On Math for Primates Episode 14! Infinity and Beyond Nick and Tom make a joke about the Aleph Null set sounding like a Mexican wrestlers name.

So I took this idea and created an image of Tom and Nick as Lucha libre wrestlers. They are the Aleph Null tag team.

Tom and Nick as Aleph Null Lucha libre wrestlers

The image is free down load under a Creative Commons attribution non-commercial licence.

CS5 AI and PNG. You can also download the mask by itself under the same CC licence. CS5 AI and PNG.

On the recent Math Factor podcast episode GR, Cheim provided several puzzles from the book Riddles of the Sphinx by David J. Bodycombe. One the puzzles was to find the hidden logic in the sequence 0 1 8 10 19 and 90 and question why it couldn’t be continued.

But it can with the addition of 10²⁴.

If you want the answer to the sequence then read below. If not look away.

So to answer the puzzle you need to spell out the numbers,

zero one eight ten nineteen ninety and yotta.

In the above sequence the last letter of the previous number is the starting letter for the following number.

Pretty simple answer, but a very clever puzzle.

Another possible extension is …

To go one number further with 10^-18, atto. The sequence thus becomes:

0 1 8 10 19 90 10²⁴ 10^-18

The addition of atto doesn’t destroy the logic but does make the sequence swing from a purely ascending series to one that descends at the end.

Also because atto ends with o you can make the sequence recur with the addition of one to become

0 1 8 10 19 90 10²⁴ 10^-18 1 8 10 19 90 10²⁴ 10^-18 …

You can also extend the initial sequence past 90 if you use 10^-24 which is yocto, and it is also recursive with

one … yocto … one … yocto …

All of the additional numbers are on wikipedia at http://en.wikipedia.org/wiki/Yotta

Here is a little function that I wrote with javascript and jQuery to iterate through all of the Fibonacci numbers that my computer was capable of generating. The computer has a maximum of 1476 interations before you just get infinity. The Fibonacci number at 1476 iterations is 1.3069892237633987e+308.

At the 1477th iteration the function is trying to add 1.3069892237633987e+308 + 8.077637632156222e+307, which is a little bit too much I guess and so all you get is ‘infinity’ as the result.

I had looked at a few other javascript functions for Fibonacci sequences before creating this one but they seemed to take forever to generate say 30-40  numbers and would just cause the browser to hang if you tried to go much higher.

So … to the code

The first part sets up the variable to be used and the array.

The function takes the current value of i and adds it to the previous one using the variable j. This new number is then appended to the array and written to screen at #fibbit which is the paragraph at the bottom.

The form lets you choose how many numbers you want to iterate through.

<script  src=”http://code.jquery.com/jquery-latest.js” language=”javascript”></script>
<script language=”javascript”>

var f = 1;
var fibrange = new Array();

fibrange[0] = 1;
fibrange[1] = fibrange[0];

function fib(x) {

$(‘#fibbit’).text(” “);
$(‘#fibbit’).append(fibrange[0]+’, ‘+fibrange[1]+’, ‘);

for (i=2; i<x; i++){
j = i-1;
k = i-2;

fibrange[i] = fibrange[j] + fibrange[k];

$(‘#fibbit’).append(fibrange[i]+’, ‘);

}

}

</script>

<p>Enter a number to generate a Fibonacci sequence and hit go.</p>

<form>

<input name=”textBox” id=”textBox” type=”text” />

<input name=”send” type=”button” id=”send” value=”go” onclick=”fib(document.getElementById(‘textBox’).value)” />

</form>

<p id=”fibbit”></p>

And that’s about it. You can see a demo of the code here (opens in a new window) .

Feel free to use the code however you like.