My PBL project

Introduction:

How can you prove Pythagorean Theorem?

The Pythagorean Theorem was founded by a mathematician named Pythagoras. The Pythagorean Theorem states that the area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the remaining sides. The formula for this is a^2+b^2=c^2. In my project I am going to make a model out of a cardboard box and beans. The cardboard box is going to represent the squares and the beads will fill in the squares to show the area of the hypotenuse after adding the beans in the first square with the beans of the second square.

Procedure:

Step 1: I am going to start off by cutting a right triangle diagram and tracing it onto my cardboard.

Step 2: Next I am going to cut out strips using a ruler for my right triangle and the perimeter.

Step 3: Then I am going to use my hot glue gun to glue the strips I used to make the perimeter onto the cardboard.

Step 4: After that I am going to use more strips to construct my right triangle while making sure it fits in between the squares. I am not going to glue on my right triangle in order to make it removable.

Step 5: Finally, I am going to put the beans in square a and square b. After doing so I am going to remove my right triangle to let the beans slide to square c while filling up proving the Pythagorean Theorem.

Scientific Principle:

In my project I used the formula

$a^2 + b^2 = c^2 .\,$

The other two formulas that could also be used are

$a = \sqrt{c^2 - b^2} \,$

$b = \sqrt{c^2 - a^2}. \,$

Materials:

- Cardboard

- Diagram

- Scissors

- Hot glue gun

- Ruler

- Beans

Safety Regulations:

Be sure to use the glue gun properly to prevent burns.

Investigation Questions:

Reflection Questions:

1. Find three different proofs of Pythagorean Theorem.

Pythagorean Theorem Bhaskara's First Proof

http://jwilson.coe.uga.edu/EMT668/emt668.student.folders/HeadAngela/essay1/image2.gif

http://jwilson.coe.uga.edu/EMT668/emt668.student.folders/HeadAngela/essay1/image6.gif

Bhaskara's Second Proof of the Pythagorean Theorem

http://jwilson.coe.uga.edu/EMT668/emt668.student.folders/HeadAngela/essay1/image4.gif

2. Explore how Pythagorean Theorem is used in real life experiences add them on your poster.

http://images.intellitxt.com/ast/adTypes/icon1.png

Painting on a Wall: Painters use ladders to paint on high buildings and often use the help of the Pythagoras theorem to complete their work. Take for example a painter who has to paint a wall which is about 8 m high. The painter has to put the ladder 6 m away to avoid a rack in between. What will be the length of the ladder required by the painter to complete his work? You can calculate it using the Pythagoras theorem:

(8)2 + (6)2 =

64 + 36 = C2

√100 = C

10 Mts. = C

Thus, the painter will need a ladder 10 meters high.

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