Understanding Pythagorean Theorem and its real life uses

Understanding Pythagorean Theorem and its real life uses

Understanding Pythagorean Theorem and its real life uses

Before I start, I believe you know what a Square is, the formula for the area of a square and what a Right angled Triangle is.

Let's start.

Let me begin with a short story.

There was one clever king in a kingdom. One day, he decided to test how intelligent his people are. So, he makes three plates of gold, of different sizes and places them as show in the figure 1 below. And he asks his people, "If I give you either these two red plates of gold or a single blue plate of gold, which would you choose?"

Figure 1

Now, you give me the answer. Which one would you choose? The single blue plate or the red two plates?
Most of the king's people chose the two red plates over the two. And I'm pretty sure, you did the same.

Any choice you make, you still are in profit. You know why? They are the same. Surprised?

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See the figure 2 below.

Take your time and count the small triangles in the square at the left. How many? 8?

Now count the small triangles in the square at the bottom. 8 again, right?

Add them. 8+8 = 16 small triangles. Remember that count.

Ok, now, count the small triangles in the slanted square. Did you count 16? Then you got it right.

So you got 16 small triangles in the a and b squares , and the same count in the c square.

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Here's another proof, a little complex, probably. via wikipedia

The two large squares shown in the figure below each contain four identical triangles, and the only difference between the two large squares is that the triangles are arranged differently. Therefore, the white space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean Theorem

Interesting Fact
It is known that the Egyptians used a knotted rope as an aid to constructing right angles in their buildings. The rope had 12 evenly spaced knots, which could be formed into a 3-4-5 right triangle, thus giving an angle of exactly 90 degrees. Can you make a rope like this? Now use your knotted rope to check some right angles in your room at school or at home.

Real life uses of Pythagoras theorem

There is a window on a house. You want to climb up to the window using a ladder. There is small bush just at the joint of the house and the ground. You could use Pythagoras theorem to calculate the length of ladder required.
There is a big pond. There are two flags at the exact two ends. How would you calculate the length between the flags?
You are flying a kite up high in the sky. Calculate the height of kite from the ground.
How do you measure the height of a big mountain?

POINTS TO REMEMBER

h^2 = p^2 + b^2 ( h = hypotenuse, p = perpendicular, b = base )
Right angled triangle!!!
Some uses in real life. Find some new, by yourself.

Sources:
http://www.ehow.com/info_8247514_real-life-uses-pythagorean-theorem.html
http://prezi.com/w64y865aea4k/how-does-the-pythagorean-theorem-work-in-the-real-world/
http://mathcentral.uregina.ca/QQ/database/QQ.09.04/tiffany1.html
http://www.geom.uiuc.edu/~demo5337/Group3/hist.html
http://www.brighthubeducation.com/homework-math-help/36639-applications-of-pythagoras-theorem-in-real-life/
http://en.wikipedia.org/wiki/Pythagorean_theorem

Comments

Understanding Pythagorean Theorem and its real life uses

Understanding Pythagorean Theorem and its real life uses

Before I start, I believe you know what a Square is, the formula for the area of a square and what a Right angled Triangle is.

Let's start.

Let me begin with a short story.

There was one clever king in a kingdom. One day, he decided to test how intelligent his people are. So, he makes three plates of gold, of different sizes and places them as show in the figure 1 below. And he asks his people, "If I give you either these two red plates of gold or a single blue plate of gold, which would you choose?"

Figure 1

Now, you give me the answer. Which one would you choose? The single blue plate or the red two plates?
Most of the king's people chose the two red plates over the two. And I'm pretty sure, you did the same.

Any choice you make, you still are in profit. You know why? They are the same. Surprised?

------------------------------------------------------------------------------------------------------------------------

See the figure 2 below.

Take your time and count the small triangles in the square at the left. How many? 8?

Now count the small triangles in the square at the bottom. 8 again, right?

Add them. 8+8 = 16 small triangles. Remember that count.

Ok, now, count the small triangles in the slanted square. Did you count 16? Then you got it right.

So you got 16 small triangles in the a and b squares , and the same count in the c square.

---------------------------------------------------------------------------------------------------------------------
Here's another proof, a little complex, probably. via wikipedia

The two large squares shown in the figure below each contain four identical triangles, and the only difference between the two large squares is that the triangles are arranged differently. Therefore, the white space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean Theorem

Interesting Fact
It is known that the Egyptians used a knotted rope as an aid to constructing right angles in their buildings. The rope had 12 evenly spaced knots, which could be formed into a 3-4-5 right triangle, thus giving an angle of exactly 90 degrees. Can you make a rope like this? Now use your knotted rope to check some right angles in your room at school or at home.

Real life uses of Pythagoras theorem

There is a window on a house. You want to climb up to the window using a ladder. There is small bush just at the joint of the house and the ground. You could use Pythagoras theorem to calculate the length of ladder required.
There is a big pond. There are two flags at the exact two ends. How would you calculate the length between the flags?
You are flying a kite up high in the sky. Calculate the height of kite from the ground.
How do you measure the height of a big mountain?

POINTS TO REMEMBER

h^2 = p^2 + b^2 ( h = hypotenuse, p = perpendicular, b = base )
Right angled triangle!!!
Some uses in real life. Find some new, by yourself.

Sources:
http://www.ehow.com/info_8247514_real-life-uses-pythagorean-theorem.html
http://prezi.com/w64y865aea4k/how-does-the-pythagorean-theorem-work-in-the-real-world/
http://mathcentral.uregina.ca/QQ/database/QQ.09.04/tiffany1.html
http://www.geom.uiuc.edu/~demo5337/Group3/hist.html
http://www.brighthubeducation.com/homework-math-help/36639-applications-of-pythagoras-theorem-in-real-life/
http://en.wikipedia.org/wiki/Pythagorean_theorem

Comments