thnik again!

- Did you know that the ratio of the cicumference and the diameter of a circle equals 3.14159… , or pi amongst friends.
- Which circle?
- Any circle.
- You mean the ratio does not change when you move from a tiny circle to a really big circle.
- Yep.
- I find that hard to believe.
- There is a simple explanation.
- I find that even harder to believe.
- Here is something more innocent to think about.
- I am all ears.
- How many pis are needed to express the first ten natural numbers?
- You mean 1 to 10?
- Yes.
- Please explain.
- You are only allowed to use pi, addition, multiplication, parentheses, square root (sqrt), and the greatest integer function ([ ]). 
- What is [pi]?
- Since [n] is the largest integer less than or equal to n, [pi] = 3.
- And I can’t use division, subtraction, or digits? 
- That’s right.
- I believe I can do all the numbers from 1 to 10 using less than fifty pis.
- How many less? 

Problem source: Dan’s problem archives.

You know, you can’t please all the people all the time … and last night, all those people were at my show. - Mitch Hedberg

- Did you win?
- The winning number was 924.
- Did you have it?
- The number of my lottery ticket was 94.
- So you did not win. What a shame!
- But I did win! You see, the tickets have only two digits, but the winning number has three.
- So it is impossible to win?
- You win if your two digits turn up in the winning number in the right order.
- So since 9 and 4 both occurs in 924 and in that order, you won?
- Exactly.
- How many tickets did you buy?
- Enough to be guaranteed to win.
- How many was that?
- I like your question. 

Problem source: Math Horizons, Sept 2008, p. 33-34, by Tom Yuster via The Math Forum.

As I was walking up the stair / I met a man who wasn’t there. / He wasn’t there again today. / I wish, I wish he’d stay away. – Hughes Mearns

… he compares his method, rather, to playing music students Beethoven, or giving English students Shakespeare. “They don’t get everything that’s going on in Shakespeare, but we’re still quite prepared to throw it at them. Well, why aren’t we throwing something like the Riemann hypothesis [which would explain how the primes are distributed through the universe of numbers] at them? It’s exciting, it’s got big ideas, it’s got things that you can engage with – although you won’t understand the whole thing. 

Read an interview with ‘the world least likely math professor’ here.

Langton’s ant travels around in a grid of black or white squares. If she exits a square, its colour inverts. If she enters a black square, she turns right, and if she enters a white square, she turns left. 

The evident long-term behaviour is remarkable, and unexplained

More from Wikipedia. Play with Langton’s ant here.

- I once had a dog.
- I once had a boat.
- I got it when it was just born, a puppy no less.
- I wonder where my boat is now.
- At one time I was three times as old as my dog.
- There is seven dog years in a normal year?
- Yes, Sir.
- So after a while the dog became older than you?
- Seven years later it was twice as old as me!
- Seven years later than what?
- Seven years later than when I was three times as old as my dog.
- How old were you when you got your dog?
- I think I know where your boat is.

Human salvation lies in the hands of the creatively maladjusted. – Martin Luther King Jr.

In some parts of the world the winter is approaching. When snow is covering the ground the birds that don’t fly to warmer climates have a hard time finding food. Some people put therefore a half coconut, seeds, grain, etc outside their kitchen window and are entertained while the birds have their meal.

One time I put starch in the shape of a ball outside my window. After two weeks and two days it was all gone. The birds ate from the ball the same amount every day and they made sure the shape of what was left was always a ball. 

Amazing!

What is equally amazing is that I don’t remember when the radius of the original ball was reduced to half of its original length. Can you help?

A bird does not sing because it has an answer. It sings because it has a song. — Chinese Proverb