## Pineapple

Last week, I gave a lecture about Fibonacci numbers. During the lecture, Ying Hong pointed out an occurrence of Fibonacci numbers in the natural world. He said that the number of bumps in a pineapple is 8 if you count from top to bottom along one direction, and 13 if you count along another (perpendicular) direction.

To visualise, look at the picture below:

If you count from the NE-SW direction (left), you will get 8 bumps, and if you count from the NW-SE direction (right), you will get 13.

I have not checked whether this is true (when I have time I will go to Giant Ulu Kelang which is in front of my office, and go to the pineapple section to count), but this fact is well-known and it is mentioned all over the internet (google “pineapple fibonacci”) so I assume it is true in general. If it’s not true, then the pineapple must be deficient in some way.

Also, for smaller pineapples, the numbers of bumps (counted along both diagonals) are 5 and 8. For larger pineapples, the numbers are 13 and 21.

Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, … . Each number in the sequence is the sum of two previous numbers (e.g., 5 = 2+3, 8 = 3+5, 987 = 377+610). I’ve bolded the numbers which count the pineapple bumps.

I think it’s amazing that a pure mathematical concept like Fibonacci numbers appears in the natural world. This is not a mere coincidence. There is a scientific explanation for this.

Another amazing fact: The number of flower petals also follows the Fibonacci sequence. For most flowers, the number of petals are 1, 2, 3, 5, 8, 13, 21, 34, 55, even 89 (An untouched daisy in its natural habitat has either 55 or 89 petals. Amazing, right? 55 and 89 sounds like a random number). For pictures, go here. Exceptions are very rare, so now you know why it’s difficult to find a four-leaf clover.

(Photo credit: http://www.roanoke.edu/staff/minton/ProjGolden.htm)