WPP#9: Unit L Concepts 4-8 - Fundamental Counting Principle, Combinations, and Permutations

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SP #6: Unit K Concept 10 - Writing repeating number as rational number using geometric series

The viewer needs to pay special attention to see if the number continues on forever. The process of infinite series must be used. All work must be shown, meaning a calculater cannot be used to get the answer, only to check it. If it has a number at the beginning of the problem next to the decimal, you must remember to add it to the sum.

Reflective Essay Assignment

Word Count: 526
Video-Golden Ratio in Human Body
In this first video, I was amazed when I saw what the Golden Ratio was. If you divide a number by the number before it, you get a number that is very close to it and after the 13th number, it is known as the Golden Ratio (1.618). Artists, scientists, and designers take the proportions of the human body
which are set out to the Golden Ratio when conducting research. Leonardo da Vinci and Le Corbusier used this ratio in their designs. The whole body can be measured out to find the Golden Ratio, even the teeth. The structure of our lungs and our DNA can also be measured to get the Golden Ratio. It is incredible all the places the Golden Ratio is found.

Website- The Beauty of the Golden Ratio
The Golden Ratio has also appeared in ancient architecture. One of the Seven Wonders of the World, The Great Pyramid of Giza, has the Golden Ratio. The Greek Parthenon is another example of where the Golden Ratio exists. The UN building had the Golden Ratio when measured height by width for every ten floors. The exterior measures of the Parthenon have the Golden Ratio as well.

Video- Natures Number:1.618...
Fibonacci was a mathematician who created the Fibonacci number. Natures Number is 1.618. The Golden Ratio is a forgotten number. Numbers like pi, infinity, etc. are more famous that the Golden Ratio. Yet, ironically, this number appears in pretty much everything. It is amazing how art like the Mona Lisa have the Golden Ratio as well. Leonardo da Vinci seemed to have thought that 1.618 was a perfect proportion. A DNA structure and the heart have the Golden Ratio. This may be a coincidence, but the precision in everything makes it seem like it was meant to be there.

Website- Golden Ratio in Art and Architecture
Le Corbusier is probably one of the most famous/strongest for the application of the Golden Ratio during the 19th and 20th centuries. Le Corbusier was facinated with Aesthetics and the Golden Ratio. Le Corbusier's search for a standardized proportion led to the creation of the Modulor. The Modulor was a proportioning system bases on the FIbonacci series. Also, it is thought that great musicians like Mozart knew about the Golden Ratio and used it to compose their music. Interestingly, musical scales are based on Fibonacci numbers. Also, musical instruments are sometimes based on phi.

Reflection
All in all, I found it very interesting how the Golden Ratio is incorporated in pretty much everything around us. It is facinating that so many ancient architecture and paintings have the Golden Ratio as their proportion. It is incredible that this ratio can determine if something is beautiful. I think that in some cases the idea that 1.618 means beauty is true. Everyone has a different perspective, so not everyone will think that something is beautiful, even if it has the proportion of the Golden Ratio. I am personally just fascinated that so many things have the same proportion. The Golden Ratio, in my opinion, does not classify something as beautiful because not everyone may feel that way.

Fibonacci Beauty Ratio Activity

Leslie E.
foot to navel: 106 cm
navel to top of head: 61 cm
ratio: 106/61= 1.747 cm

navel to chin: 48 cm
chin to top of head: 17cm
ratio: 48/17=2.823cm

knee to navel: 57 cm
foot to knee:47 cm
ratio: 57/47=1.213cm
Average: 1.927cm

Katie W.
foot to navel: 102 cm
navel to top of head: 65 cm
ratio: 102/65=1.569cm

navel to chin: 48 cm
chin to top of head: 17 cm
ratio: 46/19=2.421cm

knee to navel: 55 cm
foot to knee: 48 cm
ratio: 55/48= 1.145cm
Average: 1.711cm

Daisy L.
foot to navel: 96cm
navel to top of head: 63 cm
ratio: 96/63=1.52cm

navel to chin: 44 cm
chin to top of head: 19 cm
ratio: 44/19=2.31 cm

knee to navel:52 cm
foot to knee: 46 cm
ratio: 52/46=1.13cm
Average:1.653cm

Christine N.
foot to navel: 96 cm
navel to top of head: 59 cm
ratio: 96/59=1.627cm

navel to chin: 40cm
chin to top of head: 22 cm
ratio: 40/22= 1.818cm

knee to navel: 51 cm
foot to knee : 46 cm
ratio: 51/46=1.109cm
Average: 1.518cm

Vivian P.
foot to navel: 101 cm
navel to top of head: 68 cm
ratio: 101/68=1.481

navel to chin:51 cm
chin to top of head: 22cm
ratio: 51/22= 2.318

knee to navel: 55 cm
foot to knee : 51 cm
ratio: 55/51= 1.078 cm
Average=1.629 cm

According to the Beauty Ratio, Vivian is the most beautiful. She was closest to the Golden Ratio of 1.618. I personally feel that the Golden Ratio does not determine if a person is beautiful or not. I feel that a person is beautiful based on their personality and their characteristics. This may be valid to determine the proportion of a person, but not the personality.