User:Rscott3

From Math Images

Summer 2011

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

Contents 1 May 16 Notes 1.1 Possible Page topics: 1.2 Questions 2 May 17 Notes 3 May 23rd Ambiguous Case Pictures 4 May 25 Notes

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

• 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

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