Exam 1 Flashcards
Johnnes Kepler was the contemporary of
Galileo Galilei
Rene Descartes was the contemporary of
Girard Desargues
John Napier was the contemporary of
Henry Briggs
Blaise Pascal was the contemporary of
Pierre De Fermat
What did John Napier do
developed theory of logarithms
Who collected the data for Johannes Kepler’s laws of planetary motion
Tycho Brahe
Which mathematicians laid the foundations for probability theory
Pierre de fermat and Blaise Pascal
What type of gemoetry did Descartes develop
nalytic Geometry
What are kepler’s laws of planetary motion
(1) All planets move about the Sun in elliptical orbits, having the Sun as one of the foci. (2) A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time. (3) The squares of the sidereal periods (of revolution) of the planets are directly proportional to the cubes of their mean distances from the Sun.
What physical device based on the logarithm was used for computatoin from 17th to middle of th 20th century
slide rule
what modern mathematical subject is the language of mathematical bridges
category theory
what is the problem of the points and who was involved
two people are playing a game in a tournament but have to stop in the middle. How should the points be distributed? The idea is to base it on the probability that each competitor would win the game. The mathematicians ended up founding probability theory. Pascal and Fermat
What was one way mathematicians were solving problems related to calculus before calculus (#1)
finding derivative of equation withut knowing how to compute derivative
1. realize f(x) is equivalent to f(x-e) if e is small enough
2. set f(x) = f(x+e) and cancel terms
3. factor out e and divide by e
4. set e = 0
5. the remaining equation is the derivative
What was one way mathematicians were solving problems related to calculus before calculus (#2)
Finding vertex of parabola
1. choose a point on the function close to where you think the vertex is
2. draw a line tangent to the function at that point
3. mark where that tangent line hits the x axis
4. draw the tangent line that goes through your marked point
5. keep doing this
6. end up with an approximation of the vertex
what is a formula for kepler’s law
orbital period planet 1 squared / semimajor axis planet 1 cubed = orbital period planet 2 squared / semimajor axis planet 2 cubed
