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Pythagorean Spirals

First draw a right angled iscosceles triangle with two sides of length 1 unit. (1 unit could be 4 cm?)

Now draw a new triangle taking the hypotenuse of the first triangle to be the base of the second, and drawing a side of length 1 unit perpendicular to this.

Continue drawing new triangles so that each new triangle has its base as the hypotenuse of the previous triangle and perpendicular to it a side which is 1 "unit".

What are the lengths of the sides of the triangle each time?

How many triangles you can draw before you get an overlap?

What is the area of each triangle?

What is the total area of a spiral with n triangles?

Could you create pictures using this spiral as a starting point?

How are Fibonacci numbers connected with Pythagorean Triples...? Find out here!

 

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