Pythagoras and much more
[b]Pythagoras theorem can also be used to explore connections with many different polygons. With the use of GeoGebra, we can go beyond comparing the sum of squares and their outcome. by increasing the number of sides it is amazing to see the relationship between an infinite amount of polygons while adhering to the pythagorean theorem. As the number increases the circle imerges, and shows how iteration comes about and generates the pythagorean relationship with circles.
What is the relationship in a^2+b^2=c^2 ? Does this relationship hold true for different geometric shapes? As the applet iterates to a circle, can you determine the radius with the information given? What is the area of the circles and any given point? As the number of sides increases, how many polygons can you name? Triangle, Quadrilateral, Pentagon,Hexagon,Heptagon, Octagon,Nonagon......etc.