being treated as a branch of pure mathematics. Hamilton's first discovery was contained in one of those early papers which in 1823 Hamilton communicated to Dr Brinkley, by whom, under the title of “Caustics,” it was presented in 1824 to the Royal Irish Academy. It was referred as usual to a committee. Their report, while acknowledging the novelty and value of its contents recommended that, before being published, it should be still further developed and simplified. During the time between 1825 to 1828 the paper grew to an immense bulk, principally by the additional details which had been inserted at the desire of the committee. But it also assumed a much more intelligible form, and the features of the new method were now easily to be seen. Hamilton himself seems not until this period to have fully understood either the nature or importance of optics, as later Hamilton had intentions of applying his method to dynamics. For the book by Sir Isaac Newton, see Opticks. ... In physics, dynamics is the branch of classical mechanics that is concerned with the effects of forces on the motion of objects. ... The Royal Irish Academy (RIA) is one of Irelands premier learned societies and cultural institutions. ...


In 1827, Hamilton presented a theory that provided a single function that brings together mechanics, optics and mathematics. It helped in establishing the wave theory of light. He proposed for it when he first predicted its existence in the third supplement to his "Systems of Rays", read in 1832. The Royal Irish Academy paper was finally entitled “Theory of Systems of Rays,” (April 23, 1827) and the first part was printed in 1828 in the Transactions of the Royal Irish Academy. It is understood that the more important contents of the second and third parts appeared in the three voluminous supplements (to the first part) which were published in the same Transactions, and in the two papers “On a General Method in Dynamics,” which appeared in the Philosophical Transactions in 1834 and 1835. is the 113th day of the year (114th in leap years) in the Gregorian calendar. ... Year 1827 (MDCCCXXVII) was a common year starting on Monday (link will display the full calendar) of the Gregorian Calendar (or a common year starting on Wednesday of the 12-day slower Julian calendar). ...


The principle of “Varying Action“ is the great feature of these papers; and it is, indeed, that the one particular result of this theory which, perhaps more than anything else that Hamilton has done, something which should have been easily within the reach of Augustin Fresnel and others for many years before, and in no way required Hamilton’s new conceptions or methods, although it was by Hamilton’s new theoretical dynamics that he was led to its discovery. This singular result is still known by the name “conical refraction”. Augustin Fresnel Augustin-Jean Fresnel (pronounced fray-NELL) (May 10, 1788 – July 14, French physicist who contributed significantly to the establishment of the wave theory of light and optics. ...


The step from optics to dynamics in the application of the method of “Varying Action” was made in 1827, and communicated to the Royal Society, in whose Philosophical Transactions for 1834 and 1835 there are two papers on the subject. These display, like the “Systems of Rays,” a mastery over symbols and a flow of mathematical language almost unequalled. But they contain what is far more valuable still, the greatest addition which dynamical science had received since the strides made by Sir Isaac Newton and Joseph Louis Lagrange. C. G. J. Jacobi and other mathematicians have extended Hamilton's processes, and have thus made extensive additions to our knowledge of differential equations. The Philosophical Transactions of the Royal Society, or , is the oldest scientific journal printed in the English-speaking world, and was only three months shy of being the oldest in the world. ... Part of a scientific laboratory at the University of Cologne. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Joseph-Louis, comte de Lagrange (January 25, 1736 Turin, Kingdom of Sardinia - April 10, 1813 Paris) was an Italian-French mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics as arguably the greatest mathematician of the 18th century. ... Karl Gustav Jacob Jacobi (Potsdam December 10, 1804 - Berlin February 18, 1851), was not only a great German mathematician but also considered by many as the most inspiring teacher of his time (Bell, p. ... In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ...


And though differential equations, optics and theoretical dynamics of course are favored in which any such contribution to science can be looked at, the other must not be despised. It is characteristic of most of Hamilton's, as of nearly all great discoveries, that even their indirect consequences are of high value.


Quaternions

The other great contribution made by Hamilton to mathematical science was his discovery of quaternions in 1843. A plaque on Broom Bridge in Dublin, commemorating Hamiltons invention of Quaternions My father took the picture and agrees to transfer the copyright to me. ... In mathematics, the quaternions are a non-commutative extension of the complex numbers. ...


Hamilton was looking for ways of extending complex numbers (which can be viewed as points on a 2-dimensional plane) to higher spatial dimensions. Hamilton could not do so for 3 dimensions: in fact later mathematicians showed that this would be impossible. Eventually Hamilton tried 4 dimensions and created quaternions. According to the story Hamilton told, on October 16 Hamilton was out walking along the Royal Canal in Dublin with his wife when the solution in the form of the equation In mathematics, a complex number is a number of the form where a and b are real numbers, and i is the imaginary unit, with the property i 2 = −1. ... A spatial point is an entity with a location in space but no extent (volume, area or length). ... This article is about the mathematical construct. ... is the 289th day of the year (290th in leap years) in the Gregorian calendar. ... Picture of the Royal Canal near Mullingar taken in October 2004 The Royal Canal is a canal originally built for freight transportation from the River Liffey at Dublin to the River Shannon in the Republic of Ireland. ... Dublin city centre at night WGS-84 (GPS) Coordinates: , Statistics Province: Leinster County: Dáil Éireann: Dublin Central, Dublin North Central, Dublin North East, Dublin North West, Dublin South Central, Dublin South East European Parliament: Dublin Dialling Code: +353 1 Postal District(s): D1-24, D6W Area: 114. ... Helen Maria Bayly (1804–1869) was the wife of Irish mathematician William Rowan Hamilton. ...

i2 = j2 = k2 = ijk = − 1

suddenly occurred to him; Hamilton then promptly carved this equation into the side of the nearby Broom Bridge (which Hamilton called Brougham Bridge). Since 1989, the National University of Ireland, Maynooth has organized a pilgrimage, where mathematicians take a walk from Dunsink observatory to the bridge where, unfortunately, no trace of the carving remains, though a stone plaque does commemorate the discovery. Broom Bridge Plaque on Broom Bridge Broom Bridge, also known as Brougham Bridge, is a small bridge along Broombridge road which crosses the Royal Canal in Dublin, Ireland. ... The National University of Ireland, Maynooth (NUIM) was founded in 1997 by the Universities Act, 1997 as a constituent university of the National University of Ireland. ...


The quaternion involved abandoning commutativity, a radical step for the time. Not only this, but Hamilton had in a sense invented the cross and dot products of vector algebra. Hamilton also described a quaternion as an ordered four-element multiple of real numbers, and described the first element as the 'scalar' part, and the remaining three as the 'vector' part. Example showing the commutativity of addition (3 + 2 = 2 + 3) For other uses, see Commute (disambiguation). ...


In 1852, Hamilton introduced quaternions as a method of analysis. His first great work is Lectures on Quaternions (Dublin, 1852). Hamilton confidently declared that quaternions would be found to have a powerful influence as an instrument of research. He popularized quaternions with several books, the last of which, Elements of Quaternions, had 800 pages and was published shortly after his death.


Peter Guthrie Tait among others, advocated the use of Hamilton's quaternions. They were made a mandatory examination topic in Dublin, and for a while they were the only advanced mathematics taught in some American universities. However, controversy about the use of quaternions grew in the late 1800s. Some of Hamilton's supporters vociferously opposed the growing fields of vector algebra and vector calculus (from developers like Oliver Heaviside and Willard Gibbs), because quaternions provide superior notation. While this is undeniable for four dimensions, quaternions cannot be used with arbitrary dimensionality (though extensions like Clifford algebras can). Vector notation largely replaced the "space-time" quaternions in science and engineering by the mid-20th century. Peter Tait Peter Guthrie Tait (April 28, 1831 - July 4, 1901) was a Scottish mathematical physicist. ... Oliver Heaviside (May 18, 1850 – February 3, 1925) was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, developed techniques for applying Laplace transforms to the solution of differential equations, reformulated Maxwells field equations in terms of electric and... Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American mathematical physicist who contributed much of the theoretical foundation that led to the development of chemical thermodynamics and was one of the founders of vector analysis. ... Clifford algebras are a type of associative algebra in mathematics. ... In special relativity and general relativity, time and three-dimensional space are treated together as a single four-dimensional pseudo-Riemannian manifold called spacetime. ...


Today, the quaternions are in use by computer graphics, control theory, signal processing and orbital mechanics, mainly for representing rotations/orientations. For example, it is common for spacecraft attitude-control systems to be commanded in terms of quaternions, which are also used to telemeter their current attitude. The rationale is that combining many quaternion transformations is more numerically stable than combining many matrix transformations. In pure mathematics, quaternions show up significantly as one of the four finite-dimensional normed division algebras over the real numbers, with applications throughout algebra and geometry. This article is about the scientific discipline of computer graphics. ... For control theory in psychology and sociology, see control theory (sociology). ... Signal processing is the processing, amplification and interpretation of signals, and deals with the analysis and manipulation of signals. ... In mathematics, a normed division algebra A is a division algebra over the real or complex numbers which is also a normed vector space, with norm || . || satisfying ||xy|| = ||x|| ||y|| for all x and y in A. While the definition allows normed division algebras to be infinite-dimensional, this, in...


Hamilton also contributed an alternative formulation of the mathematical theory of classical mechanics. While adding no new physics, this formulation, which builds on that of Joseph Louis Lagrange, provides a more powerful technique for working with the equations of motion. Both the Lagrangian and Hamiltonian approaches were developed to describe the motion of discrete systems, were then extended to continuous systems and in this form can be used to define vector fields. In this way, the techniques find use in electromagnetic, quantum relativity theory and field theory. Joseph-Louis, comte de Lagrange (January 25, 1736 Turin, Kingdom of Sardinia - April 10, 1813 Paris) was an Italian-French mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics as arguably the greatest mathematician of the 18th century. ... A Lagrangian of a dynamical system, named after Joseph Louis Lagrange, is a function of the dynamical variables and concisely describes the equations of motion of the system. ... Hamiltonian mechanics is a re-formulation of classical mechanics that was invented in 1833 by William Rowan Hamilton. ... A discrete system or discrete-time system, as opposed to a continuous-time system, is one in which the signals are sampled periodically. ... Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... Quantum field theory (QFT) is the quantum theory of fields. ... Albert Einsteins theory of relativity is a set of two theories in physics: special relativity and general relativity. ... Field theory (mathematics), the theory of the algebraic concept of field. ...


Other originality

Hamilton originally matured his ideas before putting pen to paper. The discoveries, papers and treatises previously mentioned might well have formed the whole work of a long and laborious life. But not to speak of his enormous collection of books, full to overflowing with new and original matter, which have been handed over to Trinity College, Dublin, the previous mentioned works barely form the greater portion of what Hamilton has published. Hamilton developed the variational principle, which was reformulated later by Carl Gustav Jacob Jacobi. He also introduced Hamilton's puzzle which can be solved using the concept of a Hamiltonian path. Trinity College, Dublin TCD, corporately designated as the Provost, Fellows and Scholars of the College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin, was founded in 1592 by Elizabeth I, and is the only constituent college of the University of Dublin, Irelands oldest university. ... A variational principle is a principle in physics which is expressed in terms of the calculus of variations. ... Karl Gustav Jacob Jacobi (Potsdam December 10, 1804 - Berlin February 18, 1851), was not only a great German mathematician but also considered by many as the most inspiring teacher of his time (Bell, p. ... A hamiltonian path (black) over a graph (blue). ...


Hamilton's extraordinary investigations connected with the solution of algebraic equations of the fifth degree, and his examination of the results arrived at by N. H. Abel, G. B. Jerrard, and others in their researches on this subject, form another contribution to science. There is next Hamilton's paper on Fluctuating Functions, a subject which, since the time of Joseph Fourier, has been of immense and ever increasing value in physical applications of mathematics. There is also the extremely ingenious invention of the hodograph. Of his extensive investigations into the solutions (especially by numerical approximation) of certain classes of physical differential equations, only a few items have been published, at intervals, in the Philosophical Magazine. This article is about the term degree as used in mathematics. ... Niels Henrik Abel (August 5, 1802–April 6, 1829), Norwegian mathematician, was born in Nedstrand, near Finnøy where his father acted as rector. ... Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series and their application to problems of heat flow. ... Hodograph is a curve of which the radius vector is proportional to the velocity of a moving particle. ... Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). ... The Philosophical Magazine is arguably the world’s oldest commercially published scientific journal. ...


Besides all this, Hamilton was a voluminous correspondent. Often a single letter of Hamilton's occupied from fifty to a hundred or more closely written pages, all devoted to the minute consideration of every feature of some particular problem; for it was one of the peculiar characteristics of Hamilton's mind never to be satisfied with a general understanding of a question; Hamilton pursued the problem until he knew it in all its details. Hamilton was ever courteous and kind in answering applications for assistance in the study of his works, even when his compliance must have cost him much time. He was excessively precise and hard to please with reference to the final polish of his own works for publication; and it was probably for this reason that he published so little compared with the extent of his investigations.


Death and afterwards

Hamilton retained his faculties unimpaired to the very last, and steadily continued till within a day or two of his death, which occurred on 2 September 1865, the task of finishing the “Elements of Quaternions” which had occupied the last six years of his life. is the 245th day of the year (246th in leap years) in the Gregorian calendar. ... 1865 (MDCCCLXV) is a common year starting on Sunday. ...


Hamilton is recognized as one of Ireland's leading scientists and, as Ireland becomes more aware of its scientific heritage, he is increasingly celebrated. The Hamilton Institute is an applied mathematics research institute at NUI Maynooth and the Royal Irish Academy holds an annual public Hamilton lecture at which Murray Gell-Mann, Andrew Wiles and Timothy Gowers have all spoken. 2005 was the 200th anniversary of Hamilton's birth and the Irish government designated that the Hamilton Year, celebrating Irish science. Trinity College Dublin marked the year by launching the Hamilton Mathematics Institute TCD. The National University of Ireland, Maynooth (NUIM) was founded in 1997 by the Universities Act, 1997 as a constituent university of the National University of Ireland. ... The Royal Irish Academy (RIA) is one of Irelands premier learned societies and cultural institutions. ... Murray Gell-Mann (born September 15, 1929 in Manhattan, New York City, USA) is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles. ... For the French mathematician with work in the area of elliptic curves, see André Weil. ... William Timothy Gowers (born November 20, 1963, Wiltshire, United Kingdom) is a British mathematician. ... The College of the Holy and Undivided Trinity of Queen Elizabeth near Dublin or more commonly Trinity College, Dublin (TCD) was founded in 1592 by Queen Elizabeth I, is the only constituent college of the University of Dublin, Irelands oldest university. ...


Commemorations of Hamilton

  • Hamilton's equations are a formulation of classical mechanics.
  • Hamiltonian is the name of both a function (classical) and an operator (quantum) in physics, and a term from graph theory. It can be seen as the Quantum Hamiltonian.

In physics and mathematics, Hamiltons equations is the set of differential equations that arise in Hamiltonian mechanics, but also in many other related and sometimes apparently not related areas of science. ... Hamiltonian - Wikipedia, the free encyclopedia /**/ @import /skins-1. ... A pictorial representation of a graph In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. ...

Quotations

  • "Time is said to have only one dimension, and space to have three dimensions. ... The mathematical quaternion partakes of both these elements; in technical language it may be said to be "time plus space", or "space plus time": and in this sense it has, or at least involves a reference to, four dimensions. And how the One of Time, of Space the Three, Might in the Chain of Symbols girdled be." — William Rowan Hamilton (Quoted in Robert Percival Graves' "Life of Sir William Rowan Hamilton" (3 vols., 1882, 1885, 1889))
  • "He used to carry on, long trains of algebraic and arithmetical calculations in his mind, during which he was unconscious of the earthly necessity of eating; we used to bring in a ‘snack’ and leave it in his study, but a brief nod of recognition of the intrusion of the chop or cutlet was often the only result, and his thoughts went on soaring upwards." — William Edwin Hamilton (his elder son)

External links, references, and resources

Publications St Marys College Bute Medical School St Leonards College[5][6] Affiliations 1994 Group Website http://www. ...

  • Hamilton, William Rowan (Royal Astronomer Of Ireland), "Introductory Lecture on Astronomy". Dublin University Review and Quarterly Magazine Vol. I, Trinity College, January 1833.
  • Hamilton, William Rowan, "Lectures on Quaternions". Royal Irish Academy, 1853.
  • David R. Wilkins's collection of Hamilton's Mathematical Papers.

See also

Persondata
NAME Hamilton, William
ALTERNATIVE NAMES
SHORT DESCRIPTION Mathematician, physicist, and astronomer
DATE OF BIRTH August 4, 1805
PLACE OF BIRTH Dublin, Ireland
DATE OF DEATH September 2, 1865
PLACE OF DEATH Dublin, Ireland

  Results from FactBites:
 
Sir William Rowan Hamilton - LoveToKnow 1911 (1874 words)
SIR WILLIAM ROWAN HAMILTON (1805-1865), Scottish mathematician, was born in Dublin on the 4th of August 1805.
Indeed there can be little doubt that Hamilton was intended by the university authorities who elected him to the professorship of astronomy to spend his time as he best could for the advancement of science, without being tied down to any particular branch.
Hamilton himself seems not till this period to have fully understood either the nature or the importance of his discovery, for it is only now that we find him announcing his intention of applying his method to dynamics.
  More results at FactBites »

 
 

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