A short story about a magic number and sticks on a table
Once upon a time, there was a magic number that no one understood. Her name was Pi. One day, she met a group of sticks that played the following game:
The sticks jumped on a table with black marks with their eyes closed. If they opened their eyes and saw that they touched the line, they would turn green. If they would not touch the line, they would turn red.
The magic number counted 0 red and 0 green sticks.
Can it be true?
The magic number wondered: How did the sticks know her? One of the sticks sat next to her and explained: “Look at us. We are all 1 metre tall. The marks on the floor are 1 meter apart. Would you not agree that we all have the same chance to touch a line?”
Pi wondered. Yes, that has occurred to her. The stick drew a circle in the sand to explain more . “When we fall on the ground, we can point in any direction we want. But only a few directions will us to touch a line. Try to change the Angle on the diagram below!”
What’s your angle, Pi?
Ok, Pi thought, but she could not see what this has to do with her. It could be any number... Or not? The stick pointed on the diagram on the sand and explained: “I have a challenge for you, Pi. Can you find a position where we are always red, no matter at which angle? And another positon where we are always green?"
Try to move Position and Angle in the diagram above to find these positions!
This will confuse you, Pi.
Now the stick stood up. This will confuse you, Pi. Stay with me. Of all possible directions, we can find only two different sets of angles : angles that touch the line, and angles that doesn’t. Look, i have drawn it for all the sticks that you created above, here in the sand. Do you recognise something?”
Pi could not believe what is drawn in the sand in front of her. The stick has just drawn a picutre of herself, upside down on the sand. She was exactly the ratio between red and green sticks. Which means, when a stick falls on the lines, it has exactly the chance of 1/pi to touch the line!
Pi understood.
Pi was happy. Finally, she felt understood by someone! When the sticks fell on the marks, she was the likelihood that they would turn green or red. Happily, she sat together with the sticks playing the game, with the feeling that finally someone has understood her.