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# the golden ratio in architecture

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Tweet## Nicole Svoboda

on 14 September 2012#### Transcript of the golden ratio in architecture

The golden ratio in architecture The Golden ratio is a ratio when a larger number is divided by a smaller number and equals the approximate number of 1.618. This can be found in art, music, nature, architecture and in the way we think. This sign is resented by the Greek Alphabet letter Phi. This sequence of numbers (because it is an ever occurring number) when measured out on a picture, is supposed to appealing to the human eye. The person who found out the Golden ratio was Fibonacci. The sequence continued by adding the last two numbers. For example, 0,1,1,2,3,5,8,13,21,34, etc. The Golden Ratio can be also pictured as a star where the purple line and the blue line equal the Golden Ratio and the green and red line and the two combined lines of blue and purple all equal each other and the Golden ratio. The Great Pyramid of Giza and the Golden Ratio The Golden Ratio can be found in the great Pyramid of Giza when you divide the sloping height by halving the side length. What is the Golden Ratio? Fibonacci's sequence Fibonacci's sequence is very close to equaling the Golden Ratio. This is proven by dividing one of the numbers in the sequence by the previous number.

Example:

34 21 1.6190476...

21 13 1.6153846...

Fibonacci discovered this sequence when researching breading patterns of rabbits in ancient Greece. Pythagoras' Theorem Pythagoras' Theorem: a² + b² = c². This rule declares that the sides of the squares a and b added together will equal the sides of the square c. But this rule only works for right angled triangles. The Egyptian method of measuring The Egyptians had a very different way of measuring things. There measurements were based on body lengths. A digit was approximately 19mm; a palm was approximately 76mm and four digits fitted in a palm; a hand was approximately 95mm and five digits fitted in a hand; a small cubit was approximately 456mm and twenty-four digits or six palms fitted in a small cubit and the Royal Cubit (which was made out Granite) was 524mm. For the next questions, the measurement will be in cubits. The Slope Height If you apply Pythagoras' theorem to this, you will get:

a= height: 280 cubits

b= half side length: 441.9925 2

a²+b²=slop height²

280+441.9925 2

280²+219.99625²=slope height²

78400+48698.35=slope height²

129798.35=slope height

sqrt 356.090559=slope height Where is the Golden ratio found

in the pyramid? The Golden ratio can be found in the Great pyramid of Giza if we we divide the slope height by halving the side length:

Slope height half the side length

356.090559 (439.9925 2)

356.090559 219.99625

=1.6216074

1.6216074 is so close to the Golden ratio with only 0.0005444785288

off because the Golden ratio

is 1.62103398875 The Golden ratio in buildings The Golden ratio can be found in many different buildings such as: Parthenon, Notre Dame and The Taj Mahal. The Parthenon The Parthenon (which was built in 423BCE) designers made sure that the Golden ratio was applied to all the rectangles as well as the roof to the frieze, the width of all the pillars and the gaps between all of them. The Notre Dame The Notre Dame, which was built between 1345 in France, architectures made sure that the Golden ratio was in the first, second and third floor. As well as the two towers and the gap between them. The Taj Mahal The Taj Mahal (which was made in 1653) was made with the Golden Ratio in the height of the arches to the width of the arches. Conclusion I believe thought out this investigation that the Egyptians did not know about the Golden ratio because in the time that they built the Great Pyramid of Giza, the Golden Ratio had not be found that it was either a huge coincidence or that another civilization or species had built them such as aliens. Also, the scribes would have recorded it in there book known as the 'Pyramid Text' when there is no recording of it. Also, the other pyramids we not as accurate as The Great Pyramid of Giza and also they had many practice pyramids so I think that they flunked the making this Pyramid because this is the only other expatiation.

Full transcriptExample:

34 21 1.6190476...

21 13 1.6153846...

Fibonacci discovered this sequence when researching breading patterns of rabbits in ancient Greece. Pythagoras' Theorem Pythagoras' Theorem: a² + b² = c². This rule declares that the sides of the squares a and b added together will equal the sides of the square c. But this rule only works for right angled triangles. The Egyptian method of measuring The Egyptians had a very different way of measuring things. There measurements were based on body lengths. A digit was approximately 19mm; a palm was approximately 76mm and four digits fitted in a palm; a hand was approximately 95mm and five digits fitted in a hand; a small cubit was approximately 456mm and twenty-four digits or six palms fitted in a small cubit and the Royal Cubit (which was made out Granite) was 524mm. For the next questions, the measurement will be in cubits. The Slope Height If you apply Pythagoras' theorem to this, you will get:

a= height: 280 cubits

b= half side length: 441.9925 2

a²+b²=slop height²

280+441.9925 2

280²+219.99625²=slope height²

78400+48698.35=slope height²

129798.35=slope height

sqrt 356.090559=slope height Where is the Golden ratio found

in the pyramid? The Golden ratio can be found in the Great pyramid of Giza if we we divide the slope height by halving the side length:

Slope height half the side length

356.090559 (439.9925 2)

356.090559 219.99625

=1.6216074

1.6216074 is so close to the Golden ratio with only 0.0005444785288

off because the Golden ratio

is 1.62103398875 The Golden ratio in buildings The Golden ratio can be found in many different buildings such as: Parthenon, Notre Dame and The Taj Mahal. The Parthenon The Parthenon (which was built in 423BCE) designers made sure that the Golden ratio was applied to all the rectangles as well as the roof to the frieze, the width of all the pillars and the gaps between all of them. The Notre Dame The Notre Dame, which was built between 1345 in France, architectures made sure that the Golden ratio was in the first, second and third floor. As well as the two towers and the gap between them. The Taj Mahal The Taj Mahal (which was made in 1653) was made with the Golden Ratio in the height of the arches to the width of the arches. Conclusion I believe thought out this investigation that the Egyptians did not know about the Golden ratio because in the time that they built the Great Pyramid of Giza, the Golden Ratio had not be found that it was either a huge coincidence or that another civilization or species had built them such as aliens. Also, the scribes would have recorded it in there book known as the 'Pyramid Text' when there is no recording of it. Also, the other pyramids we not as accurate as The Great Pyramid of Giza and also they had many practice pyramids so I think that they flunked the making this Pyramid because this is the only other expatiation.