자연계열 2번

[제시문 2-1] Let’s take a look at sunflowers. Have you ever noticed how tightly-packed the seeds are in the center of the flower? The flower packs its seeds in neat spirals emanating from the center. Did you know that most daisies have 34, 55 or 89 petals? What about the human body? The front two incisor teeth form a golden rectangle.

[제시문 2-2] What do we know about the golden rectangle? (See the figure.) When you square it (make a square with lengths the same as the length of the short side of the rectangle), you are left with another golden rectangle with the same proportions as the original. That is, the Ⓐratios of the lengths and widths of the rectangles are the same.

[제시문 2-3] Let’s consider the following series:Ⓑ$\displaystyle 1, 1, 2, 3, 5, 8, 13, \cdots$.The first two numbers in the series are 1 and 1. To obtain each number of the series, you simply add the two numbers that came before it. In other words, each number of the series is the sum of the two numbers preceding it. Now, let’s make a ratio sequence with the series Ⓑ. We divide each number in the series by the one before it. Dividing 1 by 1 gives a value of 1, so 1 is the first number of the ratio sequence, or r(1). Then we divide 2 by 1 to get the value of 2. Continuing in this fashion, we get:Ⓒ$\displaystyle r(1)=1/1=1,\quad r(2)=2/1=2,\quad r(3)=3/2=1.5,\quad r(4)=5/3=1.67,\ \cdots$.The limit of the ratio sequence is $\displaystyle (1+\sqrt5)/2$.

spirals: 나선, emanating: 나오는, daisies: 데이지꽃, petals: 꽃잎, incisor: 앞니,square: 정사각형(을 만들다), proportions: 비/비율, length: 길이/세로, width: 가로/폭