Very clear proof of pythagorian theorem! Thank you 😊

INSANE!!! very well explained 🎉

Thank you. This is the most intuitive proof, no need to move the shapes around.

Your videos are really interesting and nice! Also, thank you for the kangaroo challenge practice course !

@Mathsaurus

Жыл бұрын

Thank you! Pleased to hear that it has been helpful!

Thank you now im more confused 😀

Very clear simple proof,very useful thank you😊!

Excellent

@Mathsaurus

Жыл бұрын

Thanks!

Try this: a²+b²=(a+b)²-2ab Consider: c²+2ab Factoring: c²(1+2(a/c)(b/c))=c²(1+2sinAcosA) The value 2ab/c² is the double angle trig ratio sin2A, (see ‡ at the bottom) Consider: (a+b)²/c² This is equivalent: (sinA+cosA)² Expanding out: sin²A+cos²A+2sinAcosA Subs for 2sinAcosA & due to “†” & “‡” (bottom), this is: 1+sin2A. From “1”, have: c²+2ab=c²(1+sin2A) From “2”, have: (a+b)²/c²=1+sin2A. Therefore: c²=(c²+2ab)/(1+sin2A)=(c²+2ab)/(a+b)²/c² Multiplying by (a+b)²/c² on both sides: (a+b)²=c²+2ab => (a+b)²-2ab=a²+b²=c² …QED 😊. (†)From the compound angle formulas(‡) for sin & cos, you get double angle formulas for those, and from cos2A you get: 1-2sin²A=2cos²A-1=cos2A => 2=2(cos²A+sin²A) Therefore: 1=(cos²A+sin²A) (‡)Proof in this video: “Angle sum identities for sine and cosine” by blackpenredpen

Thank you! Explained it very well too

@Mathsaurus

5 ай бұрын

You're welcome!

How do you know that the shape inside the outer square is a square (with right angles)? You need to prove it. ;-)

@tyleravanmeter

Жыл бұрын

I feel like it is a fairly trivial proof of simple geometry that makes it a square.

@jirifrantal2236

Жыл бұрын

@@tyleravanmeter Yes, it's simple but it's necessary. 🙂

@bienvenidos9360

Жыл бұрын

The triangles are congruent right triangles, so their 2 smaller angles add up to 90°. When you place them inside the square as shown, you get angle A + angle B + angle X = 180° since a straight line = 180°. Then angle A + angle B = 90°, angle X must be 90° to fulfill the side which is a straight line. This is a basic concept.

@shriramwarrior8936

11 ай бұрын

Side lenghts are identical, and inner angles are all identical. What else other than sqaure?

👏🏾☺️📐

One of the elegants 🎩

Clearest proof. ❤

@Mathsaurus

11 ай бұрын

thanks!

Really enjoyed bro Love from India 🇮🇳 to you❤🎉

@Mathsaurus

11 ай бұрын

thank you!

Great

Where does the 2ab come from when finding the area of the larger square?

Area is side^2 not (a+b)²

Thanks man just have an exam and saw you really helpfull

@Mathsaurus

9 ай бұрын

Glad it helped!

Very well explained

@Mathsaurus

5 ай бұрын

Glad it was helpful!

But how will you prove that the insife rhombus is a square with side c?

now do the detailed explanation

SUPERB

Im freaked out!! 👍

0:01

I've a doubt. Why we make bigger square a square having length a+b not a rectangle with Side 2a and 2b and still area of smaller square will be c^2

@rimasen4725

Ай бұрын

It won't be a square of side c but a rhombus of side c . So area wont be c2 but 2ab . Now 2ab+2ab = 2a×2b =4ab . Its not going anywhere 🙂

Beautiful

@Mathsaurus

4 ай бұрын

Thank you

Can i ask why theres only (a+b)2 why not 4?,and also where u can find that 1/2ab,

@Mathsaurus

9 ай бұрын

the 1/2 ab is for the triangles and there are 4 of them. But there is only one square so only one (a+b)^2

The problem with the proof is that it's not obvious why the sides of the large square are all a+b

@Mathsaurus

5 ай бұрын

If you prefer you could take the four congruent triangles as the starting point put together to make the large square - then I think it’s clear the lengths are the same and the shape inside is a square follows from the angles in the triangle

Bhaskaras proof

Where does the 2ab come from when finding the area of the larger square?

@hana-yr1tr

4 ай бұрын

same, im confused on this part too. if u figure it out, lmk!

@juan9154

3 ай бұрын

The whole square is essentially just (a+b)^2 cuz u have to multiply length by width to get the area. If u expand (a+b)^2 u get (a+b)(a+b) which you can then get (a^2)+2ab+(b^2) by using foil