When dealing with the Pythagorean Theorem, what is always true regarding right triangles?
When dealing with right triangles, one can always determine the length of an unknown side, so long as the other two sides are known. In order to determine the length of the unknown side, use the formula c^2 = a^2 + b^2
What was so significant about Mozart's Piano Concertos to the development of classical music?
Mozart's Piano Concertos were significant largely because they were technically written for a tuning system that had yet to be created. During the time in which these pieces were composed, the general tuning system focused on creating an even fifth interval between notes, while modern tuning systems focus on what is called "equal interval ratio". This means that each piano key is tuned to have the exact same number of "cents" between them.
According to Freud, one trained in analyzing dreams could learn a great deal about another through their dreams. He argued that during sleep our ego and superego become weaker, thus allowing for one to dream their deepest desires. How did Jung's theories about dreams agree or differ from Freud's?
Carl Jung believed, just as Freud did, that dream analysis could open up one's subconscious mind. But unlike Freud, Jung did not believe all dream content to be sexual in nature, and also rejected the notion that all symbolic imagery in a dream could be defined by a set "dream dictionary". Jung believed that dream imagery was open to interpretation dependent completely upon the dreamer.