thnik again!

- What is this?
- Oh, I am just playing with triangles.
- Can I play?
- Sure!
- What is the aim of the game?
- I am trying to find out in how many regions I can divide a table top with two triangles.
- Any triangles?
- It would be nice if they fit on the table top.
- In the image above you have created 6 regions.
- Right. I am mighty proud of it!!
- Why?
- It is the maximum number of regions possible!
- Really?!
- Now I am wondering what I can do with two quadrilaterals.
- You mean 4-gons?
- Yes, and what about n-gons?

Problem source:  Uncover a Few blog by Joshua Zucker.

If only we’d stop trying to be happy we could have a pretty good time. - Edith Wharton

The other day I got this email from David Brooks:

998001 is an interesting number.  Its inverse (1/998001) is a repeating decimal with a period of 2997.

It starts out 0.000 001 002 003 004 005 … and continues counting until it gets to 997.  Then it skips 998, does 999, and starts to repeat itself.

I was wondering if they have a name this this kind of integer - an integer whose reciprocal or inverse produces a decimal that shows a known or familiar sequence of numbers.  This one counts natural numbers.  But I have found others that count by even numbers, powers of 2, and Fibonacci numbers.

I would like to know if anyone has already researched these, or if I might have started on something new in mathematics.

Any info you have would be helpful.

Can you help?

I am patient with stupidity but not with those who are proud of it. - Edith Sitwell

In the old days I had the maths history poster made by IBM on my classroom walls.

“In 1966 IBM printed a famous timeline poster called Men of Modern Mathematics for the years 1000 AD to 1950 AD. It was based on personal stories about (mainly Western) mathematicians and their mathematical achievements. The poster was designed by the famous Charles Eames, with the content concerning mathematicians contributed by Professor Raymond Redheffer of UCLA.” – Wikipedia

What do I put up now to inspire my students? That is my puzzle lately. I would prefer things that are free and legal to copy. Any suggestions?

“Challenge your mind and have fun in this amazing puzzle game. Help your characters on various quests in Arcade and Story modes. Reunite your friends, destroy baddies, and collect goodies! Remove blocks by clicking and dragging them with your mouse. New blocks will appear from the direction which you moved the mouse. The aim is to reunite your characters by sliding them together. You will have to do other things as the game progresses such as collecting cake and flushing bad guys away.”

Play it here.

- What are you reading?
- Did you know that 3685 = ( 3⁶ + 8 ) * 5?
- My wife told me the other day.
- Some kind of wife!
- She is imaginary!
- Oh, mine is complex.
- Aren’t these numbers called Friedman numbers?
- Yes, but why?
- All it says in the book is this:

A Friedman number is a positive integer which can be written in some non-trivial way using its own digits, together with the symbols + – x / ^ ( ) and concatenation. For example, 25 = 5² and 126 = 21 * 6.

- Is 1285 a Friedman number?
- Yes.
- How do you know?
- I am not allowed to tell.

You don’t have to work very hard to achieve very little. – Jan Nordgreen

- The radius of the big circle is 10.
- You mean the circle which has the four yellow circle and five green circles within it?
- Is that green? When did you have your eyes checked the last time?
- What is the radius of circle 1?
- Let me find out.
- What is the radius of circle 2?
- Don’t talk. I am busy.

The diagram is taken from Math Magic Packing Archive.

I’ve heard that the government wants to put a tax on the mathematically ignorant. Funny, I thought that’s what the lottery was!  - Gallagher