Perfect Reasoning by Tiro Phenyo Nkau - HTML preview

11. The area circle

The area circle has a circumference of π × D. This being the case, a square that would fit around that same circle perfectly, will have a parameter of 4 × D. As two dimensional shapes, the size difference between this surrounding square and its inner circles can be used to create a ratio that compares the two shapes together using their known measurable properties which also happens to be their parameter and circumference, respectively. The formulas for these two common properties can then be used to create a ratio which allows us to compare the square's area with the circle's in the following manner: π=22/7

D = square or circle width

Circle ÷ square

= (π × D) ÷ (4 × D)

= π ÷ 4

The difference between the area of the circle and the square around it is π÷4.

The bottom D cancelled out the top D to simplify the ratio.

If π/4 gives the same result as 11/14 when it's calculated, it then means that 11/14 = π/4 of which we can then use this fraction to calculate the area of the circle by multiplying the area of the square around it with this comparison ratio to end up a total of the circle's area size.

This then concludes that the area of a circle as the size of the square's area, multiplied by 11/14.

Measurement Formula: width² × 11/14

The above formula also gives the same result as the formula π × radius²

Three dimensional wire frames