To find out if the Pythagorean Theorem works or was just a crazy theory I tested it usingan algebraic approach. I formulated the area of one of the triangles using a*b/2. Then I
multiplied that by four to find the area of all the triangles. We then subtracted a from b to
find the length of one side of the square and squared that (a-b)^2 to find the area of the square.
After I found the area of all the triangles and the square I added them together to get the total
area of the entire square. I then square rooted the total area to find the length of one side. That
one side also determines the length of the hypotenuse. After finding that I compared both my
answers (using the algebraic approach and Pythagorean Theorem) and found that the theory
works.
Algebraic Approach:
multiplied that by four to find the area of all the triangles. We then subtracted a from b to
find the length of one side of the square and squared that (a-b)^2 to find the area of the square.
After I found the area of all the triangles and the square I added them together to get the total
area of the entire square. I then square rooted the total area to find the length of one side. That
one side also determines the length of the hypotenuse. After finding that I compared both my
answers (using the algebraic approach and Pythagorean Theorem) and found that the theory
works.
Algebraic Approach:
Final Product:
Reflection:
During this project we began with determining whether or not the Pythagorean theorem
worked or was just a theory, I tested it using an algebraic approach. I formulated the area
of one of the triangles using a*b/2. Then I multiplied that by four to find the area of all the
triangles. We then subtracted a from b to find the length of one side of the square and squared
that (a-b)^2 to find the area of the square. After I found the area of all the triangles and the
square I added them together to get the total area of the entire square. I then square rooted
the total area to find the length of one side. That one side also determines the length of the
hypotenuse. After finding that I compared both my answers (using the algebraic approach
and Pythagorean Theorem) and found that the theory works. After determining it's trust worthiness
through algebra I decided to test it against another approach. That approach ended up being,
creating a spiral (shown in the picture above). Unknowingly I had begun to make a spiral with
triangles all with the same base size (3"). After the spiral had been created I put all the information
into a table and computed the hypotenuse of each triangle. Along the way I found that each
hypotenuse was 3 square root x. X seemed to go up by one each time (ex. 2, 3, 4, 5….)
beginning with 2 for the first triangle. While computing this information I didn't see the pattern
at first, as I completed the table in decimals rather than in square root form, but after I did it in
square roots I breezed through the rest of the work. Throughout this mini activity I found many
easier pieces of work, but only one challenging concept. This was coming up with a formula that
could determine whether or not the Pythagorean Theorem worked or not. Luckily we were able to
work in partners. Working with Frida on this made it ten times easier. We had more than one brain
assessing the situation which made us find a formula that could work a lot faster. After we found it
we finished it really fast and wrote our proof with ease. During this assignment to overcome the challenge
that faced me I worked on developing my collaboration skills. Not only was I able to practice collaborating
and listening with Frida I also got to experience it and know that it is better to work with someone than without.
I think knowing that will make me more open to working with others and listening to what they have to
say about our work.
During this project we began with determining whether or not the Pythagorean theorem
worked or was just a theory, I tested it using an algebraic approach. I formulated the area
of one of the triangles using a*b/2. Then I multiplied that by four to find the area of all the
triangles. We then subtracted a from b to find the length of one side of the square and squared
that (a-b)^2 to find the area of the square. After I found the area of all the triangles and the
square I added them together to get the total area of the entire square. I then square rooted
the total area to find the length of one side. That one side also determines the length of the
hypotenuse. After finding that I compared both my answers (using the algebraic approach
and Pythagorean Theorem) and found that the theory works. After determining it's trust worthiness
through algebra I decided to test it against another approach. That approach ended up being,
creating a spiral (shown in the picture above). Unknowingly I had begun to make a spiral with
triangles all with the same base size (3"). After the spiral had been created I put all the information
into a table and computed the hypotenuse of each triangle. Along the way I found that each
hypotenuse was 3 square root x. X seemed to go up by one each time (ex. 2, 3, 4, 5….)
beginning with 2 for the first triangle. While computing this information I didn't see the pattern
at first, as I completed the table in decimals rather than in square root form, but after I did it in
square roots I breezed through the rest of the work. Throughout this mini activity I found many
easier pieces of work, but only one challenging concept. This was coming up with a formula that
could determine whether or not the Pythagorean Theorem worked or not. Luckily we were able to
work in partners. Working with Frida on this made it ten times easier. We had more than one brain
assessing the situation which made us find a formula that could work a lot faster. After we found it
we finished it really fast and wrote our proof with ease. During this assignment to overcome the challenge
that faced me I worked on developing my collaboration skills. Not only was I able to practice collaborating
and listening with Frida I also got to experience it and know that it is better to work with someone than without.
I think knowing that will make me more open to working with others and listening to what they have to
say about our work.