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Exploring Irrational Lengths Through Pythagoras and Spirals

Discover a fascinating geometric pattern by extending the sequence from the diagram using Pythagoras' Theorem. Explore lengths like √3, √5, √6, √7, and more to create an intriguing shape. Unlock the beauty of irrational numbers through this visual exercise.

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Exploring Irrational Lengths Through Pythagoras and Spirals

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  1. Pythagoras and Spirals

  2. It is possible to draw a whole series of lengths that are irrational by following the pattern in the diagram below and using Pythagoras’ Theorem. Continue the diagram to produce lengths of 3, 5, 6, 7, etc. See how many you can draw. You should get an interesting shape. 1 2 1 1

  3. 1 1 1 1 1 10 1 11 9 1 12 8 13 7 1 1 14 6 15 1 1 5 16 1 4 2 1 1 3 17 1 1 18 1 1

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