Chapter 6
the mathematics of change
What is Calculus?
a relation between varibales
What is a function?
d=16t2
What is The Law of Free fall
It shows how variables behave together
What is a graph?
one of the central problems occupying philosophers, scientists and mathematicians for millennia
What is the problem of change?
quintessence
What is another name for aether?
A function of time
What is distance?
things that can change
What is a variable?
a number line on steroids
What is The Cartesian coordinate system?
the distance that a dropped object falls is equal to sixteen multiplied by the square of the time it takes to fall
What is d=16t2 translated into an English sentence?
This was said to be found in an object's nature
What is the cause of change
the algebraic representation of shapes and the geometrical representation of algebraic formulas
What is analytic geometry?
to stand for or represent things that change
What is a variables job?
Helps you see how functions behave
What are Cartesian coordinates ?
The limit of a function
The derivative of the function
The integral of the function
What is the Fundamental Theorem of Calculus
The overthrow of Aristotle
The reintroduction of the Platonic-Pythagorean Project
The mathematization of motion
What are the 3 main characteristics of the Scientific Revolution?
two number lines combined
What is a Cartesian Plane?
representing physical properties with numbers
What is quantifying?
What are formulas and graphs
He is known as the Father of Modern Philosophy
Who is Rene Descartes?
sublunary realm
What is another name for the terrestrial realm?
allows you to precisely calculate numerical values
What is the benefit of a formula?
space, time, mass, velocity, acceleration, density, force, area and volume
What are things that can be quantified?
another name for analytical
What is algebraic?
This gave the Pythagoreans and Plato the idea that the cosmos is fundamentally mathematical in the first place
What is the connection between numbers and the physical world?