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How is the area of ​​the circle πr² ?

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  How is the area of ​​the circle πr² ? figure-(a) Let S is a circle whose radius is r. Hence the circumference of the circle S is 2πr. figure-(b) Now, divide the circumference of the circle S into two equal parts. (Like in figure-(b)) ∴ Arc (ACB) = Arc (ADB) = 2πt/2 = πr Now, divide the above circle into many small sectors, where the number of sectors in the semicircle ACB is equal to the number of sectors in the semicircle ADB. (Like in figure-(c))         Then arrange these sectors as shown in figure (d). figure-(c) figure-(d) Now, the circle is converted into a parallelogram whose length is πr and its height is r towards its base. ∴ Area of ​​the parallelogram = length × height                                                   = πr × r                           ...

(a+b)^2 and (a-b)^2 proof | Why (a+b)2=a2+2ab+b2 ? Why (a-b)2=a2+b2-2ab ? — Proof by two different methods

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Proof of (a+b)² & (a–b)² by Two Different Methods.                         We know that (a+b)² = a²+2ab+b² (a–b)² = a²–2ab+b² But when someone asks how did you get these formulas ? Then, we have to show their proof.                  Let us prove these formulas. Here we will prove these formulas in two different ways one is algebraic method and another is geometric method. Proof of (a+b)² by method–1 :-               (a+b)² = (a+b)(a+b)                          = a(a+b)+b(a+b) [Distributive law]                           = a.a+a.b+b.a+b.b [Distributive law]                          = a²+ab+ba+b²             ...

The magical number 4(Four) and blackhole of it's alphabets | The blackhole number 4 | The fact about number Four.

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The magical number 4(Four) and blackhole of it's alphabets | The fact about number Four.         We all know that, 4 is a natural number but we do not know how strange this number is. If we look at the history, many civilizations said that 4 is an inauspicious number. It is a number indicating death (you can see also in religion section of Number 4 - wikipedia ) and is also called a blackhole number.So, 4 is a number that is full of mystery or we can say that 4 is a magic number.           Let us know the magic. Four(4) is a type of magic number, where everything in the universe stops or ends. Which is like a real blackhole. So 4 is called blackhole number.          ( https://www.goodfreephotos.com ) (We can consider here that 4 is a singularity point and other terms are its exterior. Like a blackhole.) Let's take any word of the English alphabet, such as any name, number or anything you can think of in this univ...