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Summer 2011 Image:Math.gif

Some important pages for me to remember: S11, Page Building Help, Image Pages by Field of Mathematics, Wiki Tricks
      - why is there not a link to the image page list?

Rscott testing  2 + 2 = 4

Contents

May 16 Notes

Possible Page topics:

  • Specific fractal types
  • Klein Bottle
  • quadrature of the lune
  • wheat on the chessboard/grains of rice problem
  • Birthday paradox/pigeonhole principle
  • Other famous problems
  • absent-minded professor?
  • ambiguous triangles

Questions

  • contacting Sweet Briar:
  • Would it be helpful for one of us to stay in touch with the summer researchers there?
  • Is there a page we can build/ look at that would show everything that they'll be putting up so we don't have any overlap?
  • What do we do about pages like Fractals?

May 17 Notes

Starting Topic Ideas:

  1. Law of Sines
  • Geometry
  • Basic Description
  • formula = a/sinA = b/sinB
  • use it to solve oblique triangles
  • introduce/mention the ambiguous case
  • Historical background: not much info found in initial research, but there's definitely enough for a few sentences
  • Why it's important
  • Real Life Application: Surveying Land
  • Surveyors can use the law of sines to help calculate the perimeter/ dimensions of a plot of land.
  • Earthquakes and triangulation
  • A More Mathematical Explanation
  • Two Different Proofs
  • use area formula to derive law of sines
  • use the formula for sine to derive the rest to
  • The Ambiguous Case, include demonstration/applet
  • other applications in mathematics
  • Law of sines for tetrahedra
  • law of sines in the spherical/hyperbolic case
  • the value given by a/sinA is the diameter of the circumcircle, that is the circle whose boundary contains all three vertices of the triangle
  • Heron's/Hero's formula
  • A= <no wiki>[s(s-a)(s-b)(s-c)]^(1/2)(/no wiki)
  • s= (a+b+c)/2 is the semi perimeter of=r half of the perimeter
  • Teaching resources
  • Teaching Activity for the ambiguous case with string
  • Challenges/Shortcomings
  • Too simple a topic? Target site audience?
  • Finding a good picture/image to represent this topic
  • may have to make applet?
2. Normal Distribution
  • Statistics?
  • Intro
  • Basic Description
  • the center of the normal distribution is the mean, what standard deviation means in terms of the bell curve
  • commonly referred to as Bell Curve
  • Origin: de Moivre used this as an original approximation for binomial distribution
  • used later by Gauss and Laplace
  • talk about different transformations and interpretations of the different variations of the bell curve
  • A More Mathematical Explanation
  • Mathematical Proof
  • Integrate under this curve to get 1
  • total probability can be no larger than 1
  • talk here about inference testing and how we measure overall significance using normal distribution
  • comparing different normal distributions to one another
  • why it's important
  • Central Limit theorem (Talk about this here or earlier?)
  • real life-example: SAT is graded on bell curve
3. Birthday Paradox

birthday-cake.png

  • Probability
  • Basic Description
  • In a group of 23 people, there is more than a 50% chance that two people within that group have the same birthday
  • there's a 99% chance with 57 people in the room
  • there's a 100% chance with 366 people in the room
  • A More mathematical Explanation
  • Calculate the probability that a match will not occur and then subtract from 1
  • Pigeonhole Principle explains the 100% certainty at the 366 person level
  • ex: with a set of unmatched black and white socks, picking three will guarantee that you pick at least one pair of matching socks
  • Challenge/shortcomings
  • needs some sort of picture/image

May 23rd Ambiguous Case Pictures

Image:Ambig_case_no_solutions.jpg

Image:Ambig_case_one_solution.jpg

Image:Ambig_case_two_solutions.jpg

May 25 Notes

  1. make Law of sines a helper page
  2. make new helper page of same format for law of cosines
    1. derive/prove formula
    2. example
    3. extensions?
      1. researching today
  3. Make shadow page
    1. http://www.imdb.com/media/rm1990178816/tt0105378
    2. http://cmex.ihmc.us/data/tutorial/ShadMeas.htm
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