Q1. The Pythagoreans had a firm belief that everything in the universe was based on numbers because by attributing a number to everything in the world, they could easily understand the geometrical properties of things. Their belief had stemmed from the observation that strings produced musical tones when then their ratios of lengths were whole numbers (Gleiser).
Q2. The reason why the Pythagorean Theorem was regarded highly is that it has had a remarkable impact on every discourse there is. Despite having its roots in geometry, the theorem has left its marks on different fields of life. The theory provides proofs for understanding the existence of everything that is present in the universe (Morris).
Q3. To the Pythagoreans, Mathematics served as a means of explaining the existence of everything regarding its ratios and proportions. Numbers such as one represented the generation of all numbers, two rendered opinions and so. The holiest number was tetractys or ten which was composed of all the numbers.
Q4. Galileo was inspired by his father’s experiments who ascertained that there was a non-linear relation in a stretched string on a musical instrument. He concluded that the pitch varied with the square root of tension. His results were similar to Pythagoras belief. From a young age, Galileo began believing that everything in the world was organized according to numerical harmonies.
Q5. In a letter to the Grand Duchess, Galileo refuted the arguments presented by Aristotle and Ptolemy and mentioned that the planets in space maintained their position not because God had created them that way but because there were specific physical effects involved. In the Assayer, Galileo mentioned that everything in the universe could only be apprehended if the symbols are interpreted first as the natural world is based on mathematics.
Q6. Galileo proposed that massive bodies fall the same way and any two falling bodies will travel the same distance and the same time. He used some balls that were rolled down on an inclined plane. Through this experiment, Galileo showed that constant acceleration depended on the angle of the plan and not the mass of the rolling body.
Gleiser, Marcelo. A Tear at the Edge of Creation: A Radical New Vision for Life in an Imperfect Universe. Simon and Schuster, 2010.
Morris, Dennis. “The Pythagorean Theorem–A 4,000-Year History, by Eli Maor. Pp. 272.\pounds 15.95. 2007. ISBN: 978-0-691-12526-8 (Princeton University Press.)# Donel0/4/08.” The Mathematical Gazette, vol. 93, no. 526, 2009, pp. 176–177.