The Greeks
The first person to view the world as fundamentally mathematical.
Who was Pythagoras?
This person replaced Aristotle as the ruler of science after the Scientific Revolution.
Something that stands for-or represents-things that change.
What is a variable?
The value you approach but never reach.
What is a limit?
Distance as a function of time.
What is "d" of "t?" or d(t)
All is number.
What is the Pythagorean motto?
The mathematics of change.
What is Calculus?
A relation between variables.
What is a function?
The limit of g(x) as x approaches 0.
lim g(x) = lim (x+1)
x->0 x->0
What is 1?
Delta d/Delta t represents what physical property?
What is average velocity?
Nonphysical objects that literally exist outside the physical world, independent of any minds. They are absolutely perfect, they exist eternally, and they never, ever change.
What are Forms?
This person fired the first shot of the Scientific Revolution?
Who was Copernicus?
A picture of a function showing how variables behave together.
What is a graph?
Daily Double!!
The three central concepts of calculus.
What is the limit of a function, the derivative of a function, and the integral of a function?
Find the formula for Delta d/Delta t.
What is the first step in the Method of Increments?
The mysterious, nonphysical "realm" or "world" where the Ideas or Forms exist.
What is "Plato's Heaven?"
A period in Western history when folks saw a chance to turn from religion to reason.
What is the Enlightenment?
A mathematical system that combines algebraic formulas with pictures in Cartesian coordinates.
What is analytical geometry?
Something that is clearly physically real but seems mathematically incoherent because it requires that we divide by zero.
What is the paradox of speed?
Take the limit of Delta d/Delta t as Delta t approaches 0.
What is the second step in the Method of Increments?
The combination of Aristotle with Christianity.
What is Scholasticism?
This person invented "new science" using the methods of mathematics and experiments, which was the science of motion.
Who was Galileo?
Daily Double!!!
This has to do with how much velocity changes as time changes.
What is acceleration?
When we imagine plugging in a forbidden value for the limit of a function.
What is the method of direct substitution?
The ability to manipulate symbols and numbers in order to arrive at knowledge of the physical world without actually doing any experiments.
What is theoretical physics?