WPP #10: Unit L Concept 9-14: Basic Probability, Events with Replacement and without Replacement, Mutually Exclusive and Non-Mutually Exclusive, Combinations and Probability

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WPP #9: Unit L Concept 4-8: Finding the Fundamental Counting Principle Combinations, Permutations,

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SP #6: Unit K Concept 10: Writing Decimals as Rational Numers

In this section, we now get a number of repeating decimals and in order to find the sum of the infinite geometric numbers, we have to do a series of steps. First, we ignore the whole number in front, so we can use it later on. We work with the repeating numbers by using summation notation. This means that we first have to change our first time into a fraction and the ratio also needs to be included. Then, we do some division with these and make sure to cancel off properly. Always be on the look out because you can some across a problem that needs to be simplified and this problem requires of that. After that, we bring back the whole number and add it to the fraction. Be careful with your multiplication and addition. Other than that, this is the answer to your problem!

Fibonacci Beauty Ratio

          The Fibonacci "Beauty Ratio" Actvity was performed in order to figure out which person from our class was the the most mathematically beautiful. I recorded Jorge, Vanessa, Judith, Ana, and Victoria and out of all of them, Victoria came out to be the most beautiful. According to the Fibonacci Golden Ratio, she got an aveage of 1.620. I got the ratio by taking everyone's meansurements from different parts of their body, such as the distance from thier foot to naval, navel to top of head, navel to chin, chin to top of head, knee to navel, and foot to knee. Altough the Golden Ratio is amazing since it is found all around nature and in a lot of beautiful art work, it might not be completely true for my measurements. I could have easily made mistakes in my measurements since the rulers were not long enough. Also, I do not agree that the Golden Ratio determines someone's beauty. Sure, it might just be mathematical, but I feel that simply having a face structure based on the Golden Ratio is not sufficient enough to determine beauty. Regardless of my opinion, I do beieve that the Golde Ratio and the math behind it all is amazing. 

Fibonacci: Reflective Essay

Word Count: 791

Golden Ration in Human Body
There far more similarities within this world's nature and our own bodies than we ever thought about. The similarities between the pyramids in Egypt, Leonardo da Vinci's Mona Lisa, snails, etc. all boils down to one mathematical ratio known as the Golden Ratio, which approximates to 1.168. This numbers begins to appear in many measurements, but begins to reoccur after the thirteenth number in the series. This series is based on the sum of two preceding numbers and when they are divided, they follow the Golden Ratio. In fact, some designers have used the Golden Ratio without realizing that they were following nature's common ratio. This ratio is so common that it even appears in the average human body as the ideal proportional ratio that allows one to be aesthetically pleasing. We can find the Golden Ration between the height of the navel and the foot, distance between the fingertip and the elbow, the distance between the shoulder line and the top of the head, the distance between the navel and the knee, etc. The Golden Ration even appears in our teeth's measurements and the length of the face over the width of the face. A study in 1985-1987 revealed that the Golden Ratio was in the structure of the lung, which is asymmetrical in the ratio of 1.618.

The Beauty of the Golden Ratio
As previously mentioned, the Golden Ratio is a repetitive number that was found in the famous Egyptian pyramids in Giza. It has also been found in the Greek Parthenon, which was constructed in 447 B.C. to 472 B.C. This was far before the Italian mathematician Fibonacci discovered the Fibonacci sequence terms (makes up the Golden Ratio). Even though the Golden Ratio does appear in very ancient or somewhat older buildings, it still appears in modern architecture. The Golden Ratio was used all throughout the Renaissance years when Renaissance artist designed Norte Dane between the 12th and 15th century. The UN Building also has the Golden Ratio in its structure since the width of the building to the height of the every ten floors leads to the Golden Ratio.

Le Blog: The Golden Ratio Revisited
The Golden Ratio has also been known as the "Divine Proportion" as you have seen since after all, it does lead to perfect structures of buildings such as the ones I previously stated. Corbusier's designs were all great examples of the architectural beauty based on these mathematical proportions. When Leonardo da Vinci drew the "Vitruvian Man", he had created an ideal human body that was completely based on the Golden Ratio. The distances and ratios between his body proportions come to make up the Golden Ratio. He also represents the Golden Ratio in his other masterpieces, such as the Mona Lisa and "De Divine Proportione". Other than the architecture and the paintings, the Golden Ratio appears on simply Mother Nature. The Golden Ratio allows plants like flowers and pineapples to be aesthetically pleasing to the eye. It is no doubt that the Golden Ratio appears on many objects and justifies the reason why some objects are more beautiful than others.

Nature's Number: 1.6180033988...
There have been many fascinating numbers that often intrigue people, such as the famous Pi or the concept of zero. There are many numbers and patterns to pay attention to and even though the Golden Ratio appears everywhere, it is often ignored. It is nature's number that has been forgotten. One can figure out how "phi" come to be by breaking down a square into part rectangles. After breaking down rectangles into smaller sections, one will get a series of small squares and rectangles that are "just right". When the bottom right corners are connected, they create a spiral that appears in nature, oh, so many times. The Golden Ratio has allowed nature to be placed into a prefect perspective.

Personal Reflection
Although I must agree that I am not a mathematical genius, I am greatly fascinated by the Golden Ratio. Yes, I do believe that the Golden Ratio does exist in many parts of nature's beauty, but I must admit that I do not see it much in the human body. It is hardly impossible for a person to be "perfect", so maybe this beautiful perfection only exists in architecture and other plants. Wherever the Golden Ratio exists, it is truly amazing to find such patterns in completely odd or different things. Whether it comes from an ancient architectural masterpiece to someone's naval and knee, or to a simple snail, the Golden Ratio has made a lot of contribution to the way we see our surroundings. The Golden Ratio allows us to admire beauty at its very best.