10.2: Ellipses

Here is a visual representation of an ellipse and it's components. 

Center

The center is (h,k) 

Foci

The foci are points on the major axis that are in between the vertecies and the center. 

Use these equations to find the foci. 

If the major axis of the ellipse is the x axis, then the ellipse is horizontal. In this case, use this equation: 

If the major axis of the ellipse is the y axis, then the ellipse is vertical. In this case, use this equation:

To find what a and b are and to determine if the ellipse is horizontal or vertical, use this rule:

Another way to find the foci if you know a and b is to use this equation: 

Once you find c, you can use it and the center to find the foci. 

If it is horizontal, the y's will stay constant, so add c to x1 and subtract c from x2 to get your foci. 

Vertex

To find the vertecies, you use a and b. 

if the ellipse is horizontal...

add b to the x value of the center point to find the x value of the first vertex. Likewise, add a to the y value of the center point to find the y value of the second vertex. 

Subtract b from the x value of the center point to find the x value of the second vertex. Likewise, subtract a from the y value of the center point to find the y value of the second vertex. 

If the ellipse is vertical...

Add a to the x value of the center point to find the x value of the first vertex. Likewise, add a to the y value of the center point to find the y value of the second vertex. 

Subtract a from the x value of the center point to find the x value of the second vertex. Likewise, subtract b from the y value of the center point to find the y value of the second vertex. 

Eccentricity of an ellipse

The eccentricity of an ellipse is "the ovalness of the ellipse."

You can find the eccentricity by using this formula:

e=c/a

Math joke of the day:

Q: What should you do when it rains? 

A: Coincide

10.1: Parabolas

To find the vertex, focus, and the directrix of a parabola, the equation of the parabola will have to be in standard form. 

The standard form of a parabolic equations is:

Often, to find the standard form, you need to complete the square. 

The vertex is (h, k) 

The focus is p units from the vertex. 

When p>0 and the x is squared, then add p to the y value. 

When p<0 and the x is squared, then subtract p from the y value. 

When p>0 and the y is squared, then add p to the x value. 

When p<0 and the y is squared, the subtract p from the x value. 

When the parabola is vertical, the directrix is y=k-p

When the parabola is horizontal, the directrix is x=h-p

Math joke of the day:

Q: Why couldn't the Möbius strip enroll at the school?

A: they required an orientation. 

Interesting Math Stuff #8: Tesselations

A tessellation is a pattern of geometric shapes with no overlaps or gaps. This is an example of a tesselation you have probably seen before. It is a floor made up of hexagon shaped tiles. 

Tessellations can be extenended to higher dimensions. 

This concept is summarized in the wikipedia article on tessellations. It says:

"Tessellations in three or more dimensions are called honeycombs. In three dimensions there is just one regular honeycomb, which has eight cubes at each polyhedron vertex. Similarly, in three dimensions there is just one quasiregular honeycomb, which has eight tetrahedra and six octahedra at each polyhedron vertex. However there are many possible semiregular honeycombs in three dimensions"

Here is an example of a three dimensional tessellation: 

Math joke of the day: 

Q: What is the definition of a polar bear? 

A: A rectangular bear after a coordinate transformation 

source: http://www.jokes4us.com/miscellaneousjokes/mathjokes/

9.8: Measures of Central Tendancy and 9.9: Exploring Data

9.8
A number that is most representative of an entire collection of numbers is a measure of central tendency. The most commonly used measures of central tendency are mean, median, and mode.

The mean or average can be found by adding all n numbers together and dividing the sum by n.

The median is the middle number when the numbers are put in order.

The mode is the number that occurs the most frequently. A group of numbers with two modes is called bimodal.

9.9
Standard Deviation

Box and Whisker Plots
Quartiles can be represented by a box and whisker plot. The five numbers are listed proportionally as if on a number line. They are listed as follows: the smallest number, the lower quartile (The average of the lower half of the data), the median, the upper quartile (the average of the upper half of the data), and the largest number.

Math Joke of the Day: 

Q: What is the difference between a Ph.D. in mathematics and a large pizza? 

A: A large pizza can feed a family of four 

source: http://www.jokes4us.com/miscellaneousjokes/mathjokes/

9.7: Probability

In this lesson, we explored how to  calculate the probability of different situations.

Important Vocabulary
Independent events: the occurrence of one event has no effect on the occurrence of one event has no effect on the occurrence of the second event. Keyword: with replacement.
Complement of an event: the probability that the event will not happen.

Mutually exclusive events
Two events A and B are mutually exclusive if A and B have no outcomes in common. The keyword is or. 

To find the probability that one or the other of two mutually exclusive events will occur, add the probabilities.

Independent Events
To find the probability that two independent events will occur, multiply the probabilities.

Complement of an Event
If the probability of  A is P(A), the probability of the complement is 1-P(A).

Q: How does a mathematician induce good behavior in her children? 
A: `I've told you n times, I've told you n+1 times...' 

source: http://www.jokes4us.com/miscellaneousjokes/mathjokes/

Google Sites Link

https://sites.google.com/a/maranathastudents.org/swag-group-2/

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'