thnik again!

The EU parliament has 736 seats for about 500 million people. How should the number of seats be allocated to the various countries?

At the moment an ‘ad hoc’ system is used.

Do you think the distribution is fair?

It’s a perfect problem for mathematicians to get their teeth into, but the experts in this case were not allowed to let their mathematical expertise run away with them. There were three non-mathematical constraints to ensure the solution is practicable. “The first was that the system should be durable with respect to changes in size and shape of the EU,” says Grimmett. “The second was that it should be transparent, we should be able to explain it to people. And the third was that the system should be impartial to politics, it shouldn’t favour particular groups or nations. We discussed a variety of different methods and decided unanimously that there was one method which met the constraints better than all the others.”

To see which system the mathematicians suggested to EU, read here.

If present trends continue, our country may soon find itself far behind many other nations in both science and technology–nations where, if you inform strangers that you are a mathematician, they respond with admiration and not by telling you how much they hated math in school, and how they sure could use you to balance their checkbooks. – Martin Gardner

Watch the video and then answer the question at the end.

There is nobody so irritating as somebody with less intelligence and more sense than we have. – Don Herold

- Have you ever wondered about the use of the words ‘proof’, ‘guess’, and ‘hypothesis’ in books?
- I wonder about it all the time. Sometimes I can not fall asleep due to it.
- The cure is called Google Labs Books Ngram Viewer.
- What is that?
- It gives you a graph of the use of words in a chosen time period. Click the image for its original size.
- What is the colour code in the diagram? Is green ‘proof’, ‘guess’, or ‘hypothesis’?

It is impossible to overstate the imporance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps. – Howard Eves

The above image is taken from the blog The Math Less Traveled. As you can see, it is an example of creative multiplication, a skill many students possess.

Will the above algorithm work for other numbers than 3 and 9?

Source

How to make teaching come alive.

I have just installed a plugin that lets you preview your comment as you type it. The plugin is called Live Comment Preview.

Preview is needed because when you type “<”, which also has an html meaning, strange things starts to happen.

swt has found that:

It seems that the problem appears when you use < followed by a letter or symbol. In such a case the text from < to the first occurence of > in the same line disappears. If no > is found, the text from < to the end of the line disappears.  If there is a space or number after < there is no problem.

He suggests that there should be a preview for comments and now there is. If your comment is not accepted the way you like it, you may, as before, post it as an image.

Update 20110327:
Anything between a < sign and the next < or > sign does not show up in the preview, but it shows in the comment when it has been submitted! So, if you want to type 2 < 5, just do so, It will show up in the posted comment, although it does not show up in the preview! Not exactly the best state of affairs!
Hopefully there is a simple solution to this mess.

Second update 20110327:
Mike may have found the solution! See his comment below.
Use &lt; for < and  &gt; for >. Use &le; for <= and &ge; for >=. You will then get a correct preview.

Third update 20110327:
I deactivated ‘Live Comment Preview’ and activated ‘Edit Comments XT’ and ‘MCEComments.’ The first is supposed to let the user edit his own comments. I did not get it to work. The second gives the user a few formatting options like bold, list, etc, but nothing interesting. It does not work with ‘Live Comment Preview.’ In the end I deactivated ’Edit Comments XT’ and ‘MCEComments’ and activated ‘Live Comment Preview’ again.

As Mike says below, it is sad that you have to write things like x^2 instead of the nicer x², but what can be done?