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PI

The Number Pi

(Poem by Wislawa Szymborska )

The number Pi is impressive
three point one four one
all following figures are also starting
five nine two it never ends.

can not cover his eyes six five three five
with estimates
with eight nine seven nine
imagination joke or three two three, that is, by comparison four six
anything else
two six four three in the world.

The longest snake after several meters

also interrupted, but a little later,
make fabulous snakes.

The procession of figures that make up the number Pi
does not stop at the margin of a page,
is able to continue for the table, through the air,
through the wall, a sheet, the nest of a bird
the clouds, straight to heaven
through the total swelling and vastness of the sky.

Oh how short is the comet's tail, like a mouse! How fragile

star Ray
that bends in any space!

But here two three fifteen three hundred and ninety
my phone number your shirt size
years 1973
sixth floor number of inhabitants sixty-five tenths
the hip measurement two fingers the charade and
code where my
nightingale flies and sings and calls for calm behavior
also pass the earth and sky
but not the number Pi, it does not,
he is still a good five
not any
eight or the last seven
getting haste oh, getting quickly to the sluggish eternity
for permanence. _________

Source: Metro mathematician.

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MISCELLANEOUS FINANCIAL POWERS

To find the power of a number used, usually, almost always, the definition of empowerment . That is: Given

and

however, sometimes do not realize that there is another way unusual to find the quadratic power a number without using explicitly the definition. For example:

One more:

What strange, no? Well, what happens is that these examples we used a very interesting discovery, we have left a legacy through the great Pythagoras.

Pythagoras discovered that there was another way to find the quadratic power of a number. This process consists of adding odd numbers starting from the unit to cover the amount of numbers that equal the given base. Symbolically:

is equivalent to the sum of the first odd natural numbers.

seems that everything is going well, but the method fails when trying to calculate the following, for example

The answer is obvious. We can not use the Pythagorean method because the base is not a number natural. Another

use. The Pythagorean method is generally used to calculate the sum of the first natural numbers. So we have:

whose proof is done using the method of proof by induction .

Source: Só mathematics.