Send the link below via email or IMCopy
Present to your audienceStart remote presentation
- Invited audience members will follow you as you navigate and present
- People invited to a presentation do not need a Prezi account
- This link expires 10 minutes after you close the presentation
- A maximum of 30 users can follow your presentation
- Learn more about this feature in our knowledge base article
Do you really want to delete this prezi?
Neither you, nor the coeditors you shared it with will be able to recover it again.
Make your likes visible on Facebook?
You can change this under Settings & Account at any time.
Great Pyramid of Giza and Golden Ratio
Transcript of Great Pyramid of Giza and Golden Ratio
The faces of the Pyramid are not right angles though, they are isosceles triangles. As seen in this diagram, there is a right angle triangle in the pyramid. A straight line from the apex down to the middle of the base, and a straight line from the middle of an edge to the middle of the base. Right angle Hypotenuse How does the Pythagorean Theorem Relate? Formula and Calculation for slanted height (A squared + B squared) = Square root of C squared
(280 x 280) + (219.99625 x 219.99625) = Square root of C squared
78400 + 48398.35 = Square Root of C squared
126798.35 = C squared
Square Root of 126798.35 = C
356.0875594 = C A=Height B=Edge to Mid-point C=Slanted Height This will be measured in Cubits Calculation for Great Pyramid of Giza's Ratio The formula for working out the Ratio of a pyramid is:
C divided by (1/2 base's edge length)
356.0875594 divided by (1/2 439.9925)
356.0875594 divided by 219.99625
= 1.618607405/Golden Ratio Bases edge length = 2 x edge to mid-point
Bases edge length = 2 x 219.99625
Bases edge length = 439.9925 Conclusion and Summary Back in the ancient times there must of been some knowledge of the Golden Ratio. From my calculations, the Great Pyramid has approximately a Ratio of 1.618607405. The Golden ratio is approximately 1.6180339887. The ancient Egyptians also, must of had a similar theorem as the Pythagorean theorem, as the Pythagorean theorem wasn't around then. This is why The Great Pyramid of Giza looks so great, because of its perfect proportion Parthenon has the Golden Ratio The Parthenon was built by the ancient Greeks with the Golden Ratio. They new about the Golden Ratio and thought it was pleasing to the eye, architects built on purpose. So, they built the Parthenon with the Golden Ratio. The Parthenon is the perfect example of the Golden Rectangle. There are many Golden rectangles in this figure. All the lines in this figure show where the Golden Rectangles' dimensions are. The Parthenon's front side is almost exactly a Golden Rectangle. The whole front side is one Golden Rectangle, from the stairway to the top of the pillars there is one, from the eave down and up there is one etc. The formula for the ratio of a rectangle is Length divided by Width (L divided by W). When using this formula on the Parthenon, on any of those rectangles it comes out approximately 1.618. When you divide the length and the width, it would come up approximately as the Golden Ratio. Inside the rectangle, there is also a spiral that can be divided into smaller sections approximately the Golden Ratio. There are triangles that fit into the Golden Ratio because they have sides that each one makes up the Golden Ratio within the next largest size. In the rectangle there are smaller rectangles when there Dimensions (Length and Width) are divided, it comes out as a number related to the Golden Ratio. Dimensions of Parthenon and Formula for Ratio L=Length of rectangle (front view) W=Width of rectangle (front view) L W = Ratio
22.19942631m 13.72 = Ratio
1.618033987m = Ratio The length and width is actually a different dimension in the 3D shape but in a front, rectangle view it the Length and width. This ratio is very close to golden Ratio: 1.6180339887 Conclusion and Summary The Golden Ratio is a very interesting theory because of the belief that it looks better to the naked eye. It deserves to be studied more into as there is a lot of unanswered questions about it. Like, why does it always end up to be approximately 1.618 and look perfect to the naked eye. Many natural and architectural designs do equal to the Golden Ratio e.g plants, shells, and even humans have parts of the body equivalent to the Golden Ratio (finger bones, face parts etc). There are many types of shapes that can be related to the Golden Ratio like triangles, rectangles and spirals. They are used in our modern day life for architecture - to make the construction a better looking merchandise. I think that this is a good idea to use it as a strategy or key tool when making designs or products. Thank
I think that the Egyptians used the Golden Ratio before. From all my research, the Egyptians did actually plan the Pyramid on walls and scrolls. On these things, were diagrams and pictures of the mathematical formulas and terms. On these there were parts wanting to design The Great Pyramid of Giza equivalent to the Golden Ratio. The only mystery I find hard to understand is that the Golden Ratio was thought of, around a thousand years ago, maybe even more. The ancient Egyptians must of had some strategy, or even knew about the Fibonacci Number Sequence, to get the Pyramid that accurate. No one knows. Do you know It's a mystery Or a World Wonder! What do you Think? Used in the Ancient times as a measurement. Everyone had a different hand size so they used one statue as the official cubit.