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  • Problem 1 - Modelling with functions and equations


    This is a hand-in written by Group 60 (FIRE) for the weekly module #1 in the mathematical modelling course (DAT026) at Chalmers University of Technology.

    Group 60 consists of:

    • Mazdak Farrokhzad

      • 901011-0279


      • Program: IT

      • Time spent: 24 hours 23 minutes

    • Niclas Alexandersson

      • 920203-0111


      • Program: IT

      • Time spent: 19 hours 22 minutes

    We hereby declare that we have both actively participated in solving every exercise, and all solutions are entirely our own work.

    Problem 1 - Equations

    A number of mathematical equations are listed below. Their justification (why they are true or reasonable), how well they model reality and a categorization of them are done for each equation.

    Pythagoras \((a^2 + b^2 = c^2)\)

    The equation describes the relationship between the catheti (\(a, b\)) and the hypotenuse (\(c\)) for a right angled triangle. It can easily be proved by considering a square with a smaller rotated square in it - which results in there being 4 right angled triangles as well it.

    • It has been a well known relationship for a few thousand years. And it is very easy to prove mathematically.

    • The solution is exact.

    shows how you can prove the pythagorean theorem with a rotated square in a square.