The Mystery of the Fibonacci Pumpkin

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.

Carnival Month! (past, current, and upcoming)

In celebration of the month of October Wait, you mean it’s October already? When did that happen? , here’s some belated Carnival News:

[picapp src=”0227/fda6d0ae-1865-438f-bdfe-747988e65087.jpg?adImageId=7027209&imageId=230872″ width=”234″ height=”350″ /]

[Hey, it’s the new PicApps!  I’m trying to decide if I like it — more pictures versus the less control thing.  And that little film strip.  Hmmm.]

Math Teachers at Play #16 appeared on October 3 over at  I Want to Teach Forever.  One of my favorite submissions was the Brain Games from mental_floss  Blog, but there’s plenty of other good stuff.    Then, two weeks later, there was Math Teachers at Play #17 over at mathrecrecreation. (who has a post on origami today!) with yet more interesting posts.  And now we jump ahead to Math Teachers at Play #19, over at Math Mama Writes [What happened to #18, you ask?  You’ll have to check it out and see!].  It’s got some cool stuff, including a post about using math to solve a murder case [but can they really neglect air resistance?  Wouldn’t that make a difference, and maybe make it possible to travel further in the x-direction?  HEY — it’s a project question for when I teach Diff Eq in the Spring!]

So there’s the way too late update!  Stay tuned for the Carnival of Mathematics next week over at The Number Warrior (who also has a cool problem-solving/communication  post currently up on the game Slitherlink).  The Carnival of Mathematics will now be appearing the first Friday of each month, with Math Teachers at Play moving to the third Friday of the month.  More details can be found here at Walking Randomly, who has taken over organzing the CoM.

Stay tuned for tomorrow:  the Mystery of the Fibonacci Pumpkin!

How about another comic?

Because comics are fun!  And Brown Sharpie by Courtney Gibbons has been amusing for several years now.

From last week:

From last month:

And from three years ago:

All images are copyrighted under a Creative Commons License [described at the bottom of the Brown Sharpie page].

A Couple Food-Related Fails

I’m a sucker for a gimmick, particularly food gimmicks.  I’ve tried just about every flavor of Mountain Dew, as well as every variety of Reese’s peanut butter whatevers.  So when Starbucks released their new VIA instant coffee, I lined up with everyone else to take the taste test.  (It’s not bad, if you like Starbucks coffee.)

As a reward for tasting the coffee, I got a coupon for $1.00 off any VIA purchase.  I then heard the barista explaining to another customer that with the coupon, the 3-pack was only $2 (actually $1.95), but the 12-pack was a better deal.  So I looked at the price of the 12-pack: $9.95, or $8.95 with the coupon.  And then I did a quick calculation in my head, and discovered that no, the 12-pack isn’t a better deal after all.  With the coupon.  Of course, it is a better deal without the coupon, and I’m sure that’s what she meant, so maybe this isn’t a FAIL, but it’s still a fail.

Next up, however, is definitely a FAIL.  The following was spotted at my local Target store, where Halloween candy is on sale right next to the Christmas decorations:

Can anyone figure out where this number came from?  The box weighs something like 38 ounces (so it’s about $4.21 per pound).  If it really were $159.84 per pound, a Butterfinger (2 oz) would cost $20.  I think I’d frame it instead of eating it.

Another Math Comic

We recently discovered a series of math comics because first a commenter and then Mike himself linked to us on Spiked Math.   Yay — more math comics! So as the weekend approaches, you can treat yourself to:

or

or

or this one which is, of course, near and dear to my heart:

All of these are copyrighted, but available for non-commercial use.

All About A4

Recently, Batman mentioned a comic he’d seen about A4 paper and the golden ratio Lichtenberg Ratio (see the comments below).  Thanks to the wonders of the  Internet, we were able to track down the comic, which makes me laugh every time I read it. We were also able to find the author, who graciously gave us permission to post the panels here.  If you click on them you’ll be directed to the Flickr site, where you can read them in a larger size.

Without further ado:

Copyright by The Valrus.  Used with permission.

Math in the 2009 Ig Nobels

The 2009 Ig Nobels were announced last week.  These are awarded “For achievements that first make people LAUGH then make them THINK”.    This year’s mathematics award is probably more of the think than laugh variety, however:

Gideon Gono, governor of Zimbabwe’s Reserve Bank, for giving people a simple, everyday way to cope with a wide range of numbers — from very small to very big — by having his bank print bank notes with denominations ranging from one cent ($.01) to one hundred trillion dollars ($100,000,000,000,000).

Poor Zimbabwe: we’ve talked about their  super-inflation difficulties and really big banknotes before.   They practically need their own category.

Most of the research is more amusing.   For example, the Peace Prize was given to Stephan Bolliger, Steffen Ross, Lars Oesterhelweg, Michael Thali and Beat Kneubuehl for their analysis of whether full beer bottles or empty ones caused more damage.  From their abstract:

Beer bottles are often used in physical disputes. If the bottles break, they may give rise to sharp trauma. However, if the bottles remain intact, they may cause blunt injuries. In order to investigate whether full or empty standard half-litre beer bottles are sturdier and if the necessary breaking energy surpasses the minimum fracture-threshold of the human skull, we tested the fracture properties of such beer bottles in a drop-tower.

(Short answer:  empties broke at a higher impact, which I think means they’re more dangerous.  I wouldn’t want to be hit by either one, though.)

But wait, there’s more.  Cows who give more milk when called by name.  A man who cracked the knuckles of his left hand — but not his right — every day for 60 years.  Giant panda poop as garbage disposal.  A bra that can turn into a pair of face masks in an emergency.  And my favorite, the Chemistry Prize, which went to Javier Morales, Miguel Apátiga, and Victor M. Castaño for creating diamonds from Tequila.

For all the winners, see the official site.

30% Hotter

I’m reading The Memorist by M. J. Rose, a book which is in the same 100+ chapter genre as The DaVinci Code but which doesn’t sport its own diet.

Early on, some criminal-guy leads some journalist-terrorist-wanna-be to an underground area beneath Vienna.  After showing him the area beneath the main concert hall, they head back towards the outside world only to discover slashes in one of their rafts — a raft that might have looked a lot like the one in the picture above except that it was in a cave.  And was inflatable.

But at any rate, they needed those rafts because there was an underground lake that was really hot.  Now here’s the confusing part:

The water was thirty percent hotter than the human body’s temperature thanks to the geothermal heat under the lake’s bed.  If you tried to swim across you’d be boiled to death.

What, exactly, does 30% hotter than the human body’s temp mean?  My first thought was that the reference point should be absolute zero, or -459.7°F.  This would make the water (1.3)(98.6+459.7)-459.7, which simplifies to about 266°F.  This matches the line about scalding, but doesn’t quite fit later on when journalist-guy pulls the remaining raft from criminal-guy and dunks him into the water:

For a second David wondered if Wassong could somehow make it out.   No, he knew that was impossible.  He knew, because Wassong had warned him — no one survived the firewater.  Wassong was splashing wildly, displacing a circle of water around him.  He continued thrashing for fifteen seconds, thirty seconds, forty, and then all movement ceased.  Hans Wassong lay still, floating facedown in the boiling lake, his glasses bobbing beside him.

Despite the reference to boiling, I’m pretty sure that splashing would be kept to a minimum if the water were really 266°F.  So I don’t think that’s it.  Maybe, since we’re in Vienna, we’re supposed to use Celsius for our reference point.  The body’s temperature is 37°C, so the lake would then be (1.3)(37°C)=48.1°C, or about 118.6°F.  That’s hot, but not really hot enough to kill so quickly — the Honeywell Burn Chart says an adult could swim for 10 minutes before getting 3rd degree burns.   So that’s not it.

Well then, maybe we should use Fahrenheit, which would lead to (1.3)(98.6°F), or about 128°F.  Now we’re getting somewhere:  the 40 seconds corresponds pretty much exactly to how long before criminal-guy gets 3rd degree burns all over his body, and that’s going to make it tough for him to escape.

I confess, I’ve been waiting to see if this guy is really dead or if he’s going to appear at the last minute.  Nothing says, “See ya later!” like a claim that no one could have survived.