Normal Numbers - A Video In Rhyme
Written by Mike James   
Thursday, 15 March 2012

Vi Hart has produced another video in rhyme - this time demonstrating that non-repeating infinite numbers don't have to be normal. If you like poetry or math this is a must-watch clip.

Following on from her Pi Day video explaining why you might or might not find all of Shakespeare in the digits of Pi, see Celebrate Pi Day It Contains All Human Knowledge, Vi Hart has another presentation with two examples of non-repeating non-normal numbers.

The whole point of showing you two such numbers are that it is a common human failing that to conclude that non-repeating infinite numbers have to be normal - they don't.

To quote Vi Hart, in verse as before:

It's easy to invent a number that's
Irrational, it goes and won't repeat,
Yet still won't ever have Macbeth with Cats
Or something short and simple as a tweet.

Imagine you put 1, then 2, then 1,
Then two 2s, one, three twos, one, dot dot dot...
It's non-repeating, and never is done.
But is there "123" in here? There's not.

Take zero, then Oh 1, and then repeat
The last two parts together. Oh Oh One.
And then repeat the last two parts again.
0-1, 0-0-1. Anyway that's neat,

And Pi is still irrational, we're sure.
And transcendental. We don't know much more.

 

        

 

Further Reading

Celebrate Pi Day It Contains All Human Knowledge

Non-computable numbers

Confronting the unprovable

Computability

60 trillionth binary digit of pi-squared calculated

Yahoo! Gets to the 2 Quadrillionth bit of Pi - it's zero

 

normalnumbers

 

blog comments powered by Disqus

 

To be informed about new articles on I Programmer, subscribe to the RSS feed, follow us on Google+, Twitter, Linkedin or Facebook or sign up for our weekly newsletter.

 

Banner


Spheree The 3D Snow Globe Breakthrough
30/08/2014

This approach to 3D projection could be the technology we have been waiting for. Multiple pico-projectors are used to create a seamless 3D experience. 



Xamarin Mac Updates
21/08/2014

Xamarin has announced a Unified API for Xamarin.iOS and Xamarin.Mac which  allows developers to support both 32-bit and 64-bit applications with the same source code (as well as binaries) on both [ ... ]


More News

Last Updated ( Thursday, 15 March 2012 )
 
 

   
RSS feed of news items only
I Programmer News
Copyright © 2014 i-programmer.info. All Rights Reserved.
Joomla! is Free Software released under the GNU/GPL License.