Today (February 15, 2014) is the 450th anniversary of the birth of Galileo Galilei. Galileo made many contributions to science including describing the motion of pendulums and falling objects, his improvements to the telescope, his astronomical discoveries (including 4 of Jupiter’s moons), and his support of heliocentrism (the astronomical model wherein the planets move around the sun, described by Copernicus).
Until Galileo, scientists typically conducted qualitative studies, meaning they relied on descriptions of characteristics rather than on measured quantities or values. One of Galileo’s most important contributions to science was that he used mathematics to describe his scientific observations. He was one of the first thinkers to state that the laws of nature are mathematical. He also understood the relationship between mathematics and physics. He understood that the parabola is a conic section , a mathematical function where the y-value is a function of the square of the x-value (for example, y=x2), and the trajectory of a falling object. If you throw ball, it follows a parabolic path.
Galileo mostly applied the standard mathematics of the day to his scientific pursuits, but he did produce the Galileo’s paradox, which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares.
Galileo also proved that objects fall at the same rate, regardless of weight. Before that, people believed that heavier objects fell faster than lighter objects. Of course, we know that sometimes lighter objects fall more slowly, but this is due to air resistance. On the Apollo 15 mission, Commander David Scott showed that in the absence of air, a feather falls at the same rate as a hammer.
Legend has it, Galileo performed the falling object experiment by dropping objects off the Tower of Pisa. In the video below, Galen Weitkamp, professor of mathematics at Western Illinois University, explains some of the math describing falling objects.