# Proving Πthagoras Theorem With Boxes

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## Introduction: Proving Πthagoras Theorem With Boxes

Hi, Math lovers I am back with another DIY.

You all know about Pythagoras theorem..................that is

(AB)(AB) +(BC)(BC) = (AC)(AC)

YOU MAY ALSO KNOW VARIOUS THEORETICAL PROOFS OF IT BUT WHAT ABOUT PRACTICAL PROOF

I have made a practical proof of πthagoras Theorem With Boxes and now it is your turn to make it and show it to your friends..........have any questions fill free to ask ...........have a good experience...........

This is a "beta" version of my tutorial. I made it quickly foe the π day contest and box contest.....But i will come back with more information and it will be before the end of the contest.....

### EXPLANATION

..

first keep the big cube down.

show that it is full and the other to are empty

now keep the big cube up and small cube down keep it like that for some time

after that show that the big cube is empty and the small cubes are full

That proves that,

Volume of big cube = Volume of small cube 1 + Volume of small cube 2

{as height is same for all,}

Area of big square = Area of small square 1 + Area of small square 2

{as area = side*side }

(side of big square)*(side of big square) = (side of small square 1)*(side of small square 1) +(side of small square 2)*(side of small square 2)

{In the image we can see that side of big square is the hypotenuse of the triangle and side of small square 1 ,side of small square 2 are the other two sides of the triangle}

(hypotenuse)*(hypotenuse) = (other side 1)*(other side 1) +(other side 2)*(other side 2)

THUS πthagoras theorem is PROVED...........

## Step 1: What Is the Theorem?

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

## Step 2: Stuffs Required

Collect the following:-

1. wood
2. water
3. putty
4. glass
5. super glue

## Step 3: Cutting the Wood and Join

you you are also under 18 like me take help of a grown up or a carpenter.

Cut the wood into following dimensions:-

• 2 square of side 10 cm.
• 2 square of side 8 cm.
• 2 square of side 6 cm.
• 1 right angled triangle of sides 10 cm,8 cm,6 cm.
• Some squares for height(you can take any height), dimension wiil be according to the height and the cube it belongs.
• join the wood according to the image given with the help of super glue and put putty at the sides

## Step 4: ​Cut the Glass

Cut the glass into following dimensions:-

• 1 square of side 10 cm.
• 1 square of side 8 cm.
• 1 square of side 6 cm.
• 1 right angled triangle of sides 10 cm,8 cm,6 cm.

## Step 5: Insert the Pipes

Insert the pipe in such a way that water can be transferred from the big cube to the smaller cube........

Connect the bid cube to 8 cm cube with one pipe and 6 cm cube with another pipe.

Make sure that there is no leakage.

the pipes are kept so that there is a better flow of water and so that no water moves to the 3D triangle (if you know the word for 3D triangle please tell me)..........

## Step 6: Fill Up Water

Fill the big cube fully with water and make sure the other cubes are dry......

## Step 7: Joining the Parts

Join the glass pieces of the glass with the cube of same side(other than the height) and put the triangle piece in the middle as shown in the image.........

Put putty so as to make it water proof ........make sure that every thing is tight........

## Step 8: Check for Leakage

When it is ready rotate it in you hand to check for leakage is any leakage is found put putty over the place to prevent from leakage............

## Step 9: It Is Now Ready Serve It With a Warm Explanation

How to explain....

• first keep the big cube down.
• show that it is full and the other to are empty
• now keep the big cube up and small cube down
• keep it like that for some time
• after that show that the big cube is empty and the small cubes are full

That proves that,

Volume of big cube = Volume of small cube 1 + Volume of small cube 2

{as height is same for all,}

Area of big square = Area of small square 1 + Area of small square 2

{as area = side*side }

(side of big square)*(side of big square) = (side of small square 1)*(side of small square 1) +(side of small square 2)*(side of small square 2)

{In the image we can see that side of big square is the hypotenuse of the triangle and side of small square 1 ,side of small square 2 are the other two sides of the triangle}

(hypotenuse)*(hypotenuse) = (other side 1)*(other side 1) +(other side 2)*(other side 2)

THUS πthagoras theorem is PROVED........... Participated in the
Make a Box Contest Participated in the
Pi Day Challenge 2016 Participated in the
Big or Small Challenge