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Tuesday, October 28, 2008

History / Geometry Session 3 : Pythagoras of Samos

Pythagoras of Samos is the next ancient Greek we are studying. He lived about 560 - 480 BC. He was a philosopher and mathematician. He is most famous for the Pythagoras theorem he discovered.

The picture book What's Your Angle, Pythagoras? by Ellis and Hornung made a good introduction to this great mathematician and his theorem. The boys were mesmerized by the story. As such their written narration (later posted on their own blogs! - See my post on Blogging) just flowed out of them quite spontaneously. I had initially assigned them to narrate just one part of the story, but they insisted on narrating almost the whole story!

Pythagoras was portrayed as a smart lad who helped the adults solve their problems. In reading the book, we gathered that in ancient times, builders use a rope with knots tied at regular intervals to find or check for right angles. The rope is a loop that can be pulled to make a triangle with 3,4 and 5 intervals on each respective side. We tried to make just such a rope. Here it is:

Pythagoras chanced on the theorem [(square of a) + (square of b) = (square of c)] when he was laying tiles around a right angle triangular base. We also tried to do the same here with our cuisenaire rods:

We were hoping to make more types of right triangles with our rods. I wrote the whole list of square numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. We stared at this list hoping to find two smaller square numbers that would add up to a bigger square numbers but couldn't. So we gave up.

The boys were introduced to square numbers in their Miquon Lab sheets. So this was not new to them.

My aim for this session was to introduce Pythagoras. I didn't expect my boys to be well-versed with the theorem. I was satisfied that they could understand that when we know the lengths of the two sides of a right triangle that make the right angle, we can calculate the length of the longest side (the hypotenuse). The specifics of actually calculating is beyond their level.

I am confident they'll recall what we have read about Pythagoras when we actually do have to master the theorem later. He will at least be a familiar "friend", not merely a dead and distant mathematician.

Visit Rumphius Mathematics Webpage or History Webpage to find out more about how we approach Mathematics or History in our homeschool.

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