Welcome to Tracey P.'s Math Analysis Blog

Sunday, November 24, 2013

Fibonacci Beauty Ratio

Measurements:
Chelsea A.:
Foot to Navel: 99 cm
Navel to top of Head: 58 cm
Ratio: 99/58=1.707 cm
Navel to chin: 39 cm
Chin to top of Head: 21 cm
Ratio: 39/21= 1.857 cm
Knee to Navel: 53 cm
Foot to Knee: 46 cm
Ratio: 53/46=1.152
Average: 1.572 cm

Christine N.:
Foot to Navel: 96 cm
Navel to top of Head: 59 cm
Ratio: 96/59=1.627 cm
Navel to Chin: 40 cm
Chin to top of Head: 22 cm
Ratio: 40/22=1.818 cm
Knee to Navel: 51cm
Foot to Knee: 48 cm
Ratio: 51/46=1.109 cm
Average: 1.518 cm

Katie W.:
Foot to Navel: 103 cm
Navel to top of Head: 63 cm
Ratio: 103/63=1.635
Navel to Chin: 44 cm
Chin to top of Head: 22 cm
Ratio: 44/22=2
Knee to Navel: 57 cm
Foot to Knee: 48 cm
Ratio: 57/48=1.188
Average: 1.608 cm


Stephanie V.:
Foot to Navel: 99 cm
Navel to top of Head: 60 cm
Ratio: 99/60=1.65 cm
Navel to Chin: 44 cm
Chin to top of Head: 22 cm
Ratio: 44/22=2 cm
Knee to Navel: 53 cm
Foot to Knee: 44 cm
Ratio: 53/44=1.205 cm
Average: 1.618 cm

Leslie N.:
Foot to Navel: 96 cm
Navel to top of Head: 63 cm
Ratio: 96/63=1.524 cm
Navel to Chin: 45 cm
Chin to top of Head: 20 cm
Ratio:45/20=2.25 cm
Knee to Navel: 53 cm
Foot to Knee: 44 cm
Ratio: 53/44=1.178 cm
Average: 1.651 cm

Based on the Beauty Ratio, Stephanie is the most beautiful because her ratio was 1.618. This also happens to be the exact number of the "Golden Ratio". I believe that a number can't decide how how beautiful someone is. Everyone is beautiful differently, whether it's their personality or intellect. In my opinion, the Beauty Ratio is valid in proving how proportionate a person is but it's not valid in proving how beautiful a person is.

Fibonacci Haiku: I Believe

Christmas
Santa
Doesn't exist
Ruined my childhood
No more presents from Santa
At least the tooth fairy is still real
http://www.celebuzz.com/photos/top-10-cutest-christmas-animals/sour-puss-2/

Saturday, November 16, 2013

SP#5: Unit J Concept 6 - Partial Fraction Decomposition w/ Repeated Factors

Remember to pay close attention when adding all the like terms and remember to show all your work because it is very easy to make mistakes, especially when you have four variables.

Step 1: You first find a common denominator and multiply it to the four varaibles. Once you've done that you add up all the like terms and separate them into the common terms. Then, you can start canceling out the like terms and the results will be the system.
Step 2: Next, you take the first and second equations and add them together. Then, you can use the elimination method in the third and fourth equation, in the picture above, I eliminated D. Once you have the two equations, you use elimination on them as well and I eliminated C.
Step 3: This picture shows what I did to solve for the four variables. The picture is pretty much self-explanatory. I just solved for A first and then used the substitution method to find the other equations.
This will be your final answer in the end.





Thursday, November 14, 2013

SP#4: Unit J Concept 5 - Partial Fraction Decomposition

Be sure to pay close attention in distributing the numerator and be very careful when plugging in the numbers into the calculator. Also, remember to use the rref feature and check if the answers are correct.

Part 1: First, you would have to find the common denominator. In this case it's (x+4)(x-2)(x+1). Then, you distribute them to the numerator but remember to foil it out first. Once you have completed this step, you add up all the like terms.
Part 2: Now you have to replace the numerator with letter values. Then, you multiply by the common denominator again. This time, instead of distributing a number, you'll be distributing a letter. Next, you set the distributed product equal to the original and add up any like terms (like terms highlighted in above picture). After, you've found the like terms, you can start canceling out and the end product will be the system (as shown above).
Part 3 : The last step is to plug in the system into the calculator. Then you use the rref feature to find your answer. Once you have found what A,B, and C equals, plug them back into the original 3 fractions.



Monday, November 11, 2013

SV#5: Unit J Concept 3-4 - Solving 3-Variable Systems w/ G-J Elimination, Matrices, REF, Back-Subs., & Solve Non-square Systems

To view my video, please click here.
(This is DP#3)
Remember to pay close attention to how I'm solving the matrices and please double-check my work by doing it yourself first. This will prove beneficial because as you watch my video, you'll see that I'll tend to mess up quite a bit, but no worries because I did catch them!
Here is what the rref will look like once you've put in the numbers into the calculator: