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The Weird Number
Back in 1970 I saw an animated film that changed my perspective on teaching fractions. It was called The Weird Number. (1) Here’s a piece of narration from the movie:
“My story concerns a strange event that took place in a little town nestled in the mountains. A little town inhabited only by natural [counting] numbers, but whenever the townspeople gathered together rumors were exchanged; rumors that other numbers lived in the dark woods beyond the mountains but no one could imagine a number that wasn’t a natural number so no one believed the rumor.”
So starts the story of the Weird Number a delightful excursion into a fantasy world of a town inhabited by natural numbers. Two citizens of this town 9 the baker and 736 the sheriff play key roles in the development of the story.
The narrator continues:
“Now one thing that never happens in this town is robberies. This is because the thief is easily identified since the number of items stolen is always the same as the number of the thief. For example, if 4 stole something, he would steal 4 of that particular item so he would be easily identified. Therefore, there were never any robberies. But one day there was a robbery. 9 who was the baker rushed over to the sheriffs office to tell him about the robbery. ‘What was stolen?’ the sheriff asked 9. “Just a little piece of bread.” replied 9. ‘One piece of bread?’ said 763. ‘I can’t believe it. One is the mayor. He would never steal.’
‘No, no,’ said 9, ‘not one piece of bread, a little piece of bread.’
‘Not one piece of bread, but a piece,’ said 763. “What kind of nonsense is that?’”
Actually this makes a lot of sense once you understand who the thief was. It turned out to be 2/3 a number totally unknown to the residents of this town. The sheriff organized a posse to catch the thief, but 2/3 was a clever escape artist because he was a master of disguise. When the posse discovered his location in a barn, he stepped out wearing his 4/6 disguise and told his pursuers that he had no idea where 2/3 was. In the meantime the posse learns from 4/6 a trick that all whole numbers are capable of since they are also masters of disguise. For example, One, the sheriff could become 2/2, 3/3, 4/4 etc. Five could become 15/3 and so on.
Soon after 4/6 left them, 763 realized that 2/3 and 4/6 were one and the same number. So he continued to pursue him. But 2/3 was always clever enough to take on a new form (in this case 18/27) to outwit the sheriff.
After the whole numbers realized their ability to transform into other forms numbers in fractional form became common site on the town square. Even 2/3 was not afraid to hangout in town, albeit in a different form. (2)
The movie ends with this cliffhanger that inspires a wannado followup.
The fractions and whole numbers are sitting around at tables in a pub pleased as punch that they were all members of the same number family when they learned of rumors that were other kinds of numbers living in the dark woods beyond the mountains. Numbers that could not be written as a natural number on top and natural number on the bottom. But no one paid any attention to that. The movie ends with a flash of lightening in the window followed by “The End” splashed on the screen.
After I saw this movie for the first time I was hoping for a sequel, but it never materialized as far as I know. So who or what were these mysterious non-rational (irrational) numbers?
Here’s a suggested activity/project for your class: Have your students create a video sequel about this mysterious number.
What kind of story line could you have? Here’s a suggestion. Start off with this:
“It’s a stormy day on the sea off the coast of Greece. The year is around 520 BC. A man, fighting for his life, is heaved over the side of a boat and plummets into the open sea to die. His crime? Stealing the crown jewels? Murdering the King? Nope. He was telling the world a mathematical secret. The secret of the dangerous ratio. This was the fate of Hippasus, a follower of Pythagoras who was forced to walk the plank and drown as a punishment for this crime. it’s difficult to imagine what a stir it created when it was first proposed! The Pythagoreans just couldn’t imagine that there was no ratio that equaled the length of the diagonal of a 1 unit square. The value was the square root of 2 – an irrational number. So they wanted to keep it a secret. Thus Hippasus who knew otherwise was doomed to his fate. (3)
1. Xerox, 1970. The Weird Number. Video.
2. A professor of math education used the Weird Number video as a motivator for a lesson development assignment for his students. Here’s what they came up with. http://edu320.blogspot.com/2006/09/weird-number.html
3. Read more about the Hippasus story in Brian Clegg’s “A Dangerous Ratio” http://nrich.maths.org/2671