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The Golden Ratio

In The Great Pyramid and Nature

Celeste Walsh

on 13 September 2012

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Transcript of The Golden Ratio

The Golden Ratio By Celeste Walsh The Golden Ratio (also known as The Golden Mean or Perfect Proportion) is a number used in art, music, architecture, advertising and is found in nature. The idea is that its number - 1.618 is said to use a balance we see all around us in our daily lives, The result is an object created using the Golden Ratio just feels and looks right to the majority of people. What is the Golden Ratio? http://www.mathsisfun.com/numbers/golden-ratio.html The Ancient Egyptians applied the Golden Ratio to the construction of the Great Pyramid. The cross section of the pyramid is in the shape of a right angle - known as "The Egyptian Triangle". The ratio of the slant height or hypotenuse of the pyramid to half the base height is 1.618, as shown in this equation. The Golden Ratio
In Relation to
The Great Pyramid
In a line: How to find
the Golden Mean If you divide a rectangle's length by its width and you get approximately 1.618, then that rectangle is considered to be a Golden Rectangle. In a rectangle: You can find a Golden Line Segment by dividing a line into 2 parts. One part would have to be 1 unit long and the other 1.618 units long. You could
double the line, but the segments must stay in the same ratio. The Golden Ratio
in Nature Phi, the symbol for the Golden Ratio http://britton.disted.camosun.bc.ca/goldslide/jbgoldslide.htm http://mathematics.knoji.com/interesting-facts-about-the-golden-ratio-in-nature-art-math-and-architecture/ A Guide to 356 / 220 = 1.618 (cubits) (cubits) hypotenuse or slant height in cubits half of base length
in cubits Fibonacci Numbers are naturally occurring patterns that are found in nature. The pattern discovered by Fibonacci of Pisa goes like this...

1, 1, 2, 3, 5, 8, 13, 21... each number is the sum of the previous 2. Fibonacci Numbers Pineapples, seed heads, pine cones, sunflowers, galaxies and shells are just to name a few aspects of nature that use the Golden Ratio. Plants naturally grow new cells in spirals, because each new cell is formed after a turn. http://www.trade-ideas.com/Glossary/Fibonacci.html http://science.howstuffworks.com/environmental/life/evolution/fibonacci-nature1.htm Most measurements in Ancient Egypt were in cubits - the average length of a forearm from the elbow to the very tip of the middle finger. The Great Pyramid is measured in cubits. The base is approximately 440 royal cubits, and the perpendicular height is about 280 royal cubits. A royal cubit is worth 52.5 cm in metric measurements. Measurements http://en.wikipedia.org/wiki/Cubit http://en.wikipedia.org/wiki/Ancient_Egyptian_units_of_measurement This Romanesco cauliflower's spiral follows the Fibonacci sequence There have been many speculations about who built the Great Pyramids, whether it be aliens or Ancient Egyptians. And if it was the Ancient Egyptians, did they knowingly build the Great Pyramid to the scale of the Golden Ratio, or was it a lucky coincidence?

I believe that the Ancient Egyptians did not create the Great Pyramid to the proportions purposely, and modern scientists have only later discovered the coincidence.

Mathematicians such as Pythagoras studied the Golden Ratio in ancient Greek times because it frequently appeared in geometry. The Egyptians started constructing the Great Pyramid around 2589 BCE. The Ancient Greeks used the Golden Ratio to build the Parthenon around 448-432 BCE - over 2000 years later. The Ancient Egyptians would not have known about the Golden Ratio at that stage, as the construction of The Great Pyramid was a milestone in their civilization, and they would have documented plans of the construction in relation to the Golden ratio. I think that the Ancient Egyptians only built the Great Pyramid to the Perfect Proportion because they believed it looked more attractive with the current lengths, and to fit Cheops' tombs and chambers inside it so that it also stood upright. Evaluation http://tinyurl.com/9y6gh53 or http://preview.tinyurl.com/9y6gh53
or http://books.google.com.au/books?id=FMYCsT-cZDUC&pg=PA133&lpg=PA133&dq=the+main+idea+behind+the+golden+ratio&source=bl&ots=bgc5San0HM&sig=Hd_pJCeAJ6rudisjmuOZzCwLcXI&hl=en&sa=X&ei=AT1FUJLpEu6MmQXLqoCADw&ved=0CC4Q6AEwAA#v=onepage&q=the%20main%20idea%20behind%20the%20golden%20ratio&f=false Bibliography http://www.mathsisfun.com/numbers/nature-golden-ratio-fibonacci.html The number 1.618 is an irrational number - it cannot be written as a simple fraction. FACTS! It can be defined in terms of itself... Can be expanded into a 'continued fraction' that is infinite... The ratio of any 2 consecutive Fibonacci numbers is very close to the Golden Ratio. The Golden Spiral http://www.teachervision.fen.com/math/resource/5989.html In sunflowers, the seeds are arranged so as to provide more space for seeds. They are tightly packed with 2 interlocking spirals - one moving clockwise and the other counterclockwise. Often, the number of clockwise spirals is 34 and anticlockwise spirals 55 - both Fibonacci numbers. The Golden Spiral is shown in the seed head because the seeds grow outwards from the center. The product is very close to the Golden Ratio when you divide the rows of seeds by each other. This will leave you with your square and another Golden Rectangle. You can repeat this process indefinitely, as the resulting Golden Rectangle can always be partitioned into smaller and smaller units. You can then draw a spiral connecting the points where the Golden Rectangle has been divided into squares, as can be seen in the animation below. The Golden spiral can be found in galaxies such as the Milky Way, DNA, fingerprints, whirlpools, shells, plants, and even hurricanes! A Golden Spiral can be developed by taking a part out of a Golden Rectangle so that the short side of the rectangle is equal to its sides. By doing this, you will get a square and another Golden Rectangle. Because the derived Golden Rectangle can always be sectioned into smaller units, this process can be repeated forever. When you connect the points (circled) where the Golden Rectangle has been sectioned into squares by drawing a spiral, you will end up with the Golden Spiral. This can be seen in this picture. THANKS FOR WATCHING!!!! I HOPE YOU HAVE LEARNED A LITTLE SOMETHING ABOUT THE GOLDEN RATIO AND ITS RELEVANCE TO THE GREAT PYRAMID AND NATURE!!!!
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