Saturday, November 23, 2013


Word Count: 532 words 

Golden Ratio in Human Body
In this video, I learned many interesting facts. If you divide a number by the number before it, you attain numbers very close to one another. After the thirteenth number, the number is fixed and known as the Golden Ratio which is 1.618. Leonardo da Vinci used the Golden Ratio in his designs. Also, architect Le Corbusier used the number for his designs. There are many features that you must measure to see how beautiful a person is overall, even the total width over the front teeth over the health equal to the Golden Ratio. The Golden Ratio is even found in the structure of the lung and in our DNA. The Golden Ratio is found in animals, paintings, buildings, and so much more. 

The Golden Ratio and Beauty in Architecture 
The Golden Ratio was used in ancient times. One of the Seven World Wonders, the Great Pyramid in Giza, Egypt, was formed using the Golden Ratio. Therefore, the Ancient Egyptians and Greeks had knowledge about the Golden Ratio. Renaissance artists used the Golden Ratio as well, in example of Notre Dame. The Parthenon has exterior dimensions that equal to the Golden Ratio. The United Nation building has the Golden Ratio in the width of the building compared with the height of every ten floors. 

The Golden Ratio Revisited 
The Golden Ratio is a mathematical formula made from Eucid, who is also known as the "Father of Geometry". It is an universal way of defining beauty. That is why some objects are aesthetical pleasing while other are not. The ratio is evident in the painting, "Vitruvian Man", by Leonardo da Vinci. It is also evident in Mona Lisa. It is present in book design, music, and Mother Nature. Adolf Zeising discovered the Golden Ratio in the branches along the stems of plants and veins in leave. A flower or a pineapple is appealing because of the Golden Ratio. It is present in almost everything. 

Nature by Numbers 
Fibonacci wanted to know how many rabbits would be produced in a year. He assumed that starting with January, each new month the rabbits would give birth to a new pair. He noticed a pattern that the rabbits were increasing in a sequence each month. This resulted in the Fibonacci numbers. The structure of flowers are based off the Fibonacci number. Sunflower have 33, 55, or 89 petals, which is a Golden Ratio. Organic growth is stimulated by the Fibonacci number. The Greeks believed that the rectangle had a mathematical beauty. 

Response and Reflection 
Overall, the information I learned was very interesting. I think it is amazing how these numbers determine how appealing something could be to the eye, such as things found in Mother Nature. In all honesty, I believe that Fibonacci's numbers do play a role in beauty. However,  I believe it doesn't play a major role. For something to be appealing to one's eye, color and such plays a role. It is not just about size. Also, everyone has a different preference when it comes to determining what is beautiful. The "Golden Ratio" is very interesting and valid, but only in a small role of beauty. 


 Measurements of Friends:

Leslie Estrada: 
Foot to Navel: 106 cm
Navel to top of Head: 61 cm
Ratio: 106/61=1.74 cm
Navel to chin: 48 cm
chin to top of head: 17 cm
Ratio: 48/18=2.82 cm
Knee to navel: 57 cm
Foot to knee: 47 cm
Ratio: 57/47=1.21 cm

Christine Nguyen
Foot to Navel: 96 cm
Navel to top of Head: 58 cm
Ratio: 96/58= 1.19 cm
Navel to chin: 44 cm
chin to top of head: 20 cm
Ratio:44/20= 1.19 cm
Knee to navel: 57 cm
Foot to knee: 48 cm
Ratio: 57/48=1.19 cm
AVERAGE: 1.35 cm

Melissa Arias
Foot to Navel: 103 cm
Navel to top of Head: 61 cm
Ratio: 103/61=1.68
Navel to chin: 45 cm
chin to top of head: 19 cm
Ratio: 45/19=2.37 cm
Knee to navel: 52 cm
Foot to knee: 50 cm
Ratio: 52/50=1.04 cm
AVERAGE: 1.69 cm

Tracey Pham
Foot to Navel: 100 cm
Navel to top of Head: 62 cm
Ratio: 100/62=1.61 cm
Navel to chin: 42 cm
chin to top of head: 20 cm
Ratio:42/20= 2.1 cm
Knee to navel: 56 cm
Foot to knee: 47 cm
Ratio: 56/47=1.19 cm
AVERAGE: 1.63 cm

Mrs. Kirch
Foot to Navel: 105 cm
Navel to top of Head: 68 cm
Ratio: 105/68=1.54 cm
Navel to chin: 49 cm
chin to top of head: 20 cm
Ratio:49/20= 2.45 cm
Knee to navel: 54 cm
Foot to knee: 48 cm
Ratio: 54/48=1.13 cm
AVERAGE: 1.71 cm

According to the beauty ratio, Tracey Pham is the most beautiful out of all five people. She was close to the "Golden Ratio" of 1.168. In my opinion, the beauty ratio does not determine how beautiful a person is. A person is beautiful by their characteristics, such as the color of their eyes, etc, not just on proportion. But, I do believe that the golden ratio is valid in that a specific measurement of a face looks more appealing on a person. But, overall, it isn't a truly valid way to define beauty, since it is based on how proportional the face is and body. 

Fibonacci Haiku: My Best Friend

Let's eat
Life is good
There is never too much
My favorite food is everything in the world

Monday, November 18, 2013

SP #5: Unit J Concept 6 - Partial Fraction Decomposition with repeated factors

The reader must be careful when doing this problem because there are four equation. Also, make sure you do your math correctly or one incorrect variable can mess up your whole system. Also, make sure that you multiply the numerators and combine like terms correctly. Check your work!

Saturday, November 16, 2013

SP #4 - Partial Fraction Decomposition with distinct factors

This part is called composing. We combine the fractions into a larger fraction. We then combine like terms. 
This part is called decomposition. We are given a large fraction and are trying to find the small fractions that multiplied to make it. 
Simply type the left part into the calculator and using rref you will get the answer on the right, which is your A, B, and C. 

This is what you started with when you plug A, B, and C, back together. CONGRATS. 

Tuesday, November 12, 2013

SV#5 - Unit J Concepts 3-4: Matrices

A viewer must pay attention to how they write their equations. Don't mistake a Z for a 2! Make you can look for equations to be simplified to make your life a little easier. A viewer must make sure to do their math correctly in the steps or your answer will be wrong and you will be very frustrated. Also, when plugging the equation in to your calculator, make sure you put the numbers in correctly or it won't match up your pair.