-Rachel Kim- The Golden Ratio This is the Great Pyramid of Giza + Golden Ratio The Golden Ratio is a mysterious number (known as Phi which is a Greek word) that approximately equals to 1.618 and has been discovered in many places, such as art, architectures, humans, and plants. According to history of mathematics, Phi was first understood and used by the ancient mathematicians of Egypt.Phidias, a Greek sculptor and mathematician, studied Phi and used the Phi in many designs of his sculptures, such as the statue of the god Zeus in Olympiad. There are many different names for the golden ratio; The Golden Mean, Phi, the Divine Section, The Golden Cut, The Golden Proportion, and The Divine Proportion History of Golden Ratio Formula Explanation The Golden Ratio is the quotient of two quantities. The equation is half the base, the slant height and the height from the vertex, when that half the base equal to 1, the slant height would equal to the square root of phi. Dividing slant height s by half base gives

186.369 ÷ 115.182 = 1.61804

which differs from (1.61803) by only one unit in the fifth decimal place. The Great Pyramid Of Giza with and without the stone casing The Great Pyramid of Giza (also known as the Pyramid of Khufu or the Pyramid of Cheops) is the oldest and largest of the three pyramids in the Giza Necropolis and is bordering what is now Cairo, Egypt. It is the oldest of the Seven Wonders of the Ancient World, and the only one to remain largely intact. Egyptologists believe that the pyramid was built as a tomb for fourth dynasty Egyptian Pharaoh Khufu over a 10 to 20 year period concluding around 2560 BCE. Its height is 146.5 meters (481 feet), which makes the Great Pyramid the tallest man-made structure in the world for over 3,800 years. Originally, the Great Pyramid was covered by stone casing that formed a smooth, pure white outer surface and what is seen today is the rough core structure. Some of the casing stones that once covered the structure can still be seen around the base. All around us! Fibonacci Sequence Mona Lisa, Last Supper, Parthenon The Golden Ratio can be found anywhere and everywhere where you least expect it to be. It could be a painting or it could be in the worlds most tallest pyramid. In the painting Mona Lisa's, her face is a perfect golden rectangle, according to the ratio of the width of her forehead compared to the length from the top of her head to her chin. Another painting, called "Last Supper," contains a golden ratio in several places, appearing in both the ceiling and the position where the people sit. Also, the painting 'Golden Stairs' have golden ratios everywhere. The golden sections appear in the stairs and the ring of the trumpet carried by the fourth woman from the top. The lengths of the gowns from the sash below the breast to the bottom hem hits the phi point at their knees. The width of the interior door at the back of the top of the stairs is a golden section of the width of the top of the opening of the skylight. The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The next number is found by adding up the two numbers before it. Here is a longer list:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, .......

Another interesting fact is that you can find the golden ratio by the Fibonacci sequence.

Also, the man who discovered the Fibonacci sequence was Leonardo Pisano Bogollo whose nickname was Fibonacci which roughly means "Son of Bonacci". He also helped spread through Europe the use of Hindu-Arabic Numerals (like our present number system 0,1,2,3,4,5,6,7,8,9) to replace Roman Numerals (I, II, III, IV, V, etc).

From my point of view, the golden ratio is getting easier for me and I am able to really understand what the golden ratio is about. I have learned new facts about nature such as the Fibonacci sequence and of how the pyramids took 20 years to be made and of how the ancient Egyptians used the golden ratio. I have also learned of different measurements such as the ‘cubits’. This investigation has been hard to understand at first, but gradually became easier and I now know how to use the website, Prezi. It has also been very fun as we could decorate and create our Prezi any way we wanted. Reflection+Evaluation Conclusion-Summary The Golden Ratio is hard and it takes time to understand the formula and how it evolves around us every day. Its very surprising how the Golden Ratio and Fibonacci Sequence can be found anywhere such as the arrangement of the seeds of a sunflower or the face of Mona Lisa. THE END 7G This is a picture of a perfect Fibonacci spiral

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# The Golden Ratio

The Golden Ratio in the pyramids

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