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1d
comment What's your favorite proof accessible to a general audience?
... in mathematics, Gauss having surpassed what the school could teach him. In 1788, Gauss started at the Gymnasium. Bartels also became a mathematician, and he and Gauss remained friends. (There is an English translation of the source by Gauss's great-granddaughter, but see Brian Hayes' article for some comments about interpolations made by the translator.)
1d
comment What's your favorite proof accessible to a general audience?
@IvoTerek: "Here says 8 years old. But I never trust a single source alone, so I'll look around a bit a more." The original source of the story appears to be Gauss zum Gedächtnis, which suggests that Gauss was nine years old when the incident occurred. He started at the Katherinenschule in 1784, at age 7, and entered the arithmetic class two years later, which is where the account says the event took place. By age 10, we find Gauss and the teacher Büttner's assistant, Martin Bartels, engaged in self-study ...
Jan
21
comment What's your favorite proof accessible to a general audience?
@guest: The story, as far as we know, doesn't appear in Gauss's own writings, if that's what you're driving at. We only have the word of one of Gauss's Göttingen colleagues that it was "an incident which he often related in old age with amusement and relish."
Jan
20
comment What's your favorite proof accessible to a general audience?
@guest: have you read the rest of the comment thread? Is there something you object to in the source already given?
Jan
20
comment What's your favorite proof accessible to a general audience?
@GabrielH: Did you look at Brian Hayes' article? The Gauss story is as close to a "known fact" as many biographical items ever get. Quite a few authors have added their own elaborations, but the basic outline goes back to the era when Gauss lived, and is a story recounted by Gauss himself. I have not seen any argument for doubting it.
Jan
19
comment What's your favorite proof accessible to a general audience?
No one should claim that Gauss deserves credit for the formula, but he may have rediscovered it at a very young age. The Brian Hayes article cited in the Wikipedia quote is well worth reading. Some highlights: the earliest known source for the story is a tribute to Gauss written a year after his death, and the story is attributed to Gauss himself. This version does not say what numbers were to be summed, or what Gauss's method was; these may be later elaborations. To say the story has "no foundation" is too strong.
Jan
13
revised Expected number of matching “cards”. Why is $\sum_{m=0}^n D_{n,m} = \sum_{m=0}^n m \cdot D_{n,m}$?
missing factor 1/n! inserted two places
Jan
13
comment A three variable binomial coefficient identity
I'm sorry to keep revising my answer. In the end, I think the bijection is fairly straightforward, and am a bit frustrated that the explanation is so cumbersome. Perhaps someone can produce a better explanation.
Jan
13
revised A three variable binomial coefficient identity
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Jan
11
awarded  Necromancer
Jan
11
revised A three variable binomial coefficient identity
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Jan
11
revised A three variable binomial coefficient identity
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Jan
11
revised A three variable binomial coefficient identity
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Jan
10
answered How many routes are there that pass through at most one congested intersection
Jan
9
revised A three variable binomial coefficient identity
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Jan
8
answered A three variable binomial coefficient identity
Dec
30
comment Is there a closed form of $a_n=\left(\prod_{k=1}^{n-1}(4^{k}-2^{k})\right)$
I doubt that the expression can be further simplified, but it can be expressed using the $q$-Pochhammer symbol, $$(a;q)_n=\prod_{k=0}^{n-1}(1-aq^k).$$ Let $a=q=2.$ Then $$a_n=2^\binom{n}{2}(-1)^{n-1}(2;2)_{n-1}.$$
Dec
29
answered Probability of getting the same 10 cards after a 104 card shuffle
Dec
28
revised Expected number of matching “cards”. Why is $\sum_{m=0}^n D_{n,m} = \sum_{m=0}^n m \cdot D_{n,m}$?
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Dec
27
comment A question on deriving d'Alembert's formula from change of variables
Hint: both the terms in brackets and the terms coming from carrying out the integral contain left-moving and right-moving parts. What conditions would have to hold for, say, the left moving parts to cancel out?