Integration tools: Answer پاي ^ 2/6: what is the question?

Pietro mingoli

Leonhard Euler

One question $\frac{\pi^2}{6}$ contains, put mingoli Pietro answer in 1644:

" $1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\ldots$ What is value?"

This became known as "Basel problem" welionhard Euler solved, and announced his solution in 1735 when he as 28 years.

Euler showed-not entirely accurate — the first

$1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\ldots =\frac{\pi^2}{6}$

Point-point slide in the plane: integer

And say $(m,n)$ chip point of origin $(0,0)$ visible upon accession to the $(0,0)$ line to $(m,n)$ contains no other points of slides.

Question $\frac{\pi^2}{6}$ also has the answer: "how many times you expect to choose a random slides until we get the point is visible from the parent?"

The reason that the probability that a randomly selected $\frac{6}{\pi^2}$ is visible from the origin, and even choose a random slides such as flipping a weighted currency that comes $\frac{6}{\pi^2}$ "visible" from reflection and $1-\frac{6}{\pi^2}$ "invisible from reflection. Time wait point visible that gives a geometric distribution, which is just the inverse of the probability of choosing point visible.

Points $(m,n)$ slides that are visible from the origin $m \textrm{ and } n$ are completely with no common factors (being, master).

Even $\frac{\pi^2}{6}$ is also the time to wait until their integers chosen at random.

Why ask the question, as a result, is that such questions to stimulate a creative solutions, answer a question that leads to the desired result being.

For example, watch a teacher mathematics relatively easily related how he knows the question of this kind.

Here is a simple but revealing ask people at all levels of sports: "the answer is 10. What is the question? "

Try on a few people, preferably in the collections: answers may amaze you.

I guarantee people will try, and you and they will be amused with various answers given.

Tagged as: Basel, Euler problem, mingoli

Integration tools

Thursday, 9 June 2011

Answer پاي ^ 2/6: what is the question?

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