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Resurrecting the Mathematics of Leonhard Euler ,,, PDF Print E-mail
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Tuesday, 24 August 2010 17:31

Leonhard Euler (15 April 1707 – 18 September 1783)

Greetings,

    We promise you to teach you Mathematics through the classical works, and of course the original.

    This lesson is very small but very important ... because only the genius in mathematics may teach fundamental trues, more clear and important that the lessons you will get from a normal or standard book.

    This lesson comes from the Leonard Euler - Introductio in Analysi Infinitorium (in Latin).

     I got two translation of this book in English but ... honestly the results seems very "approximative" ... however acceptable. Of course not to pay US$ 100 for each volume.

     I am proposing the three works:

  • The original Leonard Euler Opera -
  • The Two Volumes translated (Be a Judge about the original and the finish job)  

 

    Now the question ...

    In how many ways you can write 8 like the sum of the numbers 1,2,3,4,5,6,7 ... ? Can you get a general formula for "n"?

    I will answer the question about 8.

    (You can consult Chapter XVI in Latin edition as well Book I)

    You can write 8 in six different forms:

  1. 8=8
  2. 8=7+1
  3. 8=6+2
  4. 8=5+3
  5. 8=5+2+1
  6. 8=4+3+1

How Euler get this formula? ... He get the formula following the multiplication of the serie,

(1+x)(1+x2)(1+x3)(1+x4)(1+x5)(1+x6) ... = 1 + x + x2+2x3+2x4+3x5+4x6+5x7+6x8 ...

6 is the coefficient of x8 and therefore 6 are the different ways to get 8 like a sum.

Euler Mathematics is really vast ... I, Giovanni prefer to start with this simple comment like a mere introduction.

Students can read the entire chapter ... I will get more ideas from this chapter in the Euler book.

Thanks,

Giovanni.

 

 

 

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Last Updated on Tuesday, 24 August 2010 18:33