IA Math Rap Music Video!

For my math class, I had an assignment, which was to make a presentation on whatever mathematical thing I wanted. I chose to create a rap about some of the basic mathematical paterns and applications to music. The verses of the rap go into detail about some basic principles, but throughout the video there are some interesting relationships in music and math and I would encourage you to pause and read them maybe :) I must, admit, the singing isn't very good.

Watch the Video Here!

The lyris are in the description of the video

exponents on functions and their effects.

I've been somewhat curious about how exponents really do effect functions. Linear functions are always changing at the same rate, while parabolas take more time to pick up, but eventually change at a very quick rate. But what about when y=x^3 or y=x^4 and so on? well I decided to get some geogebra help on this one. This is what I found...

All these functions meet at the same point, at (1,1). Also, we can see that before x=1, the functions with the higher exponents have lesser y values, and after x=1 it's the opposite. One last thing, all functions with odd nuber exponents penetrate the 3rd quadrant, while the functions with even number exponents penetrate the 2nd.

idk, I kind of found this interesting, what do you think?

My elipse/circle art!

it's a chicken on it's eggs!

page 131, 1- f) As done by moi.

Alrighty, so I basically chose a random question. :)

1.f) goes as follows

Because of Pythagorean rules, we can determine that

It is possible to manipulate this into a single value, by simply subtracting 1 from both sides of this equation.

And finally, we end up with a single value

Or, you could turn it into a sine and cosine ratio

Whatever floats your boat! If you have any questions or comments on how I did this, feel free to ask!

Also Code Cogs is a pretty cool math site!

Class RECAP! with Arnold Downey.

Guess whose back? Soh, Cah and Toa are! and they brought a few friends, named Cho, Sha and Cao! Now unless you slept through a whole unit of last year's math, you should know what soh cah toa is, basic trigonometry. If you have a right triangle with an angle of 21 degrees and a hypotenuse of 12cm, you can easily find the length of the side opposite to the angle.

But, enough of that baby stuff! Time to kick it up a notch. Going by the same principles as soh cah toa, you can probably guess what we do with cho sha cao. Exact Same Thing! Of course, we have been introduced with some new words, so let's check those out.

c in cho  = cosecant
s in sha = secant
c in cao = cotangent

Moving past the first letters in cho sha cao are the final two letters in each word and just like soh cah toa, these letters stand for

o = opposite
h = hypotenuse
a = adjacent

But Arnold, if these different terms stand for the same thing, what's the difference?
I can answer that question with one unnecessarily big word...
RECIPROCATION!
or the whirly bird as I call it.

Cosecant is the reciprocal of sine
Secant is the reciprocal of cosine
Cotangent is the reciprocal of tangent

And that is about as far as we got today! hope you enjoyed the blog! Glad to be the guinea pig for this daily class blog concept :)

See ya next time!

World Population Growth.

Over the past couple years, we have learned to apply some of the mathematical theories we've learned to real life phenoms. One statistic I find interesting is the world population growth. If you look online for a grph that portrays the world population over a period of time, you should notice one thing, that it looks like an exponential equation. It makes perfect sense. Like the examples we are given about how you start off with one cell, which turns into 2, into 4, into 8 and so on and so on, we can apply that same thinking to humans. 2 humans create more humans, who create more humans, who create more human da, da da ,da da. Is this a bad thing? Possibly. Let's see what David Susuki has to say,

Nuff said.

blogs about logs? sure.

Well after finishing the most emotional math test I've ever done (lots of jumping up and pouding my fists on the table when I made breakthroughs, good thing they put us in a seperate room for tests)I can safely say that logarithms are the weirdest thing I've encountered in math so far. I mean, just the concept of it, What number when acting as the exponent to a number gives me a certain number? Learning logs is like learning a different language.

During the test there was one trick that is probably responsible for any possibility of me passing the test, the trick is what I call "The Flippy Floppy" or as Miss McGoldrick called it, "Counterclockwise trick" or something like that and it is when you need to change a logarithmic equation into an exponential equation and vice verse.

Let me show ya!

Silly, I know, but this one little rule is so important with logarithms, it's the seed from which the whole unit sprouts from! Anyways, just thought I'd express my feelings for the Flippy Floppy. Next time I'll teach you the Whirly Whirl! :D