I/D 2 unit O-how can we derive our patterns for the special right triangles

Inquiry Activity Summary

1.                                                               

We first start out with an equilateral triangle with each side length being 1. Since it is equilateral it is also equilateral so each angle measure is 60 degrees.

In order to create a 30 degree angle to give us our 30-60-90 triangle we must cut straight down splitting the 60 degree angle into two 30 degree angles while also creating a right angle with the base of the triangle.

When you cut an angle in half you also cut the side across from the angle in half. Since all the sides of the triangle started out as 1 when you cut it in half the side across form the 30 degree angle is now 1/2. So far we have the hypotenuse being unchanged and staying at 1 and the base or the side across from the 30 degree angle being cut in half into 1/2

Now that we have 2 of the three side we can now use the pythagorean theorem to solve for the 3rd side. The side across form the 30 will be a the side across from the 60 will be b and the hypotenuse will of course be c. We then plug those values into the formula and then square them. We end up with 1/4+b^2=1. From there we solve for b and end up with rad3/2 for our third side across from the 60 degree angle.

Now that we have each side of the triangle we can get rid of the fractions by multiplying each side by 2. 

By multiplying each side by 2 we get 1 rad3 and 2. This is very similar to our pattern of n n-rad3 and 2n. The only reason we have n instead of one is for it to be a generalization of the pattern for any number instead of just 1

2.

We first start with a square where all the side are equal to 1

From there we cut it diagonally in order to split the right angles and create 4 45 degree angles or two 45-45-90 triangles. Unlike the 30-60-90 triangle the sides stay unchanged at 1 since it was a diagonal cut.

We have the side across from the 2 45 degree angles and we are missing the hypotenuse. Since we have 2 sides and are missing one we can again use pythagorean theorem to find the last side. The work is shown in the picture and we end up finding out that the hypotenuse is equal to rad2

The sides of the triangle are 1 and 1 being the two legs and rad2 being the hypotenuse. This already looks very similar to our pattern and needs nothing done to it except for changing the 1's to n's to create a generalization for any number to fit in its place.

Inquiry Activity Reflection

Something i never noticed about the special right triangles is that they are derived from a square and a equilateral triangle.

Being able to derive these patterns myself aids in my learning because I now have a better understanding of the triangles now that I know where the pattern comes from and just in case i completely forget the pattern i could also just derive the two triangles from the square and the triangle.

RWA Unit m concept 5: ellipses

http://jwilson.coe.uga.edu/EMAT6680/Brown/6690/InstrUnit/DayFive.htm

Mathematical definition: The set of all points such that the sum of the distance from two points also known as the foci is a constant.

DESCRIPTION OF ELLIPSE

equation: (x-h)^2/a^2+(y-k)^2/b^2 for a "fat" ellipse (x-h)^2/ b^2+(y-k)^2/a^2

graphically: refer to above picture

description of key points: center-the center of the ellipse 2 vertices: the endpoints of the major axis Major Axis- the axis where the ellipse is wider crossing through the 2 vertices  Co vertices- points on an ellipse that lay on the minor axis   Minor Axis-axis on graph where ellipse is thinner co vertice to co vertice a is the bigger denominator and the major axis would be 2a units a B: B is the smaller denominator and the minor axis would be 2b units  away.
Foci: The father the foci are from each other the less ellipse will look like a circle and therefor the eccentricity of the ellipse will be closer to 1. ( the eccentricity of an ellipse should be between 1 and 0
(http://www.mathopenref.com/ellipsefoci.html)

REAL WORLD APPLICATION 

One real world application of an ellipse is through an lithotripsy. Extracorporeal Shockwave Lithotripsy is a practice used by doctors in order to get rid of kidney and gall stones without the use of open surgery. This way the patient has less recovery time and less risk of infection. 

 The tool used for this is called a lithotripter. An ellipse is the base of this machine. Shockwaves are shot at one focus and are supposed to reflect to the other focus. A patients kideny or gallbladder should be placed at the other foci in order to recieve the shoackwaves The stone must be at precisly the focus in order for the machine to work. (http://mathcentral.uregina.ca/beyond/articles/Lithotripsy/lithotripsy1.html)

REFERENCES

http://mathcentral.uregina.ca/beyond/articles/Lithotripsy/lithotripsy1.html

http://jwilson.coe.uga.edu/EMAT6680/Brown/6690/InstrUnit/DayFive.htm

(http://www.mathopenref.com/ellipsefoci.html)

http://www.schooltube.com/video/11b0cf3f668f40a1a210/The%20Equation%20for%20the%20Ellipse

Fibonacci Haiku "Food"

Food
toast
Bacon
I love food
Food is tasty
every hour of the day

                                               this image was found on google

SV #5 unit J concepts 3 and 4 matrixes

There are many things that can go wrong in these problems. First you have to make sure you are using the proper rows or these problems will go on forever. You also have to pay close attention too each step that you do and its helpful if you write down the steps. Good luck!

SP #5 unit j concept 6 pfd with repeating factors

In these types of problems you have to make see that the factors repeat and are not distinct. You also have to remember to "count up". You must count up on the repeating factors or the answer will be wrong.

SP #4 unit j concept 5 pfd with distinct factors

For this problem every little bit of math must be right. If it is not all right you will have to do everything step all over again. Be very careful when doing these problems and play close attention to the math.

WPP #6 unit I concepts 3-5: investments

http://bit.ly/1hLvJOg
it refused to put the playlist on here and i give up so here you go