Circle Area

Area of circles, from 1st Principles

Click on above to see first steps in this journey.

Area of triangles

Whilst calculating the perimeter, and hence circumference and approximation for π we also calculated the necessary values to calculate the areas of each triangle created by the polygon side with the circle's centre. The formula used is Area of triangle is 1/2 base x height

For diagrams and proof of values used see Circles from (nearly) first principles

For diagrams and proof of values used see Circles and 16 side polygon.

This investigation although not mathematically rigorous is sufficient evidence to satisfy me that

The circumference of a circle is proportional to it's diameter and it's area is proportional to the square of its diameter. These two facts are related by the following