Wednesday 25 January 2012

IA

Because I am an extremely indecisive person, I think I have changed my mind about the topic of my Independent Assignment close to 10 times( poor Ms. McGoldrick). HOWEVER, I have finally chosen architecture, since I have loved building model houses, whether they were made of Lego, Popsicle sticks, or even paper, since I was little. I plan to use several elements of math such as geometry, Pythagorean theorem, proportions, supplementary and complementary angles, metric relations and much more! Does anyone have any suggestions for what my model should look like??




Tuesday 24 January 2012

 I was on youtube the other day and found this funny video a school in Ohio made on exponents. The teacher in the video reviews the product rule (<a href="http://www.codecogs.com/eqnedit.php?latex=x^m * x^n = x^m*n" target="_blank"><img src="http://latex.codecogs.com/gif.latex?x^m * x^n = x^m*n" title="x^m * x^n = x^m*n" /></a>), the quotient rule(<a href="http://www.codecogs.com/eqnedit.php?latex=(x^m)/(x^n) = x^m-n" target="_blank"><img src="http://latex.codecogs.com/gif.latex?(x^m)/(x^n) = x^m-n" title="(x^m)/(x^n) = x^m-n" /></a>), the power rule(<a href="http://www.codecogs.com/eqnedit.php?latex=(x^m)^n = x^m*n" target="_blank"><img src="http://latex.codecogs.com/gif.latex?(x^m)^n = x^m*n" title="(x^m)^n = x^m*n" /></a>) and the negative exponent rule(<a href="http://www.codecogs.com/eqnedit.php?latex=x^-m =1/(x^m)" target="_blank"><img src="http://latex.codecogs.com/gif.latex?x^-m =1/(x^m)" title="x^-m =1/(x^m)" /></a>). Voila!
 


After watching the video Ms. McGoldrick posted about the Fibonacci sequence of numbers, my mind was blown. How can math be so mysterious and amazing at the same time?? How can so many things in nature have spirals that are formed using the Fibonacci sequence:
0+1=1
1+1=2
1+2=3
2+3=5
3+5=8 ... CRAZY HUH?
Turns out, the Fibonacci sequence is named after Leonardo of Pisa. Although he may not be as famous as the other Italian Leonardo, he is still a pretty cool guy! The "Golden Ratio" has been found in architecture, economics, music, aesthetics, and, of course, nature. I guess that means math really is all around us. Feast your eyes on these wondrous examples:






Tuesday 17 January 2012

Voicethread: Solving Log Equations II
In the second voicethread on solving logarithmic equations, we were introduced to something new :O ! We learned what to do when the solution to a log. equation becomes a quadratic equation! We must simply find the 2 solutions to our quadratic equation, then verify them by plugging them individually into our original log. equation. They are only solutions if they give a log with a positive argument. For example:

log(x+3)+logx=2
log((x+3)x)=2
10^2 = x^2 +3x
 x^2 + 3x-100=0

Quadratic Equation!
solutions:  8.6     -11.6

log(8.6+3)         log(8.6)  
log(-11.6+3)     log(-11.6)   X
Voicethread: Solving Log Equations I

The first voicethread of this week was a helpful review for me on solving log. equations. The first thing reviewed was solving simple logarithms:
log22 = x
2^x = 2
x=1
 
 We also reviewed the "smoosh" method:
log(x+1)+log2=3
log((x+1)2)=3
log(2x+2)=3
103 =2x+2 
1000=2x+2
998=2x 
499=x

Finally, we learned something we probably already knew:
log(x+3)=4
x+3=4