Problem (from the text):
Solution to the Problem:
Given the problem, it appears as though it may be a specific example for the Pythagorean triple (3,4,5). To solve the problem we used geometry, using the picture below. Given the picture, we can see that the area of the overall square with side a+b, minus the area of each rectangle with the sides a,b, equals the small square in the middle which has sides a-b. Thus we can solve for the formula (a+b)2 - 4A = (a - b)2. The algebraic solution is also below.
Extension to the Problem:
For our extension to the problem we decided to derive the Pythagorean formula with the use of geometry using the picture below. We thought deriving the Pythagorean theorem could help high school students gain a deeper understanding of the formula and help them identify when this formula can be applied in complex situations. Now we can see that the area of the square with sides d is equal to the square of sides a+b minus the triangles of sides a, b. This gives us the formula d2 = (a + b)2 - 4(a · b)/2. We can then use algebra to derive the Pythagorean formula.
d2 = (a + b)2 - 4(a · b)/2
d2 = a2 + 2ab + b2 - 2ab
d2 = a2 + b2
Well done Alexa and group!
ReplyDeleteHowever -- you still need to post a personal blog reflection on what you learned from the project and process, and what you take away from it....
ReplyDelete