Sometimes names aren’t what they seem in science and mathematics.  A case-in-point I will use here is an equation that you know very well: the Pythagorean Theorem.  The theorem was well known and understood long before Pythagoras and his secret cult.  Here’s a good page on it.  Besides the equation being used in the west and mideast, it was also used in China around the turn of the century.  This theorem is an example of how scientific and mathematical knowledge know no borders culturally, politically, or otherwise.  Why was it that Pythagoras was named after this most useful formula?  Did he discover it, popularize it, or were his uses of it clever/smart/useful enough to merit applying his name to it?  Is it the same type of situation that the Persian mathematician and astronomer al-Kashi, in some countries, has the ‘law of cosines’ named after him?  In French the law of cosines — a more generalized version of the Pythagorean theorem — is known as “le théorème d’Al-Kashi”.  This ambiguity of naming conventions in science and mathematics is a source of confusion.  For instance, Galileo dealt with the concept of inertia at great length before Newton wrote it down in his famous book on mechanics called the Principia.  Newton included inertia as his first law of motion.  Why isn’t it called one of Galileo’s laws?  Who deserves naming credit?

Also, as an extra credit challenge, can you derive the Pythagorean theorem from the figure above?  Hints: find the areas of all the figures that have to fit into the area of the largest square.

Incidentally, since we’re now speaking of Galileo and inertia, and since one of the questions posed below on the images of Rosetta from three different reference frames, one thing that Galileo’s name stuck to was this technical-sounding tidbit: “Galilean Transformation”.  This falls out of the Newtonian Laws of motion not depending on velocities — only accelerations.  So it doesn’t matter what the velocity is — can we ever detect how fast we’re moving if we’re not comparing to something else (remember the train with no windows question from the homework?).  This idea of being free to choose one’s frame of reference is the basis of Einstein’s Special Relativity.

1. travisphysicsaction posted this