# User:Rscott3

### From Math Images

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?

## 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:

- 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

- make Law of sines a helper page
- make new helper page of same format for law of cosines
- derive/prove formula
- example
- extensions?
- researching today

- Make shadow page