# FoxTrot by Bill Amend for February 08, 2009

#### Transcript:

Jason: One cheesy tortilla chip... Marcus: One cheesy tortilla chip... Jason: Two cheesy tortilla chips... Marcus: Three cheesy tortilla chips... Jason: Five cheesy tortilla chips... Marcus: Eight cheesy tortilla chips... Peter: Math geeks shouldn't be allowed anywhere near certain foods. Jason: What's wrong with fibonachos? Marcus: There're only 12 left...now what?

## sappha58 almost 14 years ago

For those who don’t know… Fibonacci Series: The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself, yielding the sequence 0, 1, 1, 2, 3, 5, 8, etc.

## treblemaker almost 14 years ago

Why’s Peter complaining? He gets his three squares a day.

## tiger1tt almost 14 years ago

neat method of informing d masses …i for one did not catch d pun until i read sappha 1958 comment…i have been enriched

## kfaatz925 almost 14 years ago

Only squares, treblemaker? In Peter’s case I’d have said cubes.

## m_ortal almost 14 years ago

13, 21…

## Durak Premium Member almost 14 years ago

I always appreciate how Amend expects us to know and understand the joke, and doesnt have to explain it. The ‘Fibonachos’ punchline was great though! Amend gives his readers credit for being smart enough to get his jokes. Laugh, a search for fibonacho’s on Wiki actually refers you to fibonaci!

In the book/movie, “The Phantom Tollbooth” there is a well done sequance on the Fibonaci series. Tiger itt mentioned informing the masses, getting kids to read that book would do it. Or at least see the movie.

## Mowgli-Chiara almost 14 years ago

Thanks for made my brain to work on a Sunday

## Boxknight_Jace almost 14 years ago

Dypak, The Phantom Tollbooth is one of the best novels out there. Everyone should read it as a kid and then again as an adult.

## Hugh B. Hayve almost 14 years ago

I guess when they’re older they’ll be playing Fibeernacci.

## Geekologist almost 14 years ago

Whats sad is I didn’t know what “Fibonachos” are till I read the comments…

## bigmitchperez almost 14 years ago

luckily i play video games ,like “the da vinci code”,otherwise i may seem undereducated!

## LateToTheGame almost 14 years ago

Hugh, awesome!!! Though I imagine at whatever age, Jason and Marcus would barely be able to hold a single draught, at most.

## cwreenactor almost 14 years ago

Arrrrgggghhhhh!!!!

## farren almost 14 years ago

Johndrake: they’re talking about the Alternative Minimal Fibonacci series: 0, 0, 0, 0, 0, 0, …

## Rakkav almost 14 years ago

Very clever!

## circuit7 almost 14 years ago

ROFL! What a great laugh!

And The Phantom Tollbooth should be required reading for every 12-year-old in the civilized world.

## Mickeysnotadog almost 14 years ago

Yulk! They are double dipping! Too many germos here. They could Fibonacci themselves into the ICU.

## LateToTheGame almost 14 years ago

drake, it sounds to me like the version you heard was drafted for some youngsters – I can’t imagine Fibonacci using bunny wabbits for part of his original thesis. As for the bunnies, 0 was probably left off since not too many spontaneously reproduce. Now if it were frogs or sharks perhaps…

## Liowatcher almost 14 years ago

According to Wikipedia (http://en.wikipedia.org/wiki/Fibonachi): —– Liber Abaci also posed, and solved, a problem involving the growth of a hypothetical population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century, but it was Fibonacci’s Liber Abaci that introduced it to the West. —– So he did use rabbits, and in Latin!

## tobybartels almost 14 years ago

It's arbitrary where you start the sequence. In fact, it can go infinitely far in either direction. As you go forwards, you add two numbers to get the next. But as you go backwards, you subtract them instead. So you get something like this:

…, 8, −5, 3, −2, 1, −1, 0, 1, 1, 2, 3, 5, 8, …

It is true that Fibonacci himself started with 1, 1, 2, …, whereas nowadays most people prefer to start with 0, 1, 1, …. But in the end, where you start is up to you.

You can also get fun results starting with any two numbers, even if they don't appear in the Fibonacci sequence. For example, Édouard Lucas started with 1, 3, 4, …, so those are called the Lucas numbers. Bonus points for spotting where the Lucas numbers are hiding within the Fibonacci sequence!

## tobybartels almost 14 years ago

We have a winner! Johndrake gets a cookie, or whatever the kids are giving each other on the Internet these days.

## LateToTheGame almost 14 years ago

Would that be a

virus?## slavesofspeigel almost 14 years ago

1;1;2;3;5;8;13;21;34;55;89;144;233;377;610; 987;1,597;2,584;4181;6,765

The first 20 numbers of fibonacci! (Ithink

## zev.farkas almost 14 years ago

I love when Amend gets scientific/mathematical! Thanks to all who commented. Particular thanks to johndrake for the comment about the relationship between the Fibonacci and Lucas series and Pythagorean triples! This is a fascinating result that I had not known about. I actually went to the trouble of working it out algebraically (tedious, but not too difficult) and it works out! Cool! It turns out that it works for any series where p(n)=p(n-2)+p(n-1).

as for the following:

“tobybartels says:

It’s arbitrary where you start the sequence. In fact, it can go infinitely far in either direction. As you go forwards, you add two numbers to get the next. But as you go backwards, you subtract them instead. So you get something like this:

…, 8, −5, 3, −2, 1, −1, 0, 1, 1, 2, 3, 5, 8, ”

please check the transition from alternating negatives and positives to all positives… -1+0=-1, not 1.

There is a closed-form solution to the Fibonacci series that involves the square root of 5, among other things… see what happens when you plug in negative arguments in that function (sorry, but it’s too late at night, and I’m too lazy, for figuring that one out right now - you’re on your own, math fans…)

Finally, as to whether the Fibonacci series starts with zero or one, I think it’s just a matter of taste or the particular problem you’re working on.

Reminds me of an old story. A couple comes to a Rabbi for help in settling a marital dispute. The wife tells her side, and the Rabbi says, “You’re right”. Then the husband gives his side, and the Rabbi says, “You’re right”. This seems to satisfy the couple, and they leave smiling. The Rabbi’s wife, who overheard the whole session says, “It can’t be possible that they’re both right!”, and the Rabbi says, “You’re also right!” :)

## zev.farkas almost 14 years ago

Thanks, johndrake -

As an American transplanted to Israel, that mile to kilometer converter can be pretty convenient!

Your comment on the relationship between the Fibonacci series and pythagorean triples helped me find a result I’ve been trying to come up with for some years now… a simple relationship that takes any two numbers and gives a pythagorean triple - like the age game you just described. (I’m sure I could have found it on the web, but it’s more fun to crank out the algebra yourself…)

Thanks again!

## bookworm1011 almost 8 years ago

I love the phantom tollbooth!

## Foxtrotlover almost 5 years ago

I read this, studied it, and figured out what exactly Fibonacci was.

## colBoh over 4 years ago

Should’ve started with one “1” instead of two. Then they’d have 13.

## Boxo croco is tired almost 3 years ago

How many nachos are there in that bowl?

## Empress of Dragons over 2 years ago

Huh?

## TheJustinator over 2 years ago

1 1 2 3 5 8 … hmm.