Theorem: Take A Circle, The Area Of This Circle Is The Same As Area Of A Right Triangle That Has One
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.
More Posts from Mayusthings and Others
🌟3rd August 2021 🌟
Summer Studying Challenge by @myhoneststudyblr
Q. What is your least favourite thing about the beach?
Probably getting sand in my hair lol
📷 The picture attached is my bujo spread for the first week of August.
📚Currenly Reading : Men of Mathematics by E T Bell.
I love nights because I can peacefully think about proofs without self made restrictions (To do lists and life)
Heya! I finished chapter 12 of Analysis 1.It was I think the toughest chapter so far but it's not that tough that I'll loose my sleep over it.I also got the above book from Amazon today.The title is sexist but so is history 🤷🏻♀️I started from the last chapter and made some notes on it.I also revised chapter 8 today.Otherthan that it was a pretty chill day.I also answered an ask on Tumblr.I thought it was important to answer the question correctly and so I tried to the best of my ability 🐰
Now Nighty Nighty you guys
I hope you had a good day <3
someone needs to tell Lance Armstrong about the Banach Tarski paradox
july 16, 2021
Hey everyone! For the past few days (and since I found out about energy management) I’ve actually been super productive and getting all my work done! It’s very satisfying tbh. And I’ve already started planning out my senior year again. I’m aiming for all A’s this semester! And it’s gonna be difficult because all of my courses are either honor level, accelerated honor level or college level courses because of the school I go to (besides stuff like PE, student life courses, etc) but I’m confident that I can do it! :)
16th July - Do you have any summer traditions?
I usually travel out of the country each summer, but COVID -_-
Some group theory notes that I took today.
📚Summer Studying Challenge 📚
August 8 2021: What books are you currently reading?
Yesterday I started reading 1984 by George Orwell.But I have also started two other books namely 'Men of Mathematics' by E.T.Bell and 'Music Of Primes' by Marcus du Sautoy.I have also decided to buy Anna karenina by Tolstoy after reading a post about it by @theclassicalmind.
30th July 2020
🌿What would be your perfect summer day? 🌿
Wake up late,have a light breakfast,pack a good lunch and go to a nearby scenic water place with my family.My family includes my parents,my cousins,my uncles and aunts.Eat a ton of fruits,play a lot of games,make a truck load of memories and fall asleep on my mommy's shoulder in the car on the way back home.
Heya!!
Today I revised all the topics I covered in Analysis 1 so far and did chapter 8 and 9.
Chapter 8 is about the algebra of limits.In there I learnt how to write proofs using ε-N method.There were quite a number of cases (with examples!).Most of them were good and could be deduced easily from previous theorems and axioms but I did find 4 proofs a little challenging.I have noted them down and I’ll be discussing those with my prof soon.
Chapter 9 was about monotonic sequences.In there I learnt about the monotonic sequence theorem and the proof of this theorem is very cute.This theorem's proof is very intresting because it connects to the theorem where square root of 2 is proved as irrational but it is more general.So it patches all the gaps on the real number line quit nicely.There were some examples too which I liked and I also learnt the steps of proving a theorem when monotonicity is involved.
It was a pretty cool day.
I hope you had a good day too^_^
***
The Mayuriit Project
Will I make it? Stay tuned to find out!
206 days left…
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|She/her | Maths Undergrad | I love reading too|Personal blog is @silenthoughtss| I follow and like from this account|
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