Tuesday, February 17, 2009

Curiosidades - número e

Quando estudava logaritmo na escola sempre me perguntava 'por que diabos alguém inventou essa conta amalucada e, pior ainda, para que inventaram um número irracional pra servir como base de logaritmo se logaritmo já é complicado e com base irracional fica ainda mais complicado?' os professores nunca respondiam direito pra que servia o tão misterioso número neperiano e não tinham muita paciência para esse tipo de pergunta. Mas, enfim, eu achava que era coisa de matemáticos doidos, irracionais até. hehehe

Mas, quem diria... toda essa loucura de logaritmos e números complicados foi inventada para 'facilitar' os cálculos.

E quem foi o maluco filho-da-mãe que inventou os logaritmos e para quê?
O logaritmo foi criado por Napier (Neper) no século XV para facilitar a vida dos matemáticos de antigamente (que não tinham nem calculadora, quanto menos um computador) na hora de fazer a multiplicação de números grandes. Facilitar? É, facilitar. Com o logaritmo, substitui-se a multiplicação pela soma, que é mais fácil. Abaixo vai um exemplo:
Se quisermos multiplicar 512 por 2048, basta saber que
512=29 e que 2048=211, então teremos
512 x 2048 = 29 x 211 = 29 + 11 = 220

E todos concordam que somar 9 + 11 é bem mais fácil que multiplicar 512 por 2048.

Só que para utilizar esse recurso, é preciso transformar os fatores da multiplicação em expoentes de uma determinada base. Assim:

f = ax

f = fator (número que eu quero usar na minha multiplicação)
a = base
x = expoente

sabe-se que

ax ≈ kx
onde a constante k depende apenas do valor de a.

Por exemplo, para
a = 2, k ≈ 0,7
a = 10, k≈ 2,3

A relação entre a e k é precisamente o número neperiano. Então, se

a = e, k = 1

e isso explica para que serve o tal número e. :)

Eu estou meio cansada agora, então vou pular boa parte da explicação e vou direto para a expressão que resulta no número e. Quem calculou o número neperiano foi Euler (talvez por isso o número neperiano seja designado por um e) e não por Neper (Napier) como seria mais lógico de se supor. Outro dia eu venho aqui e acabo a história.

Essa conta aí em baixo é que leva ao número neperiano:



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Expert: Anthony knee injures need to become big operation chronically
Basis " new York Post " message, after Anthony of Ni Kesi's star accepts right knee to take the therapy of seeper, will mix in los angeles now team assemble. But now Anthony whether a pair of matches of a flier return week giving fight very it's hard to say, the bishop drills Wu Desen's word sounds cannot decide Anthony even whether give fight this western the others match of the brigade of guest field. In the meantime, center money heart forces the competition that did not give battle to be the same as trailblazer today, he is opposite a match that digs gold is medium left knee contusion. Nevertheless Le Youxi of heart of Zhou Yi money hopes to reappear. The case of Anthony is more complex than Qiandele, ni Kesi respect still is not willing to divulge now is what causes the seeper in Anthony knee to form. When accepting broadcasting station to interview, wu Desen's coach ever stated he worries about the knee adjustment ability of Anthony. But later on he weighs himself to be at ease to the circumstance feeling of Anthony again, he believes this is not the problem of a how long. "I am a bit afraid, but after Anthony accepts pump water to treat I and he has talked, he feels quite marvellous, so I also feel special club, " Wu Desen expresses, "Once he has restored, he can do not have a thing. He can do not have a thing.. Wu Desen states money heart carves present position is daily observation, he perhaps will restore to train tomorrow. The reporter asks Wu Desen Anthony will restore to train tomorrow, wu Desen expresses: "This depends on completely his knee reacts how. "This depends on completely his knee reacts how.. Noted surgeon Lyons - Boboweici accepted new York Post to interview, the method that he says knee pump water is not have to when letting Anthony armistice a lot of days, ni Kesi respect is become likely with this excuse, good Rangandongni is surpassed after season a few time rest more before arrival. "He should be met sensory knee had huge to improve, but the problem is now, seeper still can relapse likely, " say of at present of wave wave dimension, "Perhaps they are to think time seeking a site will take a rest, they will be right after sports season ends perhaps the knee of Anthony makes articulatory pry inspection. They will be right after sports season ends perhaps the knee of Anthony makes articulatory pry inspection.. Be said according to Boboweici, water on the knee is an index that cartilage endangers, anthony needs to become articulatory lens operation, of course if be done now, he should be faced with sports season to submit an expense account, so he should become this operation after sports season ends. Anthony ever had become the articulatory lens operation of left knee after 2010-11 sports season ends. "If there was seeper in anybody knee, so this is a signal, the specification gave what issue in his knee, " say of at present of wave wave dimension, "Your knee is impossible that ground of for no reason at all had seeper, the commonnest cause is cartilaginous is damaged, if if fish of check of nuclear magnetic resonance comes,meniscus was not torn off, so probable it is articulatory cartilage gave an issue. So probable it is articulatory cartilage gave an issue.. Anthony suffers knee tumid worry to have 3 weeks of time of half probably, but he does not do knee to discharge seeper cure all the time at the beginning, be determined finally to do till yesterday talent. The reporter also examines minutely Wu Desen after all what is the seeper reason of Anthony, wu Desen replies: "They did not find any problems, they did drain off water to him, they found [url=http://www.stmarysmumbai.com/cheapairjordans.aspx]cheap air jordans for sale[/url] seeper in his knee, discharge seeper. Discharge seeper.. (responsibility edits: A gleam of fights)

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