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Proof for the Area of a Circle

[P6 Maths and beyond: Circles]

This is something that's exclusively useful for Mathematics. Whenever you come across a formula in your textbook, you should have the right to ask the teacher how the formula is derived, where it comes from. For example, let's say you have a scalene triangle of sides 8, 9 and 13 (clearly not a right triangle). Without knowing the height from any base to the opposite vertices, how is one meant to find out the area of this triangle without the standard methods available? (hint: Heron's formula)

The best way to learn something, is to teach. When you are in a position where you teach your friends, or your relatives, you are accountable for what you teach and convey; and that gives an incentive for you to make sure you get it right. It's incentive to make sure I know fully well what I am teaching, so I as a tuition teacher can give the kids the very best.

Today we'll cover a defining topic that will be relevant up to Secondary 4 and beyond: The Area of a Circle.

The thing to note is, the sort of process where the video starts with a simpler example (like cutting a pizza) before bringing it to an extreme by making each pizza slice really, really small in order to get as accurate a result as possible. Is it still considered a true rectangle in that case, when the pizza slice curves have an arc around the crusts?

There is, of course, another method of getting the same result using a triangle instead.

Fact of the matter is, your schools only teach the formula. They are not required (for those below uni) to teach you how it's derived, where it comes from, the creative ideas behind finding it. They treat subjects in a deadpan manner and so most people find it boring. The reality, is that it's not. And it's because they don't think you need to know, if by the hand of fate you're going to be working as an accountant, a musician who only needs to be good at their job and not at learning, so they treat you as though you do not need to know... even when knowing makes the subject so much more fun and understandable.

The next time you need to help your cousin in studying, try teaching them the area of a circle using this method. You might have the rare chance to see their faces light up from the joy of learning; and that's a mirror to what you felt when you first learned it.

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