Er pflegte selbst oft scherzweise zu sagen, er habe fruÌher rechnen als sprechen koÌnnen. Immediately, almost as soon as the teacher had the problem out of his mouth, little Friedrich raised his hand. <> An hour later, when all the slates were finally stacked and ready to be checked, BÃ¼ttner reached into his pocket to get the slip of paper with the answer on it, and then he began to check the slates. When very small, he recalled, he was once near death. Available online. Not [hesitate] really. We each worked on a different area of the project according to our strengths and then combined what we had discovered. The Gauss sum is named for a story that's described in E. T. Bell's "Men of Mathematics.'' Le dio la siguiente explicaciÃ³n: imaginÃ³ que escribÃ­a la suma dos veces, una al derecho y otra al revÃ©s una encima de la otra. This exercise was designed to keep them occupied for quite a while. 1998. Si hay 100 nÃºmeros entonces hay 50 pares que suman 101, de donde resulta que 50×101 = 5050 era la soluciÃ³n. Junge ergo omnes et invenies columbas vl. The mythology of mathematics says the teacher was furious, but BÃ¼ttner supplied Gauss with more advanced works and encouraged him to work with one of the assistant teachers, Johann Martin Bartels. Cambridge: M.I.T. Bartels subsequently rose to be a professor in the University of Dorpat, where he died. As a student finished the calculations, he would place his slate on the teacher's desk. When he did look at it, he was surprised to find that it contained just a single number, the right answer. DespuÃ©s de oÃ­r o leer el apellido de este nombre le viene a uno a la cabeza la distribuciÃ³n de errores que hoy se conoce como curva o campana de Gauss o distribuciÃ³n Normal. Der Lehrer denkt wie uÌblich an die wenig ruhmvolle Wahl zwischen Dummheit und Faulheit. Goldstein, Martin, and Inge F. Goldstein. 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. In 1784, at the age of 7, Gauss went to primary school, the Katharinenschule in Brunswick, headed by the teacher J. G. BÃ¼ttner. (p. 314). ∬ Also fÃ¼nfzig mal hunderteins. Replace it by N and you get the formula 1/2 × (N + 1) × N. Elta Universitate. BuÌttner verschrieb hierauf eigens aus Hamburg ein neues Rechnenbuch, um damit den jungen, aufstrebenden Geist nach KraÌften zu unterstuÌtzen. ∮ Carl Friedrich Gauss (1777–1855) is considered to be among the greatest mathematicians who ever lived. Gauss wrote down the answer just after Buttner finished writing the problem. Tout le monde connaît l'électricité statique car celle-ci se manifeste fréquemment dans la vie de tous les jours.Mais savez-vous exactement pourquoi se produisent de tels phénomènes ?Photographie réalisée par Christophe Finot. This is the progression. No one had taught the child numbers. The ten-year-old boy evidently had computed mentally the sum of the arithmetic progression 1 + 2 + 3 + ... + 99 + 100, presumably through the formula m(m+1)/2. {\displaystyle \mathrm {d} \Phi ={\vec {E}}(M)\,{\vec {n}}\,{\rm {d}}S}. Es ist der Sohn von Lehmmaurer und Hausschlacter Gebhard GauÃ. Karl Friedrich Gauss (1771–1855) was one of the finest mathematicians of all time. Quantum 10(2):14–19 and 10(3):10–15. Hannoversch MÃ¼nden web site. When the instructor finally looked at the results, the slate of Gauss was the only one to have the correct answer, 5050, with no further calculation. Er hatte das Summationsprinzip fÃ¼r die arithmetischen Reihen auf den ersten Blick herausgefunden. 147–148). AprendiÃ³ a calcular antes que leer. Comment cela s'est-il passÃ©? How many sniffs in all? One day Beuttner assigned the problem of adding all the numbers from 1 to 100. Maybe the story is apocryphal, but the point is clear: A great mathematician doesn't solve a problem the long and boring way because he sees what the real pattern is behind the question, and applies that pattern to find the answer in a much better way. Same answer, slightly different tactics. If you are in doubt, the top row just counts them. It would be difficult to determine which of these was ordered for Gauss, and which was used in the public school. Estep, Donald. Fericite erau clipele pe care talentatul Carl Friedrich le petrecea cu manualul de la Hamburg. Some people relish the geometric approach, some of the symbolic. Of course, Mr. BÃ¼ttner assumed Gauss had the wrong answer or cheated. All the students were shocked at how fast and seemingly effortlessly Gauss completed the problem. In Gottinger Professoren: Ein Beitrag zur deutschen Cultur- und LiterÃ¤rgeschichte in acht VortrÃ¤gen. Without the help or knowledge of others, Gauss learned to calculate before he could talk. Φ Dicat, qui potest, quot columbae in totum fuerunt? Buttner, reputed to be a rather surly man, assigned the problem when he wanted to occupy his students for up to an hour and was dismayed when Gauss, then 13 (some histories peg his age at 10, others as young as 7), solved it in about a minute, flinging his slate upon the table barely after Buttner finished stating the problem and saying "Ligget se," Brunswick German for "there 'tis.". [The lecturer points at each column in At least, that's what BÃ¼ttner expected. El jove Gauss havia advertit que la suma del primer i del darrer nÃºmero donava el mateix resultat que la suma del segon idel penÃºltim, etc, Ã©s a dir. Boca Raton, Fla.: CRC Press. The teacher assumed that Gauss had simply learned this result as a piece of trivia. Cine termină, Ã®mi aduce tăblița la catedră. Hier stellt man sich die obere Reihe von 1 bis 100 auf einen Streifen Papier geschrieben vor. Darum sei es doch gegangen, eine Addition aller Zahlen von eins bis hundert. When Karl Gauss, a brilliant German mathematician, was 10 years old in the late 18th century he was presented a very difficult problem. As can be seen below, each vertical sum is 101, and there are exactly 100 of them. Die Aufgabe lautete diesmal: Die Zahlen von 1 bis 100 sind zusammenzuzaÌhlen. (p. 56). Es zeigte sich aber auch schon frÃ¼h, daÃ dies nicht nur eine Begabung fÃ¼r rechnerische TÃ¼fteleien war, sondern daÃ sich dahinter ein tiefes VerstÃ¤ndnis einer GesetzmÃ¤Ãigkeit in der Welt der Zahlen verbarg bzw. To keep his class quiet, the teacher told them to sum all the numbers from one to a hundred. teacher's annoyance, little Gauss came up to the teacher with the answer, right Freelancer et étudiante en Sciences de la Vie et de la Terre, je suis un peu une grande sœur qui épaule et aide les autres pour observer et comprendre le monde qui nous entoure et ses curieux secrets ! I would not have thought to look for the Gauss story in PHP and PostgreSQL: Advanced Web Programming or in a book titled Puzzles of Finance: Six Practical Problems and their Remarkable Solutions. "Tell me, boy, how you got this answer!" summed to 101. such as 5192 + 5229 + 5266 + ... , where each one was 37 larger Whenever a man worked overtime he was, of course, paid proportionately more. Sein Vater war Maurer, spaÌter GaÌrtner, ein achtungswerther, aber rauher, unfeiner Mann, seine Mutter Dorothea geb. Physics for Scientists and Engineers with Modern Physics. Er befreite ihn von seinem normalen Rechenunterricht und lieÃ ihn mit seinen Gehilfen Bartels zusammenarbeiten, der zufÃ¤llig gleichfalls mathematsch begabt und mathematisch interessiert war. (The anecdote appears on pages 213â214. 2002. In der Schule hatte der Lehrer die Aufgabe gestellt, alle Zahlen von 1 bis 100 zusammenzuzÃ¤hlen. Honors paper, Miami University of Ohio. Why isn't there a Nobel prize in mathematics? En effet, la charge considérée comme "source", c'est-à-dire q1, crée en tout point de l'espace un champ électrique dont la forme est donnée par la relation exprimée ci-dessus, et une charge quelconque considérée comme "test" subira l'effet de ce champ sous la forme d'une force égale au produit de cette charge par le champ électrostatique. 3 One of the stories tells how on a Saturday evening Gauss's father was making out the weekly payroll for the laborers of the small bricklaying business that he operated in the summer. 2005. Dorothea no doubt noticed the first signs of her son's genius in the events that are recalled as anecdotes from Gauss' early years: how, for instance, when he was three, his discovered a mistake in his father's calculation of the wages for one of his servants. 1 0 obj It had the correct answer. Bos, H. J. M. 1978. A play. A l'Ã©cole primaire, Gauss, enfant prodige, agaÃ§ait pour le moins son instituteur. 7–11). 48–49). Voir le document "Calcul d'intégrales multiples vectorielles ou scalaires". Le flux du champ électrique à travers une surface fermée est égal à la somme des charges électriques contenues dans le volume délimité par cette surface, divisée par la permittivité du vide. What if we add up the even numbers (that's 49 additions), then add up the It is said that in his first arithmetic class Gauss astonished his teacher by instantly solving what was intended to be a "busy work" problem: Find the sum of all the numbers from 1 to 100. Nacido en Braunschweig en 1777 fue un niÃ±o prodigio y continuÃ³ siendo un hombre brillante toda su vida. Hawking, Stephen W. 2005. Gauss's talents were obvious as soon as he stepped into a classroom at the age of seven. Bruce, Donald, and Anthony Purdy (editors). However, Gauss noticed a pattern. Planetmath.org. GauÃ und Bessel. HabÃ­a redescubierto las progresiones aritmÃ©ticas. 9, Hiver 2000. In der dritten Volksschulklasse, also im Alter von etwa neun Jahren, demonstrierte er seine herausragenden mathematischen FÃ¤higkeiten auf eindrucksvolle Weise. Carl stood up and began to speak. By the end of the school day, the last of the boys set his slate down. At the end of an hour, during which the master paced up and down with an air of dignity, the slates were turned over, and the answer of Gauss was found to be correct while many of the rest were erroneous. GauÃ' Vater, der in Braunschweig lebte, ein einfacher, unbemittelter Mann, Maurer, war und auÃerdem ein bescheidenes Ã¶ffentliches Amt, das eines "Wasserkunstmeisters", bekleidete, schickte den Sohn, als dieser das Alter von sieben Jahren erreicht hatte, in die Katharinen-Volksschule. Washington, D.C.: National Academy Press. ( Carl Friedrich Gauss: Inaugural Lecture on Astronomy and Papers on the Foundations of Mathematics. On top of this the second placed his slate and so on. 10–13). GauÃ lÃ¶ste diese Aufgabe auf schnelle und elegante Weise. At the age of seven, Gauss went to the Catherine Parish School at Braunschweig, and remained at it for several years. Because of it he gave to half of students long $\sum^{n}_{i=1} i = \frac{n(n-1)}{2}\textrm{,}$ The custom was for the first boy who solved a problem to lay his slate on the master's table with the answer written on it, for the next boy to lay his slate on top of that one and so on. Die Rechnung wurde darauf mit grosser Aufmerksamkeit wiederholt und zum Erstaunen aller Anwesenden genau so gefunden, wie sie von dem Kleinen angegeben war. You look at the problem another way, and you have this epiphany: It was only a problem because you were looking at it the wrong way. The Mathematical Heritage of C. F. Gauss. - "There it lies." Almost immediately, GauÃ wrote "5050" on his slate and put it on the teacher's desk with the classical words "Ligget se!" Borwein, Jonathan, and David H. Bailey. A closely related numerical approach to the problem of counting handshakes comes from a story told of young Carl Friedrich Gauss (1777–1855), whose teacher is said to have asked the class to sum the numbers from 1 to 100, expecting that the task would keep the class busy for some time. age. You are à travers All this went through Gauss's little head in a flash. Gauss besuchte von 1784 an die Catharinen-Volksschule, die damals unter der Leitung eines gewissen BuÌttner stand. : Berechnungder Summe aller Zahlen von 1 bis 40. Gauss' teacher, you may recall, assigned, as busy work, the sum of the first 100 integers. On one occasion no sooner had BÃ¼ttner dictated the last number than his youngest pupil flung his slate on the desk and waited for an hour while the other boys toiled. Mais, le champ électrique reste dans la réalité un caractère relatif puisqu'il ne peut exister indépendamment du champ magnétique. In so doing, of course, he got, since the sum of each column is just 101. − Problem solvers. Rather than start in on the adding immediately, he sat and thought a minute. El niÃ±o respondiÃ³: "Mire, maestro, antes de empazar a sumar mecÃ¡nicamente los cien primeros nÃºmeros me di cuenta de que si sumaba el primero y el Ãºltimto obtenÃ­a 101; al sumar el segundo y el punÃºltimo tambiÃ©n se obtiene 101, al igual que al sumar el tercero y el antepenÃºltimo, y asÃ­ sucesivamente hasta llegar a los dos nÃºmeros centrales que son 50 y 51, que tambiÃ©n suman 101. (p. 497). Beim Eintritte wurde den Kindern aufgegeben, eine Reihe aufeinander folgender Zahlen, 1â 40, zu addiren. That's 50 pairs of 101. est traversée par des lignes de champ sortantes, donc 2 2000. It was a drab, low school-room with a worn, uneven floor. As a 10-year-old student he surprised his teacher Mr. BÃ¼ttner when he mentally determined the sum of the numbers 1 + 2 + 3 + ... + 98 + 99 + 100 by grouping them into 50 pairs that each totalled 101 to produce the result 50 × 101 = 5,050. or Ligget se!) Gauss was born in Brunswick, Germany as the only son of poor peasants living in miserable conditions. Instead of doing it as I've just described, he might've added zero and a hundred, one and 99, until he reached 49 and 51. Remarque : dans le cas d'une distribution volumique, et des symétries simples, on peut utiliser l'équation de Maxwell-Gauss au lieu du théorème de Gauss : Ecrire l'équation de Maxwell-Gauss et la simplifier dans un système de coordonnées adapté à l'allure du spectre. Carl could add and subtract almost before he could talk. Finally he came to Gauss' slate. There are exactly 50 such pairs and the sum of the integers in each pair is 101. In those days all that the students had were slates which they could write on with chalk. Thus the answer is 50×101, or 5,050." How Do You See It? 16–17). 1–3) Link to PDF file. We don't have to do 99 additions. numbers]. New York: Franklin Watts. "From the look on their faces, I could tell they were quite happy. Although Gauss showed great intelligence, his father refused to send him to school. 27. Sum the first 100 whole numbers! Ce dernier pour se "dÃ©barasser" de lui, demanda Ã  Gauss de calculer de tÃªte la somme des 50 premiers entiers positifs, c'est-Ã -dire 1+2+3+4+...+50. n There is an amusing and perhaps apocryphal story about this result and the famous mathematician Carl Friedrich Gauss, who was born in 1777 in Braunschweig, Germany. He was so impressed that he bought the best available arithmetic textbook for Gauss and thereafter did what he could to advance his progress. Link to Web page (Viewed 2007-05-22). When Gauss was 6, his schoolmaster, who wanted some peace and quiet, asked the class to add up the numbers 1 to 100. [Most That person did it much more quickly than everybody else, and did it because he or she didn't try to. His class was He had barely finished giving the assignment, when young Gauss put his slate down with simply one number on it, the correct answer! Reinbek bei Hamburg: Rowohlt. slick way to find the sum, by rearranging the order of summing. Il primo episodio della vita di Gauss come matematico viene raccontato in tanti modi differenti, ma sostanzialmente simili; il maestro della scuola di Braunscweig, volendo passare un pomeriggio tranquillo, aveva assegnato un esercizio lungo e noioso, quello di sommare i numeri da uno a 80. Der 9 jaÌhrige G. hatte das Summationsprincip fuÌr arithmetische Reihen auf den ersten Blick erkannt und angewendet. Donc, d’après le théorème de Gauss il existe une charge à l'intérieur de Es dauerte jedoch nicht lange, da erklÃ¤rte der einsichtige Lehrer, der SchÃ¼ler kÃ¶nne bei ihm Ã¼berhaupt nichts mehr lernen. Anstatt alle hundert Zahlen zusammen zu zÃ¤hlen, bildete er Zahlenpaare: Bei der Addition der ersten (1) und der letzten Zahl (100) der Folge ergibt sich 101, wie auch bei der Addition der zweiten (2) und der vorletzten (99), der dritten (3) und der drittletzten (98) ... Insgesamt ergeben sich also 50 Zahlenpaare, die jeweils die Summe 101 ergeben. (Waltershausen [1856]), We can surmise that little Gauss had reasoned in the following way: We want to know the value of, Reversing the order of the terms, we can also write this number as, Adding the terms that lie in the same vertical line we obtain, Therefore the number that Gauss wrote on his slate should have been 5050. Die erste Ausgabe, welche BÃ¼ttner, der wegen seiner Strenge gefÃ¼rchtete Lehrer, den SchÃ¼lern vorlegte, betraf die Addition von Zahlen, welche eine arithmetiche Reihe bildeten. While a powerful lesson in problem-solving has been carried out, further considerations and questions easily evolve: "Does the technique work for any consecutive series of numbers?" My guess is that Gauss figured out that the teacher had access I'm going to give you two very small At the end of the lesson there was a pile of slates on top of Gauss's, all with incorrect answers. The sum of the integers in a consecutive series, then, would be (x) * (x +1)/2. champ électrostatique en vertu du principe de Curie. "What do you mean you have the answer? At the end of this book there is the solution of a problem in the volume itself, in his handwriting, but this entry is of a later date. Ever since hearing how Gauss quickly summed the first 100 integers, I have been intrigued by sums of integers and different approaches to proving identities such as auf den Sammeltisch wirst, wÃ¤hrend alle Underen die Stunde durch rechnen und rechnen. Burrell, Brian. ("There it is!"). 3–4). Gauss was unquestionably the most precocious of them all. When each one finished, he added his slate to the pile growing on the teacher's desk. Berlin:Â Keil Verlag. At the parish school the boys of fourteen to fifteen years were being examined in arithmetic one day, when Gauss stepped forward and, to the astonishment of Buttner, requested to be examined at the same time. Immer hunderteins. At 8 a.m. one morning of the year 1788, over one hundred children sat on wooden benches in a huge classroom in Brunswick, Germany, waiting for their teacher Mr Buttner. At the end of the period the results were examined. Since there are 50 sums of 101, the total is $$50 \cdot 101 = 5050$$. 1911. While the other children were just getting started, young Gauss walked to the teacher's desk and handed in his slate. à travers dS par : 2003. Mas nem bem BÃ¼ttner havia terminado de anunciar o problema, Gauss mostrou sua lousa e exclamou em seu dialeto camponÃªs "ligget se" (Aqui jaz). The evidence of his struggles would be wiped away from the completed work in the same way. Master BÃ¼ttner thought he had trapped Carl in a lie. He had recognized that the hundred numbers can be grouped into 50 pairs (1 +100, 2 + 99, 3 + 98, ...) each summing to 101, and that 50 x 101 gave the correct answer of 5050. Right. A popular example combines a 7-point Gauss rule with a 15-point Kronrod rule (Kahaner, Moler & Nash 1989, §5.5). 2005. Leipzig: B. G. Teubner. ≠ In Carl Friedrich GauÃ in GÃ¶ttingen, edited by Elmar Mittler. We are told that this accomplishment made such an impression on BÃ¼ttner that Gauss was allowed to carry out into the yard at home his spinning wheel at which he had been compelled to spin his portion of flax, and he was allowed to chop it up with an ax for kindling. 1992. Q A Modeling Approach Using Technology: Integrated Mathematics, Level 2. It is manifest from this that one need only multiply the constant sum, 101, by 50, the number of sums. After an hour, the teacher had all the slates, and he found the right answer on that bottom one. Ross, Peter. When he went to primary school his teacher wanted to have some time for himself, so he asked his students to add all the numbers from one to a hundred. (p. 24). Gauss explained his method: Rather than to add the numbers in the order in which they appear. Link to Web page (Viewed 2007-05-22 and 2016-09-23) [Based in part on material presented here.]. Link to Web page (Viewed 2006-02-15). Nothing extraordinary happened during the first two years. Therefore, he was disagreeably surprised as the little Gauss stepped forward when the others had scarcely started working, put his slate on the teacher's desk, and said, 'Here it is.' There is a ladder which has 100 steps. \sum_{k=1}^{100} k = \frac{100\cdot101}{2}. Comment Gauss s'y est-il pris? → 22, pp. In PÃ¤dagogitches Archive 1859, Vol. ; man erhÃ¤lt daher sovielmal 101, als sich aus hundert Zahlen "Paare" bilden lassen. Every number from 1 to 100 occurs exactly once in some pair, so the sum of all those numbers is the sum of all the pairs. Der stille Junge ist ihm noch nie zuvor aufgefallen, weder in positiver noch in negativer Hinsicht. He had apparently figured out the summation formula and calculated the answer in his head. : Merriam-Webster. Die Kinder sollen nÃ¤mlich alle Zahlen swischen 1 und 100 zusammenzÃ¤hlen: Was zunÃ¤chst simpel klingt, wird die schlectausgerÃ¼steten SchÃ¼ler jedoch in grÃ¶Ãte Schwierigkeiten stÃ¼rzen. 31â36. ∭ Insights and connections—that's what mathematicians look for. Gauss's Formula for the sum of integers was born. 2005. I am far from asserting that. There is a larger question raised by the fact that apocryphal stories, such as the Nobel-math-prize myth, seem to have a life of their own.... Another example of this tendency concerns the famous story of Gauss's discovery as a ten-year old boy of a simple method for summing an arithmetic series. Der junge Gauss war kaum in die Rechenclasse eingetreten, als BÃ¼ttner die Summation eine arithmetischen Reihe aufgab. (p. 89). Video on YouTube or Vimeo. Er hatte den geometrischen Aufbau der Zahlen sofort vor Augen gehabt und erkannt: Man muÃ nur die ersten und die letzten Zahlen jeweils verknÃ¼pfen, 1+100, 2+99, 3+98... bis 50+51, dann hat man 50mal 101 zusammengezÃ¤hlt und das ist das Ergebnis. Hi ha moltes anÃ¨cdotes referents a la precocitat matemÃ tica del jove Gauss, encara que els biÃ²grafs assenyalen que bona part d'aquestes anÃ¨cdotes es basen en els relats que feia el propi Gauss en els seus darrers anys de vida, cosa que dificulta la seva comprovaciÃ³. Mi vida junto a Gauss. (p. 12). If I continued adding pairs of numbers like that, I would eventually reach 50 + 51. he demanded. Sums, Sequences, and Series in The Analysis of Algorithms. In each case the answer is 101, and since there are 100 numbers to be added, there are fifty sets of 101. Almost instantly, Gauss threw his slate onto the master's table, saying, "Ligget se!" But each pair adds up to 101. Here occurred an incident which he often related in old age with amusement and relish. Cette force se décompose ainsi : le champ électrique. 1877. he demanded. Le professeur, stupÃ©fait, demanda Ã  l'enfant ce qu'il avait fait pour trouver le bon rÃ©sultat si rapidement. 68–69), Gauss was one of those remarkable infant prodigies whose natural aptitude for mathematics soon becomes apparent. That didn't help. Link to Web page (Viewed 2006-02-02). Ivo Schneider of the Bundeswehr University, Munich, offered advice on interpreting the documentary record of Gauss's early life (but obviously he is not to be held responsible for my interpretations). Hu, R. 2003. All the students applauded, and Master BÃ¼ttner had to compliment Carl on his work. His teacher, a stern and lazy man, wrote on the board the task that these young men had to perform. Hence the sum was reduced to 50 pairs, each totalling 101, for a grand total of 5,050. Once, after the "boss" had finished his calculations for each man and was about to give out the money, the three-year-old boy got up and cried in childish voice: "Father, the calculation is wrong," and he named a certain number as the true result. I-o dărui băiatului pentru ca să-și poată domoli setea de cunoștințe mai bine decÃ¢t Ã®n timpul orelor lui de aritmetică. Unnoticed the three-year old child had been following his father's transactions. The students knew nothing about advanced arithmetic and had only one way of doing it. Tout le monde connaît l'électricité statique car celle-ci se manifeste fréquemment dans la vie de tous les jours. "Would it work for a series of even numbers?" "yes" we get the same answer [Lecturer writes "X" to the WaÌhrend die andern SchuÌler emsig weiter rechnen, geht BuÌttner auf und ab, die Karwatsche in der Hand, und wirft von Zeit zu Zeit einen mitleidigen Blick auf den kleinen GauÃ, der so rasch seine Aufgabe beendigt hatte. The 50th step, however, is alone and without a match; likewise, the 100th stair is alone. Por quase uma hora BÃ¼ttner fitou Gauss, que ficou sentado com os dedos entrelaÃ§ados enquanto os colegas esfalfavam. 2000. En effet, la somme recherchÃ©e demeure inchangÃ©e si l'on adopte la disposition classique: Mais l'avantage avec la deuxiÃ¨me disposition c'est que l'addition faite verticalement donne: 100 ajoutÃ©s Ã  1 + 99 = 100, ajoutÃ©s encore Ã  2 + 98 = 100 etc. ) En raison de limitations techniques, la typographie souhaitable du titre, « Champ électrostatique, potentiel : Théorème de Gauss Champ électrostatique, potentiel/Théorème de Gauss », n'a pu être restituée correctement ci-dessus. Mathematics: The Science of Patterns: The Search for Order in Life, Mind, and the Universe. vaut : Pour une surface When at last all pupils had finished the work, Carl having waited all the time with his arms crossed, his answer proved to be correct, much to the teacher's astonishment. He sneezed, blew his nose and said in croaky voice, "On your slates, add all the numbers from 1 to 100, then put them on my desk for marking". Portland, Maine: Walch Publishing. t (p. 4). Carl used a different approach. Lietzmann, Walther. This event happened just before Gauss turned three years old. Associative Law? Dopo pochi minuti, Gauss depose sulla cattedra la lavagnetta con il risultato, suscitando le ire del maestro che pensava a uno scherzo; tuttavia, un paio d'ore piÃ¹ tardi, quando tutti ebbero finito l'esercizio, dovette ricredersi, perchÃ© Gauss era uno dei pochi scolari che avevano trovato il risultato esatto. One imagines that the teacher registered a combination of incredulity and frustration at this unexpected turn of events, but a quick look at Gauss's answer showed it to be perfectly correct. p. 388. The story goes that the great German mathematician Carl Friedrich Gauss was in school and his teacher was bored, so to keep the students preoccupied he instructed them to add up all the numbers between 1 and 100. he and BÃ¼ttner sort of glared at each other for an hour while Gauss junior was also making similar waves at school. So the Nth triangular number is got by simply adding the first N numbers: 1 + 2 + 3 + ... + N. If you want to find the 100th triangular number, there is a long laborious method in which you attack the problem head on and add up the first 100 numbers. Winning Solutions. 98 99 100. 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. Mr Buttner was astonished. While the other pupils were figuring, multiplying, and adding, BÃ¼ttner went back and forth, conscious of his dignity; he cast a sarcastic glance at his quick pupil and showed a little scorn. Vol. Student edition. en exprimant le gradient du champ électrique dans le système de coordonnées adapté. Link to PDF file (Viewed 2006-02-15). Gauss did it almost instantly. Doch jetzt, nach zwei Jahren, brachte die Schulordnung es so mit sich, daÃ der Knabe in die Rechenklasse eintrat, in der die meisten SchÃ¼ler bis zu ihrer Konfirmation, biszum Alter von 14 Jahren also, blieben. Gauss enjoyed numerical calculation as a child. [Die ErzaÌhlung findet sich auch in W. AÌhrens. The teacher gave out an arithmetical series to be added. His teacher, intending to put everyone to work for a while, told the boys to sum all of the counting numbers from 1 to 100, and they set to work. 1999. Marymount International School, Rome (Valeria P., Mattia B., Bianca Di L., Edoardo M., Francesco C., and Ms. Derarca Lynch). Carl Friedrich Gauss: A Biography. Lietzmann, Walther. Although his teacher did not think so, Carl was a very bright student. Especial thanks to Carolina Grey at Johns Hopkins and Mary Linn Wernet in Natchitoches. (p. 229). New York: Wiley. 1994. : A K Peters. The same is definitely true in computer science, too. GÃ¶ttingen: Staats- und UniversitÃ¤tsbibliothek. The Art of Mathematics. Following Gauss's method of adding the first and nth terms gives: If we continue in this same manner until all the pairs have been added, we obtain n/2 such pairs, which gives the formula. The answer is that he had succeeded in recognizing an obvious pattern: Why not try your own hand at this kind of thinking? His teacher thought this problem would keep the class occupied for some time (busywork is not new) and was amazed when Gauss quickly made a mental calculation and supplied the correct answer, 5,050. Leipzig: Im Feuer Verlag. The story goes that when Gauss was a child, his math teacher came to class unprepared one day. GauÃ hat 1 und 100, dann 2 und 99, 3 und 98 usf zusammengezaÌhlt und so 50 Paare von Zahlen mit der Summe 101 erhalten, so daÃ er sofort das Er gebnis 5050 hinschreiben konnte. Second edition. Invitation to Mathematics. which in the low German peasant dialect of the time meant "There it is!" Although the formula was known to Buttner, no child of 10 had ever discovered it.

## formule de gauss électrostatique

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