Editing Difference of two squares (section)

===Galileo's law of odd numbers===

[[File:Galileo's_law_of_odd_numbers.svg|thumb|Galileo's law of odd numbers]]
A ramification of the difference of consecutive squares, [[Galileo's law of odd numbers]] states that the distance covered by an object falling without resistance in uniform gravity in successive equal time intervals is linearly proportional to the odd numbers. That is, if a body falling from rest covers a certain distance during an arbitrary time interval, it will cover {{math|3}}, {{math|5}}, {{math|7}}, etc. times that distance in the subsequent time intervals of the same length.

From the equation for uniform linear acceleration, the distance covered 
<math display=block>s = u t + \tfrac{1}{2} a t^2</math>
for initial speed <math>u = 0,</math> constant acceleration <math>a</math> (acceleration due to gravity without air resistance), and time elapsed <math>t,</math> it follows that the distance <math>s</math> is proportional to <math>t^2</math> (in symbols, <math>s \propto t^2</math>), thus the distance from the starting point are consecutive squares for integer values of time elapsed.<ref>RP Olenick et al., [https://books.google.com/books?id=xMWwTpn53KsC&pg=PA18 ''The Mechanical Universe: Introduction to Mechanics and Heat'']</ref>