formule de gauss électrostatique

In Gottinger Professoren: Ein Beitrag zur deutschen Cultur- und Literärgeschichte in acht Vorträgen. 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. He had barely finished explaining the assignment when Gauss wrote the single number 5050 on his slate and deposited it on the teacher's desk. In this school—which seems to have followed very much the pattern of the Middle Ages—the young Gauss remained two years without special incident. Unfortunately, Gauss inherited poor eyesight as well as genius and was unable to see the numbers. Stories of Gauss's early mathematical genius abound: when he was 3, he uncovered an error in his father's bookkeeping; when Gauss was 8, Büttner, the local school teacher, gave to the class the problem of summing the first 100 whole numbers, to which Gauss gave the correct answer—5050—almost immediately and without any obvious computation. (Google Books copy is second edition, dated 1920, but first edition was published in 1915.). He had quickly noticed that if the numbers to be added are written out and then written again below but in the opposite order, the combined (double) sum may be computed easily by first adding the pairs of numbers vertically and then adding horizontally. As Büttner turned over the slates, he saw one wrong answer after another, and his cane grew warm from constant use. When Gauss was ten years old he began his first lessons in arithmetic. He joked that he had been able to count before he could talk, and many anecdotes attest to his extraordinary gifts. Herr Büttner (aside): (That will keep those little JD's busy for a while doing 100 sums! Gauß und Bessel. In the meantime, here's a history lesson: Gauss' math teacher, J.G. On the first day that Gauss entered the arithmetic class, the students were asked to sum the numbers from 1 to 100. In those days all that the students had were slates which they could write on with chalk. Master Büttner got a nasty smile on his face and said, "Well then, come up to the board and show us all how you solved it, Carl." I will not consider how Gauss did this, but I commend Polya's delightful book to you. A popular example combines a 7-point Gauss rule with a 15-point Kronrod rule (Kahaner, Moler & Nash 1989, §5.5). To the end of his days Gauss loved to tell how the one number he had written down was the correct answer and how all the others were wrong. going to be slower than little Gauss [Lecturer hesitates, then shows "2 Il buon Buttner sarà costretto presto a ricredersi. What he possessed in abundance was a gift for spotting cryptic patterns in mathematical problems, and using them to find solutions. Er hatte die Aufgabe kaum zu Ende gestellt, schon schreibt der kleine Gauß eine Zahl auf seine Tafel, bringt diese nach vorn und legt sie vor den Lehrer mit den Worten "Ligget se" (Da liegt sie). Nordgreen, Jan. 2004. Link to Web page (Viewed 2007-05-21). Bruce, Donald, and Anthony Purdy (editors). There are many stories told about Gauss's early-developing genius, one of which comes from his mathematics class when he was 9. Hardly had the teacher given the boys this problem, when Gauss threw his slate upon the table, saying: "Ligget se!" Ann Arbor: University of Michigan Press. Bereits im zarten Alter von drei Jahren soll er seinen Vater bei einem Fehler in einer Lohnabrechnung korrigiert haben. the teacher had a secret formula for determining the answer. New York: John Wiley & Sons. A story about the young Karl Friedrich Gauss well illustrates the importance of identifying paradigms for (mental) action. Dans ce cas, ce champ électrostatique apparaîtra comme la force entre deux particules ponctuelles fixes par unité de charge. Knowing this would take his students time, the arrogant teacher began to go back to his seat and prepare himself for a long quiet day. But he thought wrong. Tan pronto el profesor acababa de anunciar la tarea, Gauss dijo "aqui está". Vol. (pp. He just represented to himself more clearly and distinctly than the other youngsters what is required: to find the sum. Undated. We can only speculate about which version is true! Je vous invite à consulter notre article sur la question : https://www.superprof.fr/ressources/scolaire/physique-chimie/resume-ps-6/cpge-1-pcsi-ps-6/champ-electricite-formules.html. Déterminer la direction du champ total au point M : Faire la somme des composantes dans une base orthonormée bien choisie. He then noticed that one plus 100 equals 101, as does two plus 99 and three plus 98. Büttner then makes use of a well-known formula for the sum of such a series: the sum is equal to the number of terms times one-half the sum of the first and last terms. New York: Oxford University Press. Dabei lassen sich die erste und die letzte Zahl, also 1 und 100, zu einem Paar zusammenfassen, das die Summe 101 ergibt, ebenso die zweite und die vorletzte Zahl, 2 und 99, usw. Gauss outwitted him and all his teacher could do was to buy him a text book and announce that the boy was beyond him. Schon in zartester Jugend zeigte Gauß einen merkwürdig entwickelten Zahlensinn. 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. Wo andere Mittel der Erziehungskunst versagten, griff der Stock ein, den Lehrer Büttner stets mit sich führte, wenn er durch die Klasse schritt. Doch den kleinen Karl schrecken die sarkastischen Blicke des gestrengen Präzeptors nicht im geringsten; ruhig und ohne Furcht sitzt er da in dem unerschütterlichen Bewußtsein der Richtigkeit seiner Lösung. Available online. The reckoning was gone over again and was found to be what the child had said. Bei einer solchen Brüfung trat auch der kleine Gauß mit blauen glänzenden Augen zum Lehrer heran und bat dielen um die Erlaubniß, jene Aufgaben mit rechnen zu dürfen. En el seno de esta humilde familia, muy alejada de los salones ilustrados de la nobleza germana, el joven Gauss va a dar muestras tempranas de su genio precoz. Alors, dans le cas d'un changement de référentiel, il est tout à fait possible de transformer un champ magnétique en champ électrique et inversement. (pp. And there it lay, the only correct answer in the lot. Ogilvy, C. Stanley, and John T. Anderson. Mathematiker- Anekdoten. La force est dirigée selon la droite reliant les deux charges ; Elle est attractive si les charges sont de signes opposée et répulsive sinon ; Son intensité est proportionnelle aux valeurs de q. Décomposer la distribution de charge en quelques distributions simples. Sein Vater war Maurer, später Gärtner, ein achtungswerther, aber rauher, unfeiner Mann, seine Mutter Dorothea geb. Giancoli, Douglas C. 2000. In der mit 100 Schülern überfüllten Schulstube erteilte der Lehrer die Aufgabe, alle Zahlen von 1 bis 100 zu addieren. This was going to take them a long time, but Herr Büttner's whip was ready to straighten out any boy who gave up on the job. It was algebra, right? Translated by Albert Froderberg. Der alte Büttner musterte den schnellfertigen Knaben mit spöttischem Mitleid, während die andern Schüler die Stunde hindurch weiter Rechneten. At the age of 3 he was correcting his father's weekly wage calculations. Der alte Büttner mustert den schnellfertigen kleinsten seiner Unglückswürmer mit spöttischem Mitleid: der Bakel wird zu thun bekommen; am Ende jedoch findet er auf Gauß' Tafel nur eine Zahl, das Ergebniß, und es ist richtig. ∬ He had apparently figured out the summation formula and calculated the answer in his head. Se había dado cuenta de que la suma de la primera y la última cifra daba el mismo resultado que la suma de la segunda y la penúltima, etc., es decir: 1+100 = 2+99 = 3+98 = ... = 101, Como hay 50 parejas de números de esta forma el resultado se obtendrá multiplicando 101 × 50 = 5.050, Perplex City Card Catalog. d Since there were 100 such pairs, the sum of the two rows was 100 × 101 or 10,100, and the sum of each row was one half of this, or 5,050. 2005. Er besuchte in seiner Jugend die Katharinenschule in Braunschweig. In der dritten Volksschulklasse, also im Alter von etwa neun Jahren, demonstrierte er seine herausragenden mathematischen Fähigkeiten auf eindrucksvolle Weise. When the instructor finally looked at the results, the slate of Guass was the only one to have the correct answer, 5050, with no further calculation. {\displaystyle {\begin{aligned}\iint _{\Sigma }{\vec {E}}(M). Young Gauss showed his mathematical ability at a very early age. (Passage appears on p. 89; transcribed by Barry Cipra.). The children usually got to the third grade at the age of 10 and stayed in that grade until confirmation (at the age of 15). Büttner was in the habit of assigning long addition problems which, unknown to his students, were arithmetic progressions that he could sum up using formulas. G. lernte lesen ohne Unterricht; er fragte die verschiedenen Hausgenossen um die Bedeutung der Buchstaben und half sich dann allein fort. {\displaystyle n} 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. 2001. Büttner looked at the top slate. The teacher wanted to get some By combining all the steps in this order, that is, one of the higher steps with one of the lower, you shall always get 100. Carl Friedrich Gauss. Lange vor seinen Mitschülern hatte der kleine Carl Friedrich das richtige Ergebnis parat. Gauss y la campana. The teacher, certain that Gauss could not possibly have the answer in so short a time, decided to wait until the next student raised his hand. It was an hour before the others finished. 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. So the double sum is 100 × 101, or 10,100, which means that the desired sum is half that, or 5050. Heroes of the Telegraph. "Well, sir, I thought about it. From that day Gauss was Right. 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. Insgesamt erhält man so 50 Zahlenpaare, die jeweils die Summe 101 ergeben, mithin insgesamt 5050 als Gesamtresultat. (pp. 2003. (p. 33). We don't know the exact question, but it was something very similar to this: add up all the numbers from 1 to 100. The problem was barely stated before Gauss threw his slate on the table with the words (in the low Braunschweig dialect): "There it lies." Eventually, the assistant announced that nobody in the whole class had the right answer, which made the teacher even grumpier. San Carlos, Calif.: Wide World Publishing/Tetra. As the story goes, Gauss's teacher tried to occupy the class during an unsupervised absence by proposing a simple problem: Find the sum of all integers from 1 to 100. The story goes that almost before the teacher could turn around, Gauss handed in his slate with the correct answer. Quelques Propriétés Cachées des Nombres. Thus, 1 + 100 = 101; 2 + 99 = 101; 3 + 98 = 101; ... ; 49 + 52 = 101; 50 + 51 = 101. Most mathematicians who teach will assert that the problem given to Gauss by his tyrannical school teacher was to sum the integers from 1 to 100. Finding patterns is the very essence of good mathematics. In einer niedrigen, dumpfen Schul stube saßen dort etwa 100 Kinder; der Lehrer Büttner ging, mit der vielgebrauchten Karbatsche in der Hand, zwischen den Reihen auf und ab und suchte den Kindern die Anfangsgründe des Wissens beizubringen. Comme Podcast and Web site. The numbers are all the same! 2000. 2006. "How did you manage to guess this number?" → Now Gauss had a rectangle with 101 rows each containing 100 beans. 7 They had recognized their son's calculating ability when, at the age of three, he corrected a mistake his father made in paying out wages to men who worked [for] him.... Hein, James L. 2002. <>>> Y a él le debemos el relato de la anécdota que le coloca como el más precoz de los matemáticos. Utilisation de l'angle solide dans le cas d'une distribution surfacique de charge plane. Master Büttner had scarcely finished stating the exercise when young Gauss flung his slate on the desk. Aici nu erau adunate numerele unul după altul la nesfârșit, ca pe celelalte tăblițe. L'Attracteur: La Revue de Physique. To Büttner's surprise and annoyance, however, Gauss, after a few seconds, raised his hand and gave the answer—5,050. [The lecturer points at each column in Espiral 11: Serie de matemáticas para secundaria y media. Büttner tinha por hábito passar longos problemas de adição que, desconhecido de seus alunos, eram progressões aritméticas que ele resolvia usando fórmulas. Norwell, Mass. Paradigms and Conventions: Uncertainty, Decision Making, and Entrepreneurship. The young boy had noted this pattern: This simple story emphasizes the importance of looking at mathematics: seeking patterns and, if possible, using those patterns to solve a problem. But little Gauss immediately raised his slate with the result. It is reported that when Gauss was a student at elementary school his teacher asked the students to add up all natural numbers from 1 to 100, hoping to keep his students busy for some time. 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. {\displaystyle 3n+1} Alamo, Fernando de. Stories tell of him being able to maintain his father's business accounts at age three. : Kendall/Hunt Publishing Company. Er fragt seinen Schüler in einer seltsamen Stimmung aus Faszination, Neugier und Skepsis, wie er das richtige Resultat in so unglaublich kurzer Zeit und vor allem ohne Hilfsmittel gefunden habe. It came to him probably more naturally than to other children of his age to grasp the purpose of a question, to pay attention to the essential point. What would you do if your teacher asked you add all the numbers from 1 to 100? Nicht oft mag es vorkommen, daß ein Kind das Lesen von selbst erlernt, indem es die Bedeutung der einzelnen Buchstaben bald diesem, bald jenem Hausgenoffen abtragt. Gauss, 1789, d. 2. 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. When they added all the numbers between 11 and 20 (11+12+13 ... +20), the sum was 155. Some say "50." 22, pp. Bändchen der Math.-phys. When we finally total them up, we get the same answer, right? It was in this hell-hole that Gauss found his fortune. He then sat down and folded his hands at his desk. Später hätte Gauß nicht mehr sagen können, ob er an diesem Tag müder gewesen war als sonst oder einfach nur gedankenlos. d Geschwinde, Ewald, and Hans-Jürgen Schönig. His teacher was J. G. Büttner. Ganz ungewöhnlich früh, schon in den Jahren da bei Underen die Seelenvermögen noch im Dunkel der Unbewußtheit schlumern. The custom then was that when sums were being done during the school period, the pupil to finish first put his slate on the teacher's table, the second quickest laid his slate on top of the first, etc. So one triangle must contain half this number, namely 1/2 × 101 × 100 = 5,050. "What do you mean you have the answer? His family was very poor as his father worked as a gardener, canal tender, and bricklayer (Bell 218). 2000. México: Pangea. Amsterdam: Editions Rodopi. Unglaublich früh trat das mathematische Talent hervor. En effet, si on observe la description correcte d'un champ électromagnétique, celui-ci fait intervenir un tenseur quadridimensionnel de champ électromagnétique dont les composantes temporelles correspondent alors à celle d'un champ électrique. He walked up to the chalk board to write the day's problem. (p. 577). agreement] Right. According to mathematical lore, one day his teacher asked the class to add all the natural numbers from 1 to 100. It wasn't anything like La Flèche, the Jesuit school Descartes entered at age eight that would later become famous. Link to PDF file (Viewed 2006-03-11). Carl sat at his desk with his hands on his chin, thinking about the problem. War Gauss ein Wunderkind? At the age of ten, he was a show-off in arithmetic class at St. Catherine elementary school, "a squalid relic of the Middle Ages... run by a virile brute, one Büttner, whose idea of teaching the hundred or so boys in his charge was to thrash them into such a state of terrified stupidity that they forgot their own names." At any rate, the elementary textbooks by Remer and Hemeling are probably those in which Gauss first studied. The whip was recognized by great and small of the day as the ultima ratio of educational method, and Büttner felt himself justified in making unsparing use of it according to caprice and need.

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