A Level 2021 - Blog Posts

Theorem: Take a circle, the area of this circle is the same as area of a right triangle that has one leg equal to the radius and one leg equal to the circumference of the circle..

A long time ago in a faraway land people led simple lives by the means of agriculture. There was plenty of food to eat and to be merry. They had roofs on their head and fresh river water flowing nearby. Life seemed perfect but it was not. Every year when the rains 🌂 began, the river nearby would flood into the village and destroy their lands and homes. The people in the village would move to a nearby village for shelter with their cattle. When the rain stopped they used to come back and each time they came back they found their place in destruction. Their houses had to be rebuilt and their lands had to be outlined again. Fights were a common scene on how the outline was before the water washed it away. So the concept of the area came to maintain peace.

Finding areas of lands made with straight lines was easy but how to find the area of a land that is a curve ?

Firstly instead of taking a land made up of crazy curves let's take a land made up of the simplest curve, the circle.Draw a circle and fill in its area. Then divide it into large equal parts and arrange them in a rectangle.

It's not yet a perfect rectangle.So divide the circle in parts and try arranging these sections into a rectangle.You'll get a thing that starts looking like rectangle.

Now as you divide the circle more and more and try to arrange those parts you'll get a more nice rectangle. This more and more is nothing but the concept of limits in calculus.

So the area of the circle is the area of the rectangle.The area of the rectangle is Base×Height. Here the height of the rectangle is the radius of the circle and Base is equal to twice the area of the circle. So cut up the rectangle diagonally and you'll get a right-angled triangle with a Base as the radius of the circle and height as the circumference of a circle.

20/05/2021

Heya, I hope today treated you well 💛

It's almost 10 pm here and I'm getting ready to go to bed.My day didn't really start well.I was panicking for my coming exams lol but it got better after my classes started at 9.The schedule was very hectic today and I was almost out of energy by 3 when the classes finally got over.I had my lunch and practised my French lessons on duolingo.Later in the evening my boyfriend sent me this beautiful video named as Slow life in French countryside and I loved every bit of It😇.Here is the link if anyone wants to watch it.

Later in the evening after having some fruits for snacks I studied the following stuff

Chemistry half a chapter

Group Theory (Quaternions and Matrix Groups)

10 problems on group theory

I also sat and decorated by bujo planner and planned out my next maths course, Linear algebra.

The day started out on a not so high note but it did end well.

Just hoping that everything works out well in the end.I wish the same to you too as well ♡