Once I ran a “Math laboratory”, a place where kids could meet for a few hours each week to tackle and discuss challenging math problems. The idea was for me to enjoy myself.
The Mathematical Sciences Research Institute has started a similar program called Math Circles where the aim is “to get the students excited about the mathematics, giving them a setting that encourages them to become passionate about mathematics.” More.
Go to the nearest puzzle shop or make your own set of Soma cubes.
“The Soma cube is a solid dissection puzzle invented by Piet Hein during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3x3x3 cube. The pieces can also be used to make a variety of other interesting 3D shapes.” (More)
You may like to find a proof of how many ways there are to assemble the seven pieces to a 3x3x3 cube, or write a computer program that finds them all.
- What do you have there?
- 100 marbles, 50 are red and 50 are blue.
- And what do you intend to do with them?
- I will put some in this jar and some in this other one.
- And then?
- I will ask you to pick a jar at random and then randomly pick a marble from the jar you chose.
- Will it be good enough if I close my eyes?
- That’ll do.
- And what is the purpose?
- I will distribute the marbles in the two jars in such a way that the chace you are picking a blue marble is maximised.
- Why blue?
- Because it is your favourite colour.
- How sweet of you! But surely you can not do better than 50%?
- That is the common opinion.
Problem source: Emissary, spring 2007.
The mediocre teachers tell. The good teachers explain. The superior teachers demonstrate. The great teachers inspire. – William Arthur Ward
- I need your mathematical expertise!
- Sure, no problem.
- In my store I have five songs I play over the loud speakers.
- Five is not a big number.
- That is why I would like to play them in random order so the customers will not hear the same song repeated immediately after it has been played.
- Then it will not be random.
- What do you mean?
- If you chose the songs randomly the same song may be repeated one thousand times in succession.
- You must be joking!
- It is not very likely, but it may happen.
- How likely is it that a song will be repeated just once?
- What an excellent question!
- Thank you!
- I have written a small computer program where you can experiment with different protection factors.
- What is a protection factor?
- If you do not want a song to be repeated if it was just played, the protection factor is 1. If you want a song to wait at least two songs before it is played again the factor is 2, and so on.
- I want maximum protection!
- With 5 songs the maximum protection is 4. Are you sure you want that?
- Yes, everything for the customer!
- Why not experiment with the program below before you decide? It selects a song 100 times.
- It is a waste of time. I am a very busy man. I know what I want.
((Blog note: To display the javascript program in the post I used iframe as adding the code in Code view did not work.))
You have delighted us long enough. – Jane Austen
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Here are the new URL feeds:
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The first is for the posts, the second for the comments.
The nice thing with RSS and readers like Bloglines is that the web pages come to you, you don’t come to them. Highly recommended!
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Baldwin Street, Dunedin, New Zealand is the steepest street in the world. Grade = 35%.
- I stumbled across a page with steep streets the other day.
- You mean on the Internet?
- Where else?
- And what did you find?
- Confusion is what I found!
- How come?
- “To explain the grade percentage: as an example, a road with a 30% grade would rise 30 feet in height for every 100 feet travelled horisontally.”
- How can one travel horisontally if the street is steep?
- Exactly!
- Why don’t they use the angle of slope?
- They must have their reasons.
“The current world record holder of ’steepest street in the world’, baldwin street is famous for its slope. it was previously thought that the road’s gradient hit 38% near the top but that was apparently a mistake.”
- Find a practical way to measure the grade so mishaps like these will not happen again!
- OK, Chief.
What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises. -
I have changed web server as the previous one was expensive and gave terrible service. The old url will redirect automatically to the new one till April 2008, but you may like to jot down the new and shorter url.
I have changed from pmachine to WordPress for a few reasons:
I will make all old posts and comments available when I find some code to transfer the pmachine records into the WordPress tables.