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# Introduction

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:

• 901011-0279

• twingoow@gmail.com

• Program: IT

• Time spent: 24 hours 23 minutes

• 920203-0111

• nicale@student.chalmers.se

• 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.