Medieval mathematician and businessman Fibonacci (Leonardo Pisano) posed the following problem in his treatise Liber Abaci (pub. 1202): How many pairs of rabbits will be produced in a year,beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?It is easy to see that 1 pair will be produced the first month, and 1 pairalso in the second month (since the new pair produced in the first month is not yet mature), and in the third month 2 pairs will be produced, one by the original pair and one by the pair which wasproduced in the first month. In the fourth month 3 pairs will be produced, and in the fifth month 5 pairs. |
This sequence of numbers is called the Fibonacci Numbers or Fibonacci sequence. The Fibonaccinumbers are interesting in that they occur throughout both nature and art. Especially of interest is what occurs when we look at the ratios of successive numbers.-------------------------------------------------
Principio del formulario
First, calculate the first 20 numbers in the Fibonacci sequence. Remember that the formula to find the nth term of the sequence (denoted by F[n]) is F[n-1] +F[n-2].
The Fibonacci numbers play a significant role in nature and in art and architecture. We will first use the rectangle to lead us to some interesting applications in these areas. Start bydrawing two, unit squares (0.5 cm is suggested) side by side. Next construct a 2-unit by 2-unit square on top of the two, unit squares. Next draw a square along the edge which borders both a unit squareand the size 2 square (that is, a 3-unit square). The next square will border the 2-unit and the 3-unit squares, and each successive square will have an edge which is the sum of the two squaresimmediately preceding it. Continue until you have drawn a final square bordering the 13-unit and 21 unit squares.
The fascinating thing about it is that this sequence is actually found in nature with...