Wednesday, February 26, 2014

Interesting Math Stuff #7: The Scary Movie Formula

An Article states:

Researchers at Kings College, London, found that it's not quite as simple as turning the lights off and spraying the disposable support cast with fake blood.

In this ridiculously complicated formula:

es is escalating music;

u is the unknown;

cs is chase scenes;

t is the sense of being trapped;

a is the character being alone;

dr is how dark the film is;

fs is the film setting;

tl stands for true life;

f stands for fantasy;

n is for number of people;

sin is blood and guts and

s is shock.


My question is: can such factors be quantified? Possibly you could calculate the gallons of blood spilled or the minutes of chase scenes but how do you assign a number to shock or the unknown? My conclusion is that, since not everything in this equation is quantifiable, then it is open to subjection and therefore false and in essence not an equation at all. 

Sources:


Math joke of the day: this logical accuracy of this 'equation' 


9.5: Pascal's Triangle

Pascal's triangle is a way to simplify binomial expansions. 

When you have a problem like this: (x-2y) ^5

1) look at the row that matches the exponent. In this case it's row 5. 
2) use the numbers shown with the first term in descending powers. In this case the first term is x.
 
3) multiply each term in the new equation by the second term in the original equation paired with ascending exponents. 

4) simplify and add the terms 

Math joke of the day:
Q: What did the little acorn say when he grew up?
A: Geometry! 




The Well Ordering Principle

The well ordering principle states that every set of positive integers that is not empty contains a least element. A least element is simply the smallest number in the set. The term 'least element' should not be confused with the term 'minimal element.' A minimal element is one that is not larger than any of the other elements in the set. 

One some occasions, the well ordering principle means that the set of integers (....-2, -1, 0, 1, 2.....) contains the natural numbers in which every non empty subset contains a least element. 

Sources: 

Math joke of the day:
Q: What keeps a square for moving?
A: Square Roots

Thursday, February 20, 2014

Interesting Math Stuff #6: The Lebombo Bone

Possibly the oldest known mathematical tool is the Lebombo bone that was discovered in the mountains of Swaziland in the 1970s. It bone was dated to about 35,000 BC. The bone is a small peace of the fibula of a baboon and has 29 markings on it. Researchers have guessed that the bone was used to mark the lunar cycles. 

The Universal Book of Mathematics says, 

"One of the oldest mathematical artifacts known, a small piece of the fibula of a baboon, found near Border Cave in the Lebombo Mountains between South Africa and Swaziland. Discovered in the 1970s during excavations of Border Cave and dated about 35,000 B.C., the Lebombo bone is marked with 29 clearly defined notches. This suggests it may have been used as a lunar phase counter, in which case African women may have been the first mathematicians, because keeping track of menstrual cycles requires a lunar calendar. Certainly, the Lebombo bone resembles calendar sticks still used by Bushmen in Namibia."



    9.2: Arithmetic Sequences


    Arithmetic sequences are when you are constantly adding the same thing to the previous term. 

    Example of a arithmetic sequence
    2, 4, 6, 8 

    The common difference is 2

    Common difference formula
    When d is the common difference...

    d=a2-a1

    Explicit formula for arithmetic sequences
    an=a+(n-1)d

    Example:
    Find the arithmetic sequence of 2, 4, 6, 8 


    Sum of an arithmetic sequence 
    Sn= n/2 (a1+an) 

    Sn=sum of the arithmetic sequence
    n=total number of terms
    a1=first term
    an=last term

    Recursive formula
    Use the recursive formula when you have to find the first n terms of a formula where you add on to the term before. 

    Math joke of the day:



    9.1: Sequences and Summation

    Sequences
    Infinite Sequences: simply sequences that do not stop
    A1, A2, A3.....An.......

    Finite sequences: sequences that end
    A1, A2, A3.....An

    Example:

    Factorials
    -a factorial is hard to define, so here is the formula:
    n!=1 x 2 x 3......(n x 1) x n

    Example:
    3!= 3 x 2 x 1= 6

    Example 


    Summation Notation




    Math joke of the day:
    Q: If I had seven oranges in one hand and eight oranges in the other hand, what would I have? 
    A: Big Hands



    Thursday, February 13, 2014

    Educreations Video: finding the determinant of a 4 by 4 matrix

    Here is the educreations video Alec A, Aidan, Sabrina, Mason, and I made. It shows us solving #36 on pg. 635. 


    Math joke of the day:
    Q: What do you say when you see an empty parrot cage?
    A: Polygon