## The Mystery of the Fibonacci Pumpkin

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We have a mystery on our hands.  Greater than the mystery of what Frankenstein has to do with polygons.  Greater even than the mystery of how to come up with a good Math Halloween Costume.    The mystery is:  Do pumpkins have some strange connection with the number 3?

It all started when we were getting ready to carve Jack O’Lanterns.

And we noticed this odd thing at the bottom of the pumpkin:

See it down there?

What the heck is that?  The hole in the center goes all the way through to the outside, but the perfect 120° angle markers are only on the inside of the pumpkin.  Did this come from a metal spike or something, and it’s just artificial?  Or do pumpkins somehow naturally divide into three parts, like a banana.  Hey kids — you can try this at home!  Take a banana, break it in half, and then stick your finger down the middle.  It will naturally split into 3 pieces lengthwise.  I learned this in college [in the dining halls, not a classroom].

Apparently, I just now discovered via The Sneeze,  this happens to bananas because the ones sold in the supermarket are triploid organisms, which means that they have 3 sets of each chromosome instead of 2.  That’s a little weird, no?  A little unnatural?  Actually, unnatural is exactly what it is:  triploid organisms occur (exclusively?  This part I’m not sure on) when a biploid organism is crossed with a tetraploid, giving the average of 2 and 4 sets of chromosomes.  This is bad for the resulting triploid banana, which is sterile, but good for the person who eats it, because the sterile banana contains no seeds.  [No, not even those black spots, which according to this official sounding page are “the remains of aborted ovules that did not mature into seeds”  and EEEWWWW who else is suddenly grossed out by bananas?]

But pumpkins don’t seem to be triploid organisms.  At least, they aren’t on the list of examples I found on Wikipedia, though watermelons are.  So the mystery remains:  is this figure naturally occurring, or artificial?

Happy Halloween!

The Fibonacci connection:  I’ve seen the fact that bananas split into 3 pieces used as an example of how Fibonacci numbers appear in nature.  That our bananas might be a hybrid of those that have 2 and 4 sets of chromosomes, though, and that presumably split into 2 or 4 pieces seems to discount the whole Fibonacci relationship for bananas since 4 isn’t a Fibonacci number.

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### 3 Responses to “The Mystery of the Fibonacci Pumpkin”

1. Brent Says:

I think it’s probably artificial. Pumpkin flowers and stems have five-fold symmetry.

2. Ξ Says:

I suspect it’s artificial too, but I think it’s strange.

Is it the case that flowers display the same symmetry as their fruits? I looked up banana flowers, but they look more like artichokes so that wasn’t revealing.

3. Brent Says:

It definitely is strange! And yes, flowers and fruits usually do display the same symmetry. I don’t know about the particular case of bananas, I had never heard the thing about them being triploid before.