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:
Time spent: 24 hours 23 minutes
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.
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.
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.