- #1

paulb203

- 72

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- TL;DR Summary
- A kind of personal 'proof' to help me grasp πr^2

I know there are videos etc explaining why but I thought I would try to find a way to understand this myself.

Imagine a version of πr^2, but instead of being for the area of a circle, it’s for the area of a square.

Call it sqi ar ^2

sqi = the ratio of the ‘diameter’ of the square to the square’s ‘circumference’ (the ‘diameter’ of the square being a vertical or horizontal line through the square’s centre, and the ‘circumference’ being its perimeter).

So, sqi=4 (like π=3.14...)

ar = the ‘radius’ of the square (half it’s ‘diameter’, just like with a circe and it’s radius)

Now take a square 4 cm by 4cm

And apply sqi ar ^2

Which gives us 4x2^2

Which = 16cm^2

Which matches with the 16cm^2 we would get from the conventional way of finding the area of the square.

This helps make sense of πr^2, for me at least

Any thoughts?

Imagine a version of πr^2, but instead of being for the area of a circle, it’s for the area of a square.

Call it sqi ar ^2

sqi = the ratio of the ‘diameter’ of the square to the square’s ‘circumference’ (the ‘diameter’ of the square being a vertical or horizontal line through the square’s centre, and the ‘circumference’ being its perimeter).

So, sqi=4 (like π=3.14...)

ar = the ‘radius’ of the square (half it’s ‘diameter’, just like with a circe and it’s radius)

Now take a square 4 cm by 4cm

And apply sqi ar ^2

Which gives us 4x2^2

Which = 16cm^2

Which matches with the 16cm^2 we would get from the conventional way of finding the area of the square.

This helps make sense of πr^2, for me at least

Any thoughts?