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Mystery man Pythagoras meets his match

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Handwriting on paper reads "Pythagoras, Mathematician or murderer?"
Mystery man Pythagoras meets his match

SUBJECTS:  Maths

YEARS:  7–8, 9–10


What do you know about Pythagoras?

Join Vi Hart as she not only explains the Pythagoras theorem but also raises some legends about his dark past!


Things to think about

  1. 1.Can you recall Pythagoras' theorem? It goes like this: the sum of the squares of two sides of a right-angled triangle is equal to the square of the hypotenuse. How is it written as an algebraic formula? In which century did Pythagoras live?
  2. 2.Look at the number line which shows positive and negative integers. Note the numbers Vi writes in between these integers. What numbers are they? How does this view of a continuous line of numbers compare to the way Pythagoras thought about numbers? How does Vi draw Pythagoras' theorem using squares? Which irrational number is the value of the hypotenuse of a right-angled triangle that has sides both equal to 1?
  3. 3.In Pythagoras' day whole numbers were commonly used. Which type of numbers did Pythagoreans find problematic? Why? Draw a 3-4-5 right-angled triangle. Show how Pythagoras would have used squares to prove his theorem. What does the sum of the area of the 4x4 and 3x3 squares add up to? What does this show? Try some other right-angled triangles to test the theorem, including one that has two equal sides of 1.
  4. 4.Use Pythagoras' theorem to explain how irrational numbers like the square root of 2 exist. Find out about other irrational numbers such as pi (?). Why is 22/7 a close approximation of pi (?) but not accurate? Use a circle to explain pi (?) as a ratio.


Acknowledgements

Video courtesy of Vi Hart.


Production Date: 2012


Copyright

Metadata © Australian Broadcasting Corporation and Education Services Australia Ltd 2012 (except where otherwise indicated). Digital content © Australian Broadcasting Corporation (except where otherwise indicated). Video © Australian Broadcasting Corporation (except where otherwise indicated). All images copyright their respective owners. Text © Australian Broadcasting Corporation and Education Services Australia is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0).

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