What is calculus (details provided)

It’s those deposits that build up on your teeth that the dentist has to remove with a scraper.

@phoenyx, nice answer. i wish i would have known that for the answer haha

calculus is Latin for: calculate

The way it was taught to me was that its basically a way of calculating rates of change. My highest calculus class is just from high school so its quite possible I’m only scraping the surface.

Classically, calculus is the study of motion. More generally, it is the study of smooth change. It gets quite deep, but that tends to be the unifying principle of the subject.

I read somewhere that it was an an ancient Roman abacus-like device which used stones to help the user calculate sums, etc.

That’s right—technically “calculus” means “pebble,” which were used as part of the calculating devices.

weird question you had in your exam.

the only reason we had it was because we technically HAD to have a final, required by the school, but our teacher didn’t want to give us one because we had taken the AP exam

Euclid, the famed Greek mathematician and pedagogue, once had a young pupil (most likely one of the several Ptolemys of Alexandria) who asked him if there was any quicker way to learn geometry than to read the Elements. Euclid is fabled to have told him, ”οὐκ ἔστι βασιλικὴ ἀτροπὸς ἐπι γεωμετρίαν,” or “there is no royal road to geometry.”

About some 2000 years later, give or take some centuries, D’Alembert, a famed French mathematician, told one of his pupils who was having difficulties understanding the “vanishing and nascent quantities” of the calculus, “Allez en avant, la foi vous viendra,” or “Forge ahead, the faith will come to you.”

I think Calculus is the royal road to geometry. Anyone reading through the elements or apollonius’ conics will see very soon how greatly it has abbreviated every part of geometry. Sometimes I wonder what has been lost, though. If you liked Calculus, I highly recommend the textbook, Calculus: the elements, by Michael Comenetz, from which I stole those epigraphs.

Newton writes in his preface to the Principia Mathematica that what he describes there (a strange kind of geometrically-based Calculus), is “rational mechanics,” and that geometry itself is founded upon the axioms of this mechanics, For instance, he gives as an example, the drawing of the circle is a postulate of euclidean geometry, but mechanics can describe how to draw a circle, and so on.

Archimedes found the area under a segment of a parabola by weighing it. Perhaps Calculus is a way of weighing functions.

That is a freaking awesome question to ask on an exam. What did you answer?

I like to think of calculus as a tool for coping with slopes of slopes =)