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Differential Calculus and by Era Integral Calculus, Which Are Related by in Early Cultures in Classical Antiquity the Fundamental Theorem of Calculus
History of calculus - Wikipedia, the free encyclopedia 1/1/10 5:02 PM History of calculus From Wikipedia, the free encyclopedia History of science This is a sub-article to Calculus and History of mathematics. History of Calculus is part of the history of mathematics focused on limits, functions, derivatives, integrals, and infinite series. The subject, known Background historically as infinitesimal calculus, Theories/sociology constitutes a major part of modern Historiography mathematics education. It has two major Pseudoscience branches, differential calculus and By era integral calculus, which are related by In early cultures in Classical Antiquity the fundamental theorem of calculus. In the Middle Ages Calculus is the study of change, in the In the Renaissance same way that geometry is the study of Scientific Revolution shape and algebra is the study of By topic operations and their application to Natural sciences solving equations. A course in calculus Astronomy is a gateway to other, more advanced Biology courses in mathematics devoted to the Botany study of functions and limits, broadly Chemistry Ecology called mathematical analysis. Calculus Geography has widespread applications in science, Geology economics, and engineering and can Paleontology solve many problems for which algebra Physics alone is insufficient. Mathematics Algebra Calculus Combinatorics Contents Geometry Logic Statistics 1 Development of calculus Trigonometry 1.1 Integral calculus Social sciences 1.2 Differential calculus Anthropology 1.3 Mathematical analysis -
Henri Lebesgue and the End of Classical Theories on Calculus
Henri Lebesgue and the End of Classical Theories on Calculus Xiaoping Ding Beijing institute of pharmacology of 21st century Abstract In this paper a novel calculus system has been established based on the concept of ‘werden’. The basis of logic self-contraction of the theories on current calculus was shown. Mistakes and defects in the structure and meaning of the theories on current calculus were exposed. A new quantity-figure model as the premise of mathematics has been formed after the correction of definition of the real number and the point. Basic concepts such as the derivative, the differential, the primitive function and the integral have been redefined and the theories on calculus have been reestablished. By historical verification of theories on calculus, it is demonstrated that the Newton-Leibniz theories on calculus have returned in the form of the novel theories established in this paper. Keywords: Theories on calculus, differentials, derivatives, integrals, quantity-figure model Introduction The combination of theories and methods on calculus is called calculus. The calculus, in the period from Isaac Newton, Gottfried Leibniz, Leonhard Euler to Joseph Lagrange, is essentially different from the one in the period from Augustin Cauchy to Henri Lebesgue. The sign for the division is the publication of the monograph ‘cours d’analyse’ by Cauchy in 1821. In this paper the period from 1667 to 1821 is called the first period of history of calculus, when Newton and Leibniz established initial theories and methods on calculus; the period after 1821 is called the second period of history of calculus, when Cauchy denied the common ideas of Newton and Leibniz and established new theories on calculus (i.e., current theories on calculus) using the concept of the limit in the form of the expression invented by Leibniz. -
The Controversial History of Calculus
The Controversial History of Calculus Edgar Jasko March 2021 1 What is Calculus? In simple terms Calculus can be split up into two parts: Differential Calculus and Integral Calculus. Differential calculus deals with changing gradients and the idea of a gradient at a point. Integral Calculus deals with the area under a curve. However this does not capture all of Calculus, which is, to be technical, the study of continuous change. One of the difficulties in really defining calculus simply is the generality in which it must be described, due to its many applications across the sciences and other branches of maths and since its original `conception' many thousands of years ago many problems have arisen, of which I will discuss some of them in this essay. 2 The Beginnings of a Mathematical Revolution Calculus, like many other important mathematical discoveries, was not just the work of a few people over a generation. Some of the earliest evidence we have about the discovery of calculus comes from approximately 1800 BC in Ancient Egypt. However, this evidence only shows the beginnings of the most rudimentary parts of Integral Calculus and it is not for another 1500 years until more known discoveries are made. Many important ideas in Maths and the sciences have their roots in the ideas of the philosophers and polymaths of Ancient Greece. Calculus is no exception, since in Ancient Greece both the idea of infinitesimals and the beginnings of the idea of a limit were began forming. The idea of infinitesimals was used often by mathematicians in Ancient Greece, however there were many who had their doubts, including Zeno of Elea, the famous paradox creator, who found a paradox seemingly inherent in the concept. -
Benjamin Franklin 1 Benjamin Franklin
Benjamin Franklin 1 Benjamin Franklin Benjamin Franklin 6th President of the Supreme Executive Council of Pennsylvania In office October 18, 1785 – December 1, 1788 Preceded by John Dickinson Succeeded by Thomas Mifflin 23rd Speaker of the Pennsylvania Assembly In office 1765–1765 Preceded by Isaac Norris Succeeded by Isaac Norris United States Minister to France In office 1778–1785 Appointed by Congress of the Confederation Preceded by New office Succeeded by Thomas Jefferson United States Minister to Sweden In office 1782–1783 Appointed by Congress of the Confederation Preceded by New office Succeeded by Jonathan Russell 1st United States Postmaster General In office 1775–1776 Appointed by Continental Congress Preceded by New office Succeeded by Richard Bache Personal details Benjamin Franklin 2 Born January 17, 1706 Boston, Massachusetts Bay Died April 17, 1790 (aged 84) Philadelphia, Pennsylvania Nationality American Political party None Spouse(s) Deborah Read Children William Franklin Francis Folger Franklin Sarah Franklin Bache Profession Scientist Writer Politician Signature [1] Benjamin Franklin (January 17, 1706 [O.S. January 6, 1705 ] – April 17, 1790) was one of the Founding Fathers of the United States. A noted polymath, Franklin was a leading author, printer, political theorist, politician, postmaster, scientist, musician, inventor, satirist, civic activist, statesman, and diplomat. As a scientist, he was a major figure in the American Enlightenment and the history of physics for his discoveries and theories regarding electricity. He invented the lightning rod, bifocals, the Franklin stove, a carriage odometer, and the glass 'armonica'. He formed both the first public lending library in America and the first fire department in Pennsylvania. -
Mercredi 3 Juin 2015
MERCREDI 3 JUIN 2015 ART AFRICAIN - OCÉANIEN - PRÉCOLOMBIEN MINIATURES TABLEAUX ANCIENS ET MODERNES OBJETS D’ART ET D’AMEUBLEMENT TAPISSERIES EXPERTS Olivier BORÉ 7 rue Charlot 75003 Paris +33 (0)1 42 88 62 97 [email protected] Lots : 22 à 47 Patrick de BUTTET – Carl de LENCQUESAING 5 bis rue de Montenotte 75017 Paris +33 (0)1 45 72 01 89 [email protected] Rim MEZGHANI [email protected] 78 rue du Temple 75003 Paris Lots : 48, 52, 77 à 96, 98 à 103 +33 (0)6 76 64 49 41 [email protected] Bernard DULON Lots : 73 à 75 10 rue Jacques Callot 75006 Paris +33 (0)1 43 25 25 00 René MILLET [email protected] 12 rue Rossini 75009 Paris Lots : 1 à 14 +33 (0)1 44 51 05 90 [email protected] Laurence FLIGNY Lots : 49 à 51, 53, 54 Expert près la cour d'appel de Paris +33 (0)1 45 48 53 65 Anthony JP MEYER [email protected] 17 rue des Beaux-Arts 75006 Paris Lot : 72 +33 (0)1 43 54 85 74 [email protected] Amélie MARCILHAC Lot : 15 Cabinet d’Expertise Marcilhac 8 rue Bonaparte 75006 Paris Nicole de PAZZIS-CHEVALIER +33 (0)1 43 26 00 47 Syndicat Français des Experts professionnels en œuvres d’art (SFEP) [email protected] 17 quai Voltaire 75007 PARIS Lots : 60 à 66, 105 +33 (0)1 42 60 72 68 [email protected] MEZCALA Expertises Lot : 106 259 boulevard Raspail 75014 Paris Jacques BLAZY Cabinet PORTIER ET ASSOCIES +33 (0)6 07 12 46 39 Thierry PORTIER et Alice JOSSAUME [email protected] 26 boulevard Poissonnière 75009 Paris assisté de Quentin BLAZY +33 (0)1 48 00 03 41/45 [email protected] [email protected] Lots : 16 à 21 Lot : 76 ART AFRICAIN - OCÉANIEN - PRÉCOLOMBIEN MINIATURES - TABLEAUX ANCIENS ET MODERNES OBJETS D’ART ET D’AMEUBLEMENT TAPISSERIES MERCREDI 3 JUIN 2015 PARIS DROUOT - SALLE 4 - 14 H15 EXPOSITIONS PUBLIQUES Hôtel Drouot - salle 4 mardi 2 juin de 11h à 18h et mercredi 3 juin de 11h à 12h Téléphone pendant l’exposition +33 (0)1 48 00 20 04 5, rue La Boétie - 75008 Paris - tél. -
Collection D'autographes, De Dessins Et De Portraits De Personnages Célèbres, Français Et Étrangers, Du Xvie Au Xixe Siècle, Formée Par Alexandre Bixio
BnF Archives et manuscrits Collection d'autographes, de dessins et de portraits de personnages célèbres, français et étrangers, du XVIe au XIXe siècle, formée par Alexandre Bixio. XVIe-XIXe siècle. Cote : NAF 22734-22741 Collection d'autographes, de dessins et de portraits de personnages célèbres, français et étrangers, du XVIe au XIXe siècle, formée par Alexandre Bixio. XVIe-XIXe siècle. Papier.Huit volumes, montés in-fol.Demi-reliure. Bibliothèque nationale de France. Département des Manuscrits Document en français. Présentation du contenu Un inventaire détaillé de cette collection a été publié par Léon Dorez dans le Bulletin d'histoire du Comité des travaux historiques (1916), p. 276 et suiv : http://gallica.bnf.fr/ark:/12148/bpt6k5787089t/f284.image. Informations sur les modalités d’entrée Don de Mmes Rouen-Bixio et Depret-Bixio, 1916 (D 5005) I. A - B Cote : NAF 22734 Réserver I. A - B 250 f. Ce document est conservé sur un site distant. Conditions d'accès Un délai est nécessaire pour la communication de ce document. En savoir plus. Documents de substitution Il existe une version numérisée de ce document. Numérisation effectuée à partir d'un document original : NAF 22734. http://gallica.bnf.fr/ark:/12148/btv1b100272996 Lettre de Mehmet-Emin Aali-Pacha division : F. 1 Lettre de Mehmet-Emin Aali-Pacha 1856 ? Portrait de Mehmet-Emin Aali-Pacha division : F. 2 Portrait de Mehmet-Emin Aali-Pacha Dessin à la plume et encre brune ; 170 x 113 mm. Présentation du contenu Attribué à Nadar par Léon Dorez. 01/10/2021 https://archivesetmanuscrits.bnf.fr/ark:/12148/cc4092h Page 1 / 238 BnF Archives et manuscrits Lettre d'Abd el Kader au général Bugeaud division : F. -
A Very Short History of Calculus
A VERY SHORT HISTORY OF CALCULUS The history of calculus consists of several phases. The first one is the ‘prehistory’, which goes up to the discovery of the fundamental theorem of calculus. It includes the contributions of Eudoxus and Archimedes on exhaustion as well as research by Fermat and his contemporaries (like Cavalieri), who – in modern terms – computed the area beneath the graph of functions lixe xr for rational values of r 6= −1. Calculus as we know it was invented (Phase II) by Leibniz; Newton’s theory of fluxions is equivalent to it, and in fact Newton came up with the theory first (using results of his teacher Barrow), but Leibniz published them first. The dispute over priority was fought out between mathematicians on the continent (later on including the Bernoullis) and the British mathematicians. Essentially all the techniques covered in the first courses on calculus (and many more, like the calculus of variations and differential equations) were discovered shortly after Newton’s and Leibniz’s publications, mainly by Jakob and Johann Bernoulli (two brothers) and Euler (there were, of course, a lot of other mathe- maticians involved: L’Hospital, Taylor, . ). As an example of the analytic powers of Johann Bernoulli, let us consider his R 1 x evaluation of 0 x dx. First he developed x2(ln x)2 x3(ln x)3 xx = ex ln x = 1 + x ln x + + + ... 2! 3! into a power series, then exchanged the two limits (the power series is a limit, and the integral is the limit of Riemann sums), integrated the individual terms n n (integration by parts), used the fact that limx→0 x (ln x) = 0 and finally came up with the answer Z 1 x 1 1 1 x dx = 1 − 2 + 3 − 4 + ... -
Theodore William Dwight
Appendix Beta2: The Nantes Intellectual Line Connecting brothers of Phi Kappa Psi Fraternity at Cornell University, tracing their fraternal Big Brother/Little Brother line to the tri-Founders and their Pledges . Joseph Benson Foraker was a founder of New York Alpha, in the Class of 1869, and studied under . . .Theodore Dwight in those first years . Professor Theodore William Dwight . William Smith was brought to Penn by was influenced by Samuel Finley Benjamin Franklin . Breese Morse . . Samuel Finley Breese Morse was, . Benjamin Franklin’s endeavors were in turn, influenced by sponsored by the Frenchman Washington Allston . Jacques-Donatien Le Ray . . Washington Allston was influenced by . Jacques-Donatien Le Ray was the son Benjamin West . of René François Le Ray . . Benjamin West was influenced by . René François Le Ray was the son of William Smith . Jean Le Ray of Nantes. Below we present short biographies of the Nantes intellectual line of the Phi Kappa Psi Fraternity at Cornell University. “Who defends the House.” We begin with brother Joseph Benson Foraker of the Class of 1869, who studied under Professor Theodore Dwight in the University’s first years of existence. Theodore William Dwight (1822- 1892), American jurist and educator, cousin of Theodore Dwight Woolsey and of Timothy Dwight V, was born July 18, 1822 in Catskill, New York. His father was Benjamin Woolsey Dwight (1780-1850), a physician and merchant, and his grandfather was Timothy Dwight IV (1752- 1817), a prominent theologian, educator, author, and president of Yale University from 1795-1817. Theodore Dwight graduated from Hamilton College in 1840 where he studied physics under SFB Morse and John William Draper. -
We Need an Ecological Revolution
WE NEED AN ECOLOGICAL REVOLUTION John Scales Avery March 24, 2019 INTRODUCTION1 The present crisis of civilization is unique Does history repeat itself? Is it cyclic, or is it unidirectional? Certainly many aspects of history are repetitive - the rise and fall of empires, cycles of war and peace, cycles of construction and destruction. But on the other hand, if we look at the long-term history of human progress, we can see that it is clearly unidirectional. An explosion of knowledge has created the modern world. This is something that never happened before. Never before has the world had a population of more than 7 billion people, to which a billion are added every decade. Never before have we had the power to destroy human civilization and the biosphere with thermonuclear weapons or catastrophic anthropogenic climate change. Our situation today is unique. We cannot rely on old habits, old traditions or old institutions. To save the long-term future for our children and grandchildren, and for all the other creatures with which we share the gift of life, we must overcome the inertia of our institutions and our culture. The Nobel-Laureate biochemist Albert Szent-Gy¨orgyi once wrote: “The story of man consists of two parts, divided by the appearance of modern science at the turn of the century. In the first period, man lived in the world in which his species was born and to which his senses were adapted. In the second, man stepped into a new, cosmic world to which he was a complete stranger.... The forces at man’s disposal were no longer terrestrial forces, of human dimension, but were cosmic forces, the forces which shaped the universe. -
On the Didactical Function of Some Items from the History of Calculus Stephan Berendonk
On the didactical function of some items from the history of calculus Stephan Berendonk To cite this version: Stephan Berendonk. On the didactical function of some items from the history of calculus. Eleventh Congress of the European Society for Research in Mathematics Education, Utrecht University, Feb 2019, Utrecht, Netherlands. hal-02421842 HAL Id: hal-02421842 https://hal.archives-ouvertes.fr/hal-02421842 Submitted on 20 Dec 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. On the didactical function of some items from the history of calculus Stephan Berendonk1 1Universität Duisburg-Essen, Germany; [email protected] The article draws attention to some individual results from the history of calculus and explains their appearance in a course on the didactics of analysis for future high school mathematics teachers. Specifically it is shown how these results may serve as a vehicle to address and reflect on three major didactical challenges: determining the meaning of a result, concept or topic to be taught, teaching mathematics as a coherent subject and understanding the source of misconceptions. Keywords: Didactics of analysis, meaning, coherence, misconceptions. Why do we have to learn this historical stuff, although this is a course on didactics? This is a question frequently posed by future high school mathematics teachers taking my third semester course on the didactics of analysis at the university of Duisburg-Essen. -
History of Calculus
History of Calculus Let’s start with the definition of mathematics and calculus. Mathematics – from the Greek knowledge, study learning. Is the study of quantity, structure, space and change. Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. Is the mathematics of instantaneous rates of change – how rapidly is some particular quantity changing at this very instant? Calculus has two main branches. Differential calculus provides methods for calculating rates of change and it has many geometric applications, in particular finding tangents to curves. Integral calculus does the opposite: give the rates of chance of some quantity, it specifies the quantity itself. Geometric applications of integral calculus include the computation of areas and volumes. Perhaps the most significant is this unexpected connection between two apparently unrelated classical geometric questions: finding tangents to a curve and finding areas. Why do we have to learn mathematics? Where mathematics came from? Mathematics came from our imagination; it is a complete invention of the human brain. With the invention of mathematics we create science. Mathematics makes up human, because it’s a distinction that we have from all others animals in the animal’s kingdom. The important of mathematics and science is so great that no person living in the twentieth century can claim to be educated if they are unaware of the modern vision of the physical universe and the history of the magnificent concepts that it embodies. Science is not rigid. Dogmas are rigid. We should understand that science is the business of measuring things. -
When We Were Young: the American Philosophical Society in the 18Th Century1
When We Were Young: The American Philosophical Society in the 18th Century1 GARY B. NASH Distinguished Research Professor University of California, Los Angeles n 2018 the American Philosophical Society celebrated its 275th anniversary, though in truth, 1743 is a shadowy date. Some think Ithe APS began in 1727, when Benjamin Franklin, at age 21—having resided in Philadelphia for less than two years since he first arrived in late 1723—convened his famous Junto of leather apron men (Figure 1). Drawing up rules for this private self-improvement group, 12 in number and limited to that size, he tasked “every Member in his Turn” to produce “one or more Queries . to be discuss’d by the Company.’’2 Among the founding group, four were from Samuel Keimer’s print shop (Franklin, Hugh Meredith, Stephen Potts, and George Webb) while the others were shoemakers (John Jones and William Parsons); a surveyor (Nicholas Scull); a scrivener (Joseph Breitnall); a carpenter (William Coleman); an ironmaker (Robert Grace); a glass maker (Thomas Godfrey); and a cabinet maker (William Mangrudge). It was a noble start, indeed an astounding venture, ushered into the world by such a youth striving to implant himself in a young river port, where Quaker merchants and landowners of growing wealth held sway.3 The APS website today claims our Society as an “offshoot” of 1 Read 26 April 2018. My thanks to the anonymous reviewers for their comments and suggestions for this paper. 2 The editors of the comprehensive edition of the Papers of Benjamin Franklin aver that Franklin had been influenced by Boston’s venerable Cotton Mather’s Essays to Do Good (1710), which proposed voluntary groups to encourage morality and religion.