keep making the square bigger and look for patterns we’ve started above….

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Ever wondered what irrational meant?

Imagine that the area of one surface of a 1 rod is 2. You can if you want too. There’s no law against it.

In that case the length of one side is the square root of two.

This really upset Pythagoras. This length, or number, cannot be written down exactly. It cannot be written as a fraction with two wholes, top and bottom. It can be written as an approximate decimal but the trouble is its only approximate no matter how many decimal places you use.

You have come face to face with infinity.

You could not write down this number exactly, even if you were to use the WHOLE SPACE OF THE UNIVERSE.

That’s wondrous.

Pythagoras tried to hide this from general view.

But not us!