Büttner hatte die Auf gabe kaum ausgesprochen, als Gauß die Tafel mit den im Braunschweiger Platt gesprochenen Worten auf den Tisch wirft: "Ligget se" (Da liegt sie). Băiatul adunase un număr de la început cu unul de la sfârșit: 1+40, 2+39, 3+38, 4+37 până când a format douăzeci de perechi a căror suma făcea mereu 41. So I multiplied 101 by 50 in my head and got 5,050. Hier ging Büttner zwischen etwa hundert Schülern auf und ab, mit der Karwatsche in der Hand, welche damals als ultima ratio seiner Erziehungsmethode von Gross und von Klein anerkannt wurde und von der er nach Laune und Bedürfniss einen schonungslosen Gebrauch zu machen sich berechtigt fühlte. (p. 89). Numbers of the form n(n+1)/2 are called triangular numbers, since they are exactly the numbers you can obtain by arranging balls in an equilateral triangle. When Büttner looked at Gauss' slate, he found there a single number—no calculation at all. There will be as many as follows: Take the dove sitting on the first step and add to it the 99 doves sitting on the 99th step, thus getting 100. 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101....there are 50 such pairs, 101 x 50 = 5050. Q The number of risk parameters in a portfolio equals the sum of the number of assets it includes. Anton, Howard, in collaboration with Albert Herr. Bulletin Institute of Mathematics and its Applications 13(3–4):68–76. - "There it lies." ( Link to Web page (Viewed 2005-11-25). It wasn't anything like La Flèche, the Jesuit school Descartes entered at age eight that would later become famous. A word about how I collected these accounts: Many were found through conventional methods of library research. Le preguntó cómo lo había hecho. Gauss did it almost instantly. Mollin, Richard A. My thanks to the librarians of the following institutions: Boston College, the Boston Public Library, Boston University, Brown University, Duke University, Mt. However, Gauss discovered the trick for himself and quickly solved the problem while all the other students worked for hours and all the answers were wrong except for Gauss's. He had been following his father's actions unnoticed, but the figuring was carefully repeated and to the astonishment of all present was found to be exactly as the little boy had said. New York: Springer Science+Business Media. ", "You!" Nous allons ici faire la liste des différentes méthodes à utiliser afin que vous soyez prêt pour vos concours. he shouted, pointing at little Gauss, "How would you estimate your chances of succeeding at this task? 2005. El profesor, ante un grupo de niños de alrededor do 10 años de edad, estaba molesto por algún mal comportamiento del grupo y decidió poner a trabajar a sus alumnos en un problema de matemáticas que segun él les llevaría un buen rato terminar; así, de paso, podría descansar un poco. He picked it up on his own.   Aujourd'hui, la psychologie cognitive définie la compréhension comme étant une opération mentale impliquant des processus complexes parmi lesquelles la représentation mentale occupe une place de choix. He did not know the formula (3.1), he just derived it using the following clever argument. Herr Büttner (agitatedly): Everyone, listen up! By the end of the school day, the last of the boys set his slate down. Law? "Students, for math work today, I want you to add the whole numbers from 1 to 100." (p. 112, item 319). Es zeigte sich aber auch schon früh, daß dies nicht nur eine Begabung für rechnerische Tüfteleien war, sondern daß sich dahinter ein tiefes Verständnis einer Gesetzmäßigkeit in der Welt der Zahlen verbarg bzw. The answer was wrong. We can do one multiplication. Reinbek bei Hamburg: Rowohlt. Knowing that exactly 50 pairs of numbers between 1 and 100, this led Gauss to just simply multiply 101 by 50= 5050. I am far from asserting that. G. schrieb nach kurzem Besinnen das Ergebniss auf die Tafel und warf sie mit den Worten "da ligget se!" Gauss was born on April 30, 1777 in Brunswick (now it is Western Germany). So he decided to give the class a problem that would take a long time to work out. Gauss stayed in these surroundings for two years without any ill consequences. There is a simple but not particularly obvious trick for adding the numbers in an arithmetic progression, but the class had not been taught it, so they had to laboriously add the numbers one at a time. Whenever a man worked overtime he was, of course, paid proportionately more. Posting on open forum for class Soc 15, Quantitative Analysis of Social Data. Dort legt er sie—einem alten Brauch gehorchend—selbsbewusst mit der beschrifteten Seite nach unten und ruft, vermutlich nicht ohne Stolz: “Ligget se!” So viel Frechheit verschlägt Büttner dann doch die Sprache.   Die Karbatsche Büttners trat nicht in Tätigkeit; der Lehrer erkannte die ungewöhnlichen Geisteskräfte des Knaben, und das Nächste, wasertat, war, da ßereigensfürihnein besonderes Rechen buch aus Hamburg kommen ließ. Probably the most famous story about young Gauss occured in 1786, when he was nine years old. Gauss' confidence in his own reasoning then and in later years was unshakable. 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. New York: Springer-Verlag. The teacher looked at him scornfully while the others worked diligently. Büttner verschrieb hierauf eigen« aus Hamburg ein neues Rechenbuch, um damit den jungen aufstrebenden Geist nach Kräften zu unterstützen.). Die Ausgabe ist kaum gestellt, als Gauß seine Tafel mit einem übermüthigen 'Dar licht se!' 1998. There are 100 vertical pairs, each summing to 101. Depending upon their proficiency in addition, some were speedy and some were slow; some were accurate and some were not. Most likely, the numbers were not as nice as that, but there was a hidden pattern to them: they formed an arithmetic progression, meaning that the difference between any two consecutive numbers was always the same. The Pleasures of Counting. (p. April 1777 in einem kleinen ärmlichen Haus als einziges Kind von Dorothea und Gerhard Diederich Gauß in Braunschweig geboren und zeigte schon sehr früh eine außerordentliche Begabung im Erfassen von Zahlen. This act was apparently so astonishing that Herr Buttner was transformed into a champion for this young boy. To keep the class busy one day, he assigned them the problem of adding all the numbers from one through a hundred. There are a couple of oft-told stories illustrating the boy's unusual ability. 106–107. Hu, R. 2003. In old age he liked to recall characteristic little episodes which reflected the outwardly restricted, modest homelife, but in which one detected the sparks of genius which later rose to such heights. What a pleasure it would be to correct that child when it was time to check the answers! Wir besitzen eine kleine Sammlung beglaubigter Anekdoten in einem Bändchen der Mathematisch-Physikalischen Bibliothek: W. Ahrens, Mathematiker-Anekdoten (2. 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. His teacher, suitably impressed, supplied the boy with literature to encourage his intellectual development. Er pflegte selbst oft scherzweise zu sagen, er habe früher rechnen als sprechen können. 4–6). It was 1787 and Herr Büttner was in the habit of handing out brutally long sums like these, which the children had to labor over. An Invitation to Mathematics. [Note: although the Möbius cites Winneke 1877, the text actually seems closer to Sommer 1877.]. Darum sei es doch gegangen, eine Addition aller Zahlen von eins bis hundert. Born in Brunswick, Germany, in 1777, Karl Friedrich Gauss displayed immense mathematical talent from a very early age. Gauss had written the number 5050, and nothing else. "Warte nur! So the answer is 100 times 101 divided by 2, since each number is counted twice. Wie viel hat dieser einfache, schlichte Mann der Welt gerettet und erhalten! Festrede zur 100 jährigen Jubelfeier des Mathematikers Gauss. Kaum war die Aufgabe gestellt, schrieb der kleine Gauss die Lösung auf seine Tafel, legte diese auf den Tisch und rief, echt braunschweigerisch: "Ligget se!" 8, pp. Pues si sumamos el primer y el último número resulta que 1 + 100 = 101, el segundo y el anteúltimo dan 2 + 99 = 101, etc. Why isn't there a Nobel prize in mathematics? Lorsqu'une action proposée est impossible, passer à la méthode suivante. Then 3 and 98 is 101. teacher's annoyance, little Gauss came up to the teacher with the answer, right Dicat, qui potest, quot columbae in totum fuerunt? Er könne es doch unmöglich im Kopf... Doch, natürlich im Kopf. Most of them were wrong and were corrected with the rattan cane. zuzuzählen braucht, um immer die gleiche Summe 101 zu bekommen. In this school, which seems to have had the cut and style of the middle ages, young Gauss remained for two years without any incident worth recording. 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. While the other pupils continued to work on this problem, Mr. Büttner, conscious of his dignity, walked up and down the room, and occasionally threw a contemptuous and caustic glance at the smallest of his pupils, who had finished the task too quickly. He immediately realized that if he multiplied 100 by 101 and divided by 2, so as not to double count, he would arrive at the answer. Mi vida junto a Gauss. Some waited until close to the end to make their first mistakes, but even so their answers were wrong. n When Gauss was eight years old, he and his classmates were asked by their teacher to find the sum of the integers from 1 to 100. trick [doubt in the audience]. (pp. stream 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). Aus seinem siebenten Lebensjahr erzählt Gauss selbst, er habe in der Schule eine langwierige Rechenaufgabe in wenigen Augenblicken gelöst, indem er auf das Gesetz der arithmetischen Reihe aufmerksam wurde, und während seine Kameraden sich eben anschickten, durch mühsames Addieren die Lösung zu finden, habe er seine nur eine einzige Zahl enthaltende Tafel mit dem übermütigen Ausruf im Braunschweiger Dialekt: "Dar licht se" auf das Katheder geworfen. 1878. Then I added the second number to second last number and got 101 again. When the rest of the students' calculations were collected an hour later, all were found to be incorrect except Gauss's! It is said that one day before he was three years old his father was making out the weekly payroll for the laborers in his charge, unaware that his son was observing the process intently. Link to Web page (Viewed 2006-02-15). (pp. He would know to write a beautiful program that attacks the problem in a new way that, in the end, is the right way. Link to Web page (Viewed 2007-05-21). Sein Blick fiel auf des Ergebnis, und seine Hand erstarrte. Choi, Young Back. Dunham, William. Jedenfalls hatte er sich nicht unter Kontrolle gehabt und stand nach drei Minuten mit seiner Schiefertafel, auf die nur eine einzige Zeile geschrieben war, vor dem Lehrerpult. La somme de chacune de ces paires — il y en avait 50 — était 101. Gaea, Natur, und Leben. Link to Web page (Viewed 2007-05-22). Burton, David M. 1976. or Ligget se!) When children in his class were asked to sum the numbers one through ten, most used the procedure 1+2=3, 3+3=6, 6+4=10, ... , 45+10=55. Ann Arbor: University of Michigan Press. You have not written anything on your slate," retorted Master Grumple. Wahrscheinlich ist Büttner an diesem Morgen schlecht gelaunt und will von seiner nichtsnutzigen Meute einfach mal nichts sehen und hören. Problem solvers. en exprimant le gradient du champ électrique dans le système de coordonnées adapté. Si hay 100 números entonces hay 50 pares que suman 101, de donde resulta que 50×101 = 5050 era la solución. Rather than start in on the adding immediately, he sat and thought a minute. Avec cette formule, on peut alors définir le champ électrique comme étant le champ traduisant l'action à distance subie par une charge électrique fixe dans un référentiel défini de la part de toutes les autres charges, qu'elles soient mobiles ou fixes. D'après le théorème de Gauss, ce flux est aussi égal à la somme des charges internes à divisée par plus la somme des charges surfaciques divisée par . (Of course?) Gauss easily did the arithmetic in his head. Well, you can see that it is a tedious calculation. Wer seine Rechnung fertig hatte, musste seine Tafel auf den Classentisch legen. (pp. Hamburg: Rowohlt, Reinbek. Link to Web page (Viewed 2006-02-18). 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. To his teacher's surprise, however, Gauss immediately responded "5050", remarking that it's a simple matter to sum the arithmetic series. But at a very early age it was clear that his son had unusual talents. | n Gauss bewahrte dem engen kleinen Kreise des elterlichen Hauses, worin seine erste Jugend verstrich, bis an sein Lebensende ein Andenken voll rührender Pietät und wandte gern noch im hohen Alter seine Erinnerung auf unzählige kleine charakteristische Züge aus seiner frühsten Kindheit zurück, welche die äuserlich beschränkten, bescheidenen Verhältnisse derselben wiederspiegeln und in denen man die wunderbare Begabung des später so grossartig entfalteten Geistes schon einzelne Funken sprühen sieht. La disciplina férrea parecía ser el único argumento pedagógico de Büttner, y de casi todos los maestros de la época. 60–61). Finishing his calculations, the elder Gauss was startled to hear a tiny voice saying: "Father, the reckoning is wrong, it should be...." When the computation was checked, the child's figure was found to be the right one. Arithmetic series: In 5th grade, Karl Frederick Gauss's teacher attempted to punish him by demanding that he sum the integers from 1 to 100. It should be–––." Am Ende der Stunde wurden darauf die Rechnen tafeln umgekehrt; die von Gauß mit einer einzigen Zahl lag oben; sie gab die richtige Lösung, während viele der übrigen falsch waren und alsbald mit der Karwatsche rektifiziert wurden. {\overrightarrow {{\rm {d}}S}}&=\iiint _{V}\mathrm {div} ({\vec {E}})~{\rm {d}}\tau \\&=\iiint _{V}{\frac {\rho }{\varepsilon _{0}}}~{\rm {d}}\tau \\&={\frac {Q_{int}}{\varepsilon _{0}}}\end{aligned}}}. The son of a bricklayer, it is said that he spotted formulae for certain arithmetic sums for himself at the age of 10. d In some, Gauss is the youngest student. Hi ha moltes anècdotes referents a la precocitat matemàtica del jove Gauss, encara que els biògrafs assenyalen que bona part d'aquestes anècdotes es basen en els relats que feia el propi Gauss en els seus darrers anys de vida, cosa que dificulta la seva comprovació. Auf diese Weise gelange man—von außen nach innen vordringend—bis zum letzten Zahlenpaar 50 + 51 in der Mitte der Reihe. For example, 5,050, the total number of volatilities and correlations for a 100 asset portfolio equals 1 + 2 + 3 + ... + 100. Probability Distributions Involving Gaussian Random Variables: A Handbook for Engineers and Scientists. After he had asked various members of the household about the pronunciation of letters of the alphabet, he learned to read by himself, we are told, even before he went to school, and showed such remarkable comprehension of number relationships and such an incredible facility and correctness in mental arithmetic that he soon attracted the attention of his parents and the interest of intimate friends. At the end of the lesson, when the teacher collected all the slates, precisely one had the correct answer: Gauss's. These extra points are the zeros of Stieltjes polynomials. → Gauss showed his talents early. Herr Büttner was dumbfounded. 5–7). During the day he is said to have been compelled by his father to help earn the living and in the long winter evenings to sit at the spinning wheel. He was quick to reach the answer not necessarily because of his facility in addition, but because he saw the situation differently than his classmates. Any other way? In the meantime, here's a history lesson: Gauss' math teacher, J.G. Căci băiatul care se foia nerăbdător în banca lui, descoperise cu propriile lui forțe metoda adunării numerelor dintr-un șir natural, fără să-i fi spus nimeni nimic despre asta vreodată. He exhibited such early genius that his family and neighbors called him the "wonder child". Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. His teacher had a habit of setting the class long strings of numbers to add up to keep them occupied, all the time knowing a formula for the answer. (p. 967) (Added 2006-04-14). = The Gauss–Kronrod quadrature formula is an adaptive method for numerical integration. increment, but they formed an arithmetic progression, the kids He remembered these incidents accurately and in recounting them he never varied the details. ). — In seine frühste Jugendzeit reichte seine Erinnerung daran zurück, das er als kleines Kind einst nahe dem Tode gewesen war. − His teacher, J. G. Büttner, assigned his class the task of adding all of the numbers from 1 to 100. Est scala una habens gradus c. In primo gradu sedebat columba una; in secundo duae; in tertio tres; in quarto iiii; in quinto v. Sic in omni gradu usque ad centesimum. Singapore: World Scientific. On the slate was written a single figure, 5050. Gaudet, Keith. In dieser Schule, die noch sehr den Zuschnitt des Mittelalters gehabt zu haben scheint, blieb der junge Gauss zwei Jahre lang ohne durch etwas Ausserordentliches aufzufallen. This tells you at once that personality plays as central a role in mathematics as in any of the arts. Gauss enjoyed numerical computation as a child; an anecdote told of his early schooling is characteristic: One day, in order to keep the class occupied, the teacher had the students add up all the numbers from one to a hundred, with instructions that each should place his slate on a table as soon as he had completed the task. Bei so vielen Additionen am Stück lauert der Fehlerteufel hinter jeder Zwischensumme. it? 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. : Addison-Wesley Publishing Company. Johann Carl Friedrich Gauss was born on April 30, 1777, in Brunswick, Germany. So the total is 50 x 101 = 5050. Gauss used to say laughingly that he could reckon before he could talk. I don't know the starting number nor the Insgesamt erhält man so 50 Zahlenpaare, die jeweils die Summe 101 ergeben, mithin insgesamt 5050 als Gesamtresultat. His mother outlived her husband by another thirty-one years, and she resided with Carl Friedrich and his family for most of that time. 2005. Translated by Albert Froderberg. The teacher, amazed, asked him how he came up with the answer so quickly. Another invaluable resource was the Google Book Search. Let's see: 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, 10 + Oh, what was the last number we used? Da es 50 dieser Paare gibt, beläuft sich die Gesamtsumme auf 50 x 101” [Hay]. Vol. Gauss, l'enfant prodige. Pettit, Annie. Carl Friedrich Gauss (1777-1855): "El príncipe de los matemáticos." Il représente alors l'une des deux branches du calcul dit infinitésimal, également appelé... Les méthodes sont numérotées par ordre de priorité. {\displaystyle 2n-1} We are told that he did it by pairing the terms and then mentally multiplying the value of each pair by the number of pairs. New York: Oxford University Press. 3–4). For example, the sum of the first 100 numbers can be written as the arithmetic series S100: Ford, Clay. His contributions to science have been so great that Some Great Mathematicians of the Nineteenth Century: Their Lives and their Works. Kritzman, Mark P. 2000. ''O să le trebuiască ceva timp pentru asta, se gândi profesorul. Hijo de un modesto albañil, desde los tres años dio muestras de su genio al aprender a leer y hacer cálculos mentalmente (le gustaba decir que había aprendido primero a contar y luego a hablar) Su genio pudo desarrollarse gracias a su madre Dorothea, quien hizo lo imposible para que su hijo no siguiese el camino que su padre quería imponerle. Today's math lesson was no different. His teacher, Büttner, and his assistant, Martin Bartels, were amazed when Gauss summed the integers from 1 to 100 instantly by spotting that the sum was 50 pairs of numbers each pair summing to 101. Also, at the age of eight, he astonished his teacher, Büttner, by rapidly adding the integers from 1 to 100 via the observation that the fifty pairs (j+1, 100–j) for j = 0, 1, ..., 49 each sum to 101 for a total of 5050. 7–8). Ad ogni modo, Buttner deve arrendersi di fronte all'enorme talento del giovane allievo e, con uno slancio che dopotutto lo riscatta di parecchio rispetto ai pregiudizi che aveva maturato, lo raccomanda al duca di Brunswick, supplicandolo di assicurare i mezzi economici sufficienti perché il genio in erba possa finire gli studi secondari e quelli universitari. → Some versions have the teacher knowing the answer when he makes the assignment, others don't. (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. The story goes that when Gauss was a child, his math teacher came to class unprepared one day. Pour simplifier le calcul ultérieur du flux, la surface doit suivre les lignes de champ ou les couper orthogonalement. Calculus with Analytic Geometry. Now Gauss had to explain to the amazed Büttner how he had found his result: 1+100=101, 2+99=101, 3+98=101, and so on, until finally 49+52=101 and 50+51=101. Many of the other answers were wrong and were at once "rectified" by the whip. Karl Friedrich Gauss, von Franz Mathé. 2–3). 2002. {\displaystyle |G7-K15|} Aus sich selbst, mit gelegentlicher Nachfrage bei seiner Umgebung, lernt er lesen; am erstaunlichsten aber zeigt sich von frühester Kindheit an die intuitive Kraft seiner Auffassung von Zahlenverhältnissen: er durste scherzend wohl von sich sagen, daß er eher habe rechnen als sprechen sönnen. (pp. such as 5192 + 5229 + 5266 + ... , where each one was 37 larger son spotted an error while he was calculating his payroll. Σ Some boys had made their first mistake early in their calculations, so naturally they were doomed to failure almost from the beginning, and most of their hard work was completely wasted. Now Gauss had a rectangle with 101 rows each containing 100 beans. His father was an upright but autocratic Brunswick cooper who died shortly before Gauss's thirty-first birthday.