Why Do Grapefruits Have 13 Sections?

Ever since I can remember, I have been counting the segments of grapefruits whenever I section them. The count is virtually always thirteen. It seems I'm the only one I know who's ever bothered to observe this, let alone explain why it is.

We tend to think of organisms in nature as symmetrical, and many are. Cells multiply by dividing in two, then dividing and dividing again. But there are other mathematical sequences which are common in nature. The Fibonacci sequence is one.

The sequence is created by adding each number to the number before it to create the next number. 0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21, 13 + 21 = 34, and so on. So the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144....

If you start studying arrangements of petals, seed heads, leaves, etc., you will see the Fibonacci numbers popping up again and again. Buttercups have 5 petals; delphiniums, 8, cineraria, 13, black-eyed Susans, 21, plantain, 34, Michaelmas daisies, 55 or 89. (Some are not exact for every flower, but always average out to the Fibonacci number.) Apples have 5 carpels, or seed compartments.

Many plants exhibit spiral formations in the arrangement of their petals, leaves and seeds. Think of pineapples and pinecones, cauliflower and cacti. The numbers of spirals in each direction are usually Fibonacci numbers. Looking at a plant from above, you can see that these arrangements allow seeds to be packed optimally into seedheads, leaves to overlap so that lower ones get the maximum amount of light, and so forth.

The Fibonacci sequence is closely related to phi (the golden mean or golden ratio; 1 plus the square root of 5 divided by 2). Both were objects of study of Leonardo of Pisa, a.k.a. Fibonacci, generally considered the greatest European mathematician of the Middle Ages. Studying phi and the Fibonacci sequence takes you from Nautilus shells and pentagrams to Euclid, Kepler, Bartok, Debussy and Turing. To fibonomials, Lucas numbers, the Golden string....I'm going to stop now. But Dr. Ron Knotts at the University of Surrey has some very interesting pages on the subject here: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fib.html If you're like me, you'll find yourself doing the puzzles, following the links, and listening to Fibonacci-sequence-inspired musical compositions on youtube. It's a mind-suck, in a good way.