In this note, we will show how transformations can be used to obtain a radically simple derivation of the equation of the line of best fit. Our approach also gives a simple geometric interpretation of the Pearson correlation coefficient.
In this experiment we conducted bending tests on several different specimens of Aluminum as well as Ceramics. Using the data gathered from these tests as well as measurements we took of their primary dimensions, we calculated (for each specimen) modulus of rupture, flexure strain, Young's modulus, as well as specific strength and stiffness. These tests gave us insight into new characteristics of aluminum and ceramics that allowed us to better understand their applications in industry.
A derivation for finding the coefficient of static friction between an object and an inclined surface the object rests on using the minimum angle of the inclined plane at which the object starts to accelerate.