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:

http://www.cracked.com/article_19360_7-questions-you-didnt-know-could-be-answered-with-math.html

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: 

http://www.physicsforums.com/showthread.php?t=380114

http://en.wikipedia.org/wiki/Well-ordering_principle

Math joke of the day:

Q: What keeps a square for moving?

A: Square Roots

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

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. 

http://www.educreations.com/lesson/view/determinant/17085405/?s=C5mF1r&ref=app

Math joke of the day:

Q: What do you say when you see an empty parrot cage?

A: Polygon 

Voice Thread: Cramer's Rule

Check out this voicethread me, Alec A., Sabrina, and Mason made. It goes over an example of Cramer's rule. 

https://ed.voicethread.com/share/5445245

Math joke of the day:

Q: What do you call an Englishman who has spent all summer at the beach?

A: Tangent! 

Interesting Math Stuff #5: Mathematics and Logic

Mathematics and Logic. Why do these two words always come together? Mathematics on its basic level might be logical, but as we delve into the higher mathematics such as algebra, geometry, trig, and even (shudder) calculus, where does this logic go? Mathematics seems to be governed less by clear and logical common sense and more by a long list of meticulous steps, identities and rules to be memorized that only make logical sense to the select and brilliant few while the rest of us mechanically follow the steps Outlined for us with no real understanding of how or why we get the answer we do. -A question to ponder: do mathematics and logic really go hand in hand for the common person? 

A few somewhat humorous examples of when logic and mathematics produce some truly tragic results. 

 

8.1: Matricies Introduction-infinite or no solution?

If there are infinitely many solutions, you can tell by converting the matrix back into a system of equations and solving the system. If you come up with a true statement such as 2=2, then you know that the matrix has infinitely many solutions. 

Alternately, if you can use this method:

An example of the matrix with infinitely many solutions is this:

A system has no solution if the numbers are all zeros except for the last column that represents the constant. 

This is an example of a system with no solution:

You can see that in the final form, the third row is all zeros except for the fourth column, 

Math joke of the day:

8.3: Inverse Matrices

Finding Inverses to Matrices 

In this post, I work out two problems. One has an answer and one does not. When a matrix has no inverse, it is called a singular matrix. 

Math joke of the day:

Q: Do you know a statistics joke?

A: Probably, but it's mean!

Source:  http://www.enchantedlearning.com/jokes/topics/math.shtml

8.1 Video

Here is a video of me solving a matrix by the Gauss-Jordan Method.

http://www.educreations.com/lesson/view/solving-a-matrix-by-gauss-jordan-method/16644872/?s=TWUDFD&ref=app

Math joke of the day:

The shortest math book: An Unabridged List of the Even Primes

Source: http://www.math.psu.edu/tseng/mathjoke1.html

Interesting Math Stuff #4: The Origin of the X

X is the letter most commonly used to represent a variable. X also stands for the horizontal axis in a 2D graph and the first number in an ordered pair. 

During Islamic times, Arabic was the predominant language of sciences. In Arabic the word for thing or object is "shei". Translated into Greek is xei, which is then shortened to x. also, the word "xenos" is the greek word for unknown or stranger, so this could also be a reason that we use x for the unknown variable in math. 

Source: http://www.newton.dep.anl.gov/askasci/math99/math99228.htm

Math joke of the day: