### Present Remotely

Send the link below via email or IM

CopyPresent to your audience

Start 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?

Connect your Facebook account to Prezi and let your likes appear on your timeline.

You can change this under Settings & Account at any time.

# Great Pyramid of Giza and Golden Ratio

They relate.

by

Tweet## gabriel ioukhnovitch

on 5 September 2012#### Transcript of Great Pyramid of Giza and Golden Ratio

Golden Ratio and the Great Pyramid of Giza The Golden Ratio is when the ratio of an object, when the larger number (length) and the smaller number (width) divided equals approximately 1.618. The Golden ratio originates from the Fibonacci sequence, discovered by Leonardo Fibonacci. The Fibonacci sequence is basically a pattern of numbers where the 2 numbers before a number add up to it. e.g 1,1,2,3,5,8,13,21... It is thought to be that the golden ratio makes things look better to the naked eye. The Golden Ratio can refer as the Golden Mean, Golden Number, Divine Section, Golden Cut, Golden Proportion, Golden Section and Divine Proportion. In the Greek Alphabet the Golden ratio is is called Phi and the symbol is as shown: Many objects of the world-natural or man built- do equal to the golden ratio. For example: The Mona Lisa and the Great Pyramid of Giza. The Golden Rectangle has perfect proportion sides and it's ratio is the Golden ratio: . The Great Pyramid of Giza One of the wonders of the world in Egypt, the Great Pyramid of Giza has also got a Golden Ratio. It's angles are almost perfect and this is what makes the Pyramid look good to the naked eye. Golden Triangles are found on the Great Pyramid of Giza. To find out what the ratio of the Pyramid is, you need to use the Pythagorean Theorem (this is to work out the slope height). If a human was to choose out of three rectangles, of which one was the most pleasing, and there was a rectangle with perfect proportions. The average human would choose the one with the perfect proportions. The golden rectangle, if you cut out a rectangle the result is a golden rectangle. Also, the golden rectangle contains a Golden Spiral can be cut into smaller sections approximately the Golden Ratio. It is almost impossible for a human to measure the slope height of the Pyramid Physically. The slope height can be worked out by using this theorem though. The Pythagorean Theorem does state that any right angle triangle, the square opposite to the right angle (the Hypotenuse) equals the sum of the other 2 squares whose sides meet to the right angle. The formula is .

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

You Evaluation

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.

Full transcriptThe 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

You Evaluation

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.