HÃ¤nselmann, Ludwig. The reaction of Gauss's classmates -- and his teacher -- to his shortcut remains a mystery. The father was quite unaware that his young three-year-old son Carl was following the calculations with critical attention, as so was surprised at the end of the computation to hear the little boy announce that the reckoning was wrong and that it should be so and so instead. For his own convenience, so that he would not have to do the tedious arithmetic involved to check his pupils' almost invariably erroneous answers, the sequences of numbers he assigned his classes to add were chosen to form what it called an arithmetic series—the successive numbers in the long list differed by a constant amount. Link to Web page (Viewed 2005-11-24). Ã peine l'exercice posÃ©, un de ses plus jeunes disciple, Ã  peine agÃ© de neuf ans, donne la rÃ©ponse: 10100/2! "Tell me, boy, how you got this answer!" Calculating the total number of beans in this rectangle built from the two triangles was easy: there are in total 101 × 100 = 10,100 beans. Intrigued, he went to check the child's copybook and found that, after a few additions, Gauss had multiplied 100 by 101 and then divided the product by 2, obtaining 5,050, which is the right answer. It wasn't anything like La FlÃ¨che, the Jesuit school Descartes entered at age eight that would later become famous. As it was the beginning class none of the boys had ever heard of an arithmetic progression. → {\displaystyle {\vec {E}}} Eventually he entered the arithmetic class, in which most pupils remained until their confirmation, that is, until about their fifteenth year. Aici nu erau adunate numerele unul după altul la nesfÃ¢rșit, ca pe celelalte tăblițe. Many biographists think that he got his good health from his father. Later in life Gauss liked to recount how his was the only correct answer, even though his classmates worked for hours laboriously adding number after number. Jeder, der die Rechnung beendet haben wÃ¼rde, sollte die Tafel auf einen Sammeltisch legen. New York: John Wiley & Sons. In three volumes. Then I saw that they all did the same and there would be 50 of them. It seems that Gauss' third grade teacher needed a break so she assigned the class the problem of totaling the sum of the first 100 integers thinking that this would occupy the students for most of the afternoon. We can do one multiplication. Er habe nur ein wenig Ã¼ber die Aufgabe nachgedacht sich dann die Zahlenreihe von 1 bis 100 genau angesehen und bald ein paar bemerkenswerte Ãbereinstimmungen entdeckt. In this he entered his name "J.C.F. It is the earliest such instance I have found, more than 30 years ahead of Ludwig Beiberbach's account. Méthode 2 : trouver un plan d'antisymétrie ou deux plans de symétrie de la distribution de charge, passant par M. Déterminer les variables dont dépend la norme du champ dans l'espace, en invoquant des arguments d'invariance du problème vu par l'observateur par translation ou rotation du point M. Choisir une surface de Gauss passant par le point où on cherche le champ. Wer seine Rechnung fertig hatte, musste seine Tafel auf den Classentisch legen. This allows for computing higher-order estimates while reusing the function values of a lower-order estimate. How to be a little Gauss. Es war eine dumpfe, niedrige Schulstube mit einem unebenen ausgelaufenen Fussboden, von der man nach der einen Seite gegen die beiden schlanken gothischen ThÃ¼rme der Catherinen-Kirche, nach der andern gegen StÃ¤lle und armselige HintergebÃ¤ude hinaus blickte. When Gauss was 7 years old he went to school. The teacher had set the class the task of calculating the sum 1 + 2 + 3 + .... + 100 — probably to get a bit of peace for himself. El primero en acabar el ejercicio debÃ­a dejar su pizarra sobre la mesa del maestro, el siguiente alumno encima de la del primero y asÃ­ sucesivamente. Asked to explain himself, Gauss said he noticed that the sum of the first and last numbers is 101 (1 + 100), and that each pair working in from the outside also summed to 101—that is, 2 + 99, 3 + 98, 4 + 97, all the way to 50 + 51. This led to a much simpler addition: Simply put, there are 50 pairs of numbers, each of which totals 101. Aus sich selbst, mit gelegentlicher Nachfrage bei seiner Umgebung, lernt er lesen; am erstaunlichsten aber zeigt sich von frÃ¼hester Kindheit an die intuitive Kraft seiner Auffassung von ZahlenverhÃ¤ltnissen: er durste scherzend wohl von sich sagen, daÃ er eher habe rechnen als sprechen sÃ¶nnen. The tenth number on the list is the number of beans required to build a triangle with ten rows, starting with one bean in the first row and ending with ten beans in the last row. NÃ© Ã  Braunschweig (Allemagne), le 30 avril 1777, Gauss montra, dÃ¨s son jeune Ã¢ge, des aptitudes hors du commun pour les mathÃ©matiques (il faut mentionner qu'il avait appris Ã  lire et Ã  compter, par lui-mÃªme, Ã  l'Ã¢ge de 3 ans!). Gauss of course was able to tabulate the sum in a matter of seconds to the chagrin of his teacher. The teacher assumed that Gauss had simply learned this result as a piece of trivia. So he just multiplied 101 by 50 to get 5050. Link to Web page (Viewed 2006-03-11). 0 One day he gave Among the great mathematicians there are about as many who showed mathematical talents in chidhood as there are those who showed none at all until they were older. [Eric Temple Bell, Men Of Mathematics , Simon Schuster, Inc., New York, 1937]. Carl Friedrich GauÃ wurde am 30. The story goes that when Gauss was a child, his math teacher came to class unprepared one day. New York: Simon and Schuster. hingeworfen, waÌhrend die anderen SchuÌler sich in den muÌhsamsten Rechnungen ergingen und erst lange nachher fertig wurden. On today's computers that would be a snap. Diese LÃ¶sung ist zwar nicht erst von GauÃ entwickelt worden: Sie war schon in der griechischen Antike bekannt, etwa im 2. This version follows Polya (1962), who also uses it to introduce recursion in mathematical problems. Gauss' method is wonderful to look at but there still must be an easier way to figure out the sum of a finite arithmetic series. 2–3). Carl Friedrich Gauss: A Biography. Then, in his tenth year, Gauss was admitted to the class in arithmetic. ) WÃ¤hrend die andern SchÃ¼ler emsig weiter rechnen, multipliciren und addiren, geht BÃ¼ttner sich sich seiner WÃ¼rde bewusst auf und ab, indem er nur von Zeit zu Zeit einem mitleidigen und sarcastischen Blick auf den kleinsten der SchÃ¼ler wirft, der lÃ¤ngst seine Aufgabe beendigt hatte. He said: "100+1=101; 99+2=101, 98+3=101, etc., and so we have as many 'pairs' as there are in 100. n But the budding mathematician came back five minutes later with the correct answer: 5,050. $\sum^{n}_{i=1} i^2 = \frac{n(n-1)(2n+1)}{6}\textrm{, and}$ He traces them from 1856 to the present, and what he learns is quite amazing. It soon happened that soon after his admission into the Arithmetic class, when a sum was set to the class Gauss put his slate within a minute of the announcement of the sum. EsperÃ³ una hora a que finalizaran sus compaÃ±eros. Si on se veut plus précis, on peut définir dans un référentiel galiléen défini, une charge q définie de vecteur vitesse v qui subit de la part des autres charges présentes, qu'elles soient fixes ou mobiles, une force qu'on définira de force de Lorentz. The teacher, amazed, asked him how he came up with the answer so quickly. It is related that at this school during Gauss's 10th year an event took place which produced a great impression on the teachers and the students. Finally, upon looking at Gauss's slate, he found but one number written there. 1998. Link to Web page (p. 9). Dies Ereignis ist auf das spaÌtere Leben des jungen GauÃ von nicht geringem EinfluÌsse gewesen. 5, pp. Benze, eines Steinhauers Tochter. Pereira, Egmon. V As a student finished the calculations, he would place his slate on the teacher's desk. One day, to keep the boys busy, the teacher gave the class the exercise of writing down all the numbers from 1 to 100 and then finding their sum. No one had taught the child numbers. 3 little boy, his teacher asked the class to add up the numbers one through a I think that ∮ Gauss was unquestionably the most precocious of them all. New York: Simon & Schuster. Kaum hat er das getan, als schon der kleine GauÃ vor kommt, die Tafel auf den Tisch des Lehrers legt: "Ligget se!". Zum Erstaunen aller Anwesenden zeigte es sich bei sorgsamer Neuberechnung, daÃ die von dem Kinde angegebene Summe die richtige war. the story has the ring of truth to it. Link to Web page (Viewed 2006-02-15). The master had barely finished stating the problem when Gauss put his slate on the table. Die anderen SchÃ¼ler, klein und groÃ, rechnen unterdessen, addieren und addieren eine Zahl nach der anderen; BÃ¼ttner geht im Schulzimmer auf und ab und wirft nur einen stummen, mitleidigen Blick auf den Knirps, der so schnellfertig mit der Aufgabe sich abgefunden hat. 2000. Gauss' teacher set the class the task of adding all the numbers from 1 to 100 on purpose to keep them busy for a long time, while the teacher would go to work at his vegetable garden, it was an urgent job. (p. 123). Karl Friedrich Gauss, von Franz MathÃ©. {\displaystyle {\vec {E}}} GauÃ versagte die Stimme, er rÃ¤usperte sich, er schwitzte. Le théorème de Gauss seul ne permet pas de déterminer entièrement le champ électrostatique, il faut connaître ces symétries, d’où cette étude préalable. Vieweg und Sohn) wurde am 30 April 1777 in Braunschweig geboren. The teacher was incredulous. Looking at another combination, 2 and 99 is also 101 and so forth. Gauss entered the St. Katharine's Volksschule in 1784, after he had reached his seventh year. One of the youngest and most famous mathematicians in all of history was Carl Friedrich Gauss who was born in Germany in 1777 and died in 1855. IV. RÃ©pondre Ã  cette question n'est certainement simple, mais l'on peut avancer que la prÃ©sentation d'une solution Ã©lÃ©gante a pour prÃ©alable une bonne comprÃ©hension du problÃ¨me. It started to make sense. Mathematics department, Austin Community College, Austin, Texas. t BÃ¼ttner once gave the class the exercise of writing down all the numbers from 1 to 100 and adding them. 1992. Thus the answer is 50×101, or 5,050." When BÃ¼ttner examined the slates at the end of the period, Gauss's slate contained a single number, 5050—the only correct solution in the class. Boyer, Carl B. The teacher expected that while the students were busy adding all those numbers, he could enjoy a peaceful break, long enough to digest his meal. Er war aber auch in der Lage, dem Lehrer auseinanderzusetzen, wie er sum Resultate gelangt war. 101 Great Ideas for Introducing Key Concepts in Mathematics: A Resource for Secondary School Teachers. Una de les mÃ©s conegudes i contrastades Ã©s la del «descobriment» de la suma d'una progressiÃ³ aritmÃ¨tica: als nou anys Gauss va assistir a la seva primera classe d'aritmÃ¨tica, on el professor BÃ¼ttner va proposar als estudiants que calculessin la suma dels cent primers nÃºmeros.
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