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The Golden Mean The Mathematical Formula of Life Life Adapted from Adapted from Grace Hall, Wilkes Central High School in Wilkesboro, NC.

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Presentation on theme: "The Golden Mean The Mathematical Formula of Life Life Adapted from Adapted from Grace Hall, Wilkes Central High School in Wilkesboro, NC."— Presentation transcript:

1 The Golden Mean The Mathematical Formula of Life Life Adapted from Adapted from Grace Hall, Wilkes Central High School in Wilkesboro, NC

2 The poet John Keats, in his Ode on a Grecian Urn, said: "Beauty is truth, truth beauty," - that is all Ye know on earth, and all ye need to know. The poet John Keats, in his Ode on a Grecian Urn, said: "Beauty is truth, truth beauty," - that is all Ye know on earth, and all ye need to know. What does he mean? What does he mean? This statement is the basis for the short story Beauty is Truth. This statement is the basis for the short story Beauty is Truth. Ode to a Grecian Urn

3 Keats is not the first person to consider the concepts or themes of beauty and truth. Keats is not the first person to consider the concepts or themes of beauty and truth. A short story with the theme of beauty and truth is trying to make meaning out of what makes something beautiful or true. A short story with the theme of beauty and truth is trying to make meaning out of what makes something beautiful or true. Today, well look at the following: Today, well look at the following: What is beauty? What is beauty? How is beauty measured? How is beauty measured? Goal: To understand the Golden Mean as a means of organizing a work of art. Goal: To understand the Golden Mean as a means of organizing a work of art. Beauty and Truth

4 The golden mean is the most mysterious of all compositional strategies. We know that by creating something visual based on the golden mean will be more likely to appeal to the human eye, but we dont know why. The golden mean is the most mysterious of all compositional strategies. We know that by creating something visual based on the golden mean will be more likely to appeal to the human eye, but we dont know why. Some scholars argue that the Egyptians applied the golden ratio when building the great pyramids, as far back as 3000 B.C. Some scholars argue that the Egyptians applied the golden ratio when building the great pyramids, as far back as 3000 B.C. Golden Mean

5 The Golden Mean Proportions The beautiful Golden Mean Proportions and the mysterious Fibonacci numbers have fascinated philosophers for thousands of years and are still the subject of inquiry in the field of art, architecture, music, botany, biology, astronomy, physics, and more. The beautiful Golden Mean Proportions and the mysterious Fibonacci numbers have fascinated philosophers for thousands of years and are still the subject of inquiry in the field of art, architecture, music, botany, biology, astronomy, physics, and more. So far, science has documented its existence, but no one has fully understood the complete mystery. So far, science has documented its existence, but no one has fully understood the complete mystery. Let's watch (6:57 min) Let's watch (6:57 min) Let's watch6:57 min) Let's watch6:57 min)

6 The Golden Mean The golden ratio is 1.618034 (or the Greek letter Phi Φ). The golden ratio is 1.618034 (or the Greek letter Phi Φ). The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13,... (add the last two to get the next). The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13,... (add the last two to get the next). Theres a mathematical ratio commonly found in naturethe ratio of 1 to 1.618that has many names. Most often we call it the Golden Section, Golden Ratio, or Golden Mean, but its also occasionally referred to as the Golden Number, Divine Proportion, Golden Proportion, Fibonacci Number, and Phi. Theres a mathematical ratio commonly found in naturethe ratio of 1 to 1.618that has many names. Most often we call it the Golden Section, Golden Ratio, or Golden Mean, but its also occasionally referred to as the Golden Number, Divine Proportion, Golden Proportion, Fibonacci Number, and Phi.

7 Have You Seen This? Note that each new square has a side which is as long as the sum of the latest two square's sides.

8 The Golden Rectangle The golden ratio is typically depicted as a single large rectangle formed by a square and another rectangle. The golden ratio is typically depicted as a single large rectangle formed by a square and another rectangle. You can repeat the sequence infinitely and perfectly within each section. If you take away the big square on the left, what remains is yet another golden rectangle, and so on. You can repeat the sequence infinitely and perfectly within each section. If you take away the big square on the left, what remains is yet another golden rectangle, and so on. Whats unique about this is that you can repeat the sequence infinitely and perfectly within each section. Whats unique about this is that you can repeat the sequence infinitely and perfectly within each section.

9 The Golden Triangle The golden ratio is also depicted as a triangle formed by a triangle and another triangle. The golden ratio is also depicted as a triangle formed by a triangle and another triangle. You can repeat the sequence infinitely and perfectly within each section. If you take away the big triangle, what remains is yet another golden triangle, and so on. You can repeat the sequence infinitely and perfectly within each section. If you take away the big triangle, what remains is yet another golden triangle, and so on.

10 The Parthenon Phi was named for the Greek sculptor Phidias. Phi was named for the Greek sculptor Phidias. The ancient Greeks also used the golden ratio when building the Parthenon, in Athens, in about 440BC. The exterior dimensions, form a perfect golden rectangle. The ancient Greeks also used the golden ratio when building the Parthenon, in Athens, in about 440BC. The exterior dimensions, form a perfect golden rectangle. Artists often use the Golden Mean in the creation of great works. Artists often use the Golden Mean in the creation of great works.

11 The Last Supper Artists throughout history, like Botticelli and Leonardo daVinci, have used the golden rectangle, or variations of it, as the basis for their compositions. Leonardo daVinciLeonardo daVinci Heres da Vincis painting, The Last Supper, with golden sections highlighted. Golden rectangles are still the most visually pleasing rectangles known, and although theyre based on a mathematical ratio. The appearance of this ratio in music, in patterns of human behavior, even in the proportion of the human body, all point to its universality as a principle of good structure and design.

12 Mona Lisa Many artists who lived after Phidias have used this proportion. Leonardo Da Vinci called it the "divine proportion" and featured it in many of his paintings, for example in the famous "Mona Lisa.

13 Da Vincis Vitruvian Man Leonardo Da Vinci depicts ratios of the lengths of body parts in his Vitruvian Man, which illustrates that the human body is proportioned according to the Golden Ratiosimilar to Euclid in 300 B.C. and before that, Pythagoras around 500 B.C.

14 The golden ratio involve seashell shapes, branching plants, flower petals and seeds, leaves and petal arrangements. TheGolden Mean in Nature The Golden Mean in Nature

15 The Golden Mean spirals are evident in an ordinary pinecone seen from its base where the stalk connects it to the tree.

16 Golden Mean in Ideal Beauty From Queen Nefertiti in 1350 BC to Angelina Jolie today, you can see that they both share similar facial proportions conforming to this ideal beauty. Beauty may be timeless after all.

17 Golden Mean is Everywhere Understand how you can use the golden mean in your visual projects for home, school, college, and future career. Understand how you can use the golden mean in your visual projects for home, school, college, and future career. Consider how advertisers use the golden mean to tap into your subconscious attraction to an ideal beauty and aesthetic (or beautiful) proportions. Consider how advertisers use the golden mean to tap into your subconscious attraction to an ideal beauty and aesthetic (or beautiful) proportions. Look for the golden mean everywhere. Look for the golden mean everywhere.

18 Golden Ratio Today, we looked at the following: Today, we looked at the following: What is beauty? What is beauty? How is beauty measured? How is beauty measured? Goal: To understand the Golden Ratio as a means of organizing a work of art. Goal: To understand the Golden Ratio as a means of organizing a work of art. Next, well do an activity to practice what weve learned. Next, well do an activity to practice what weve learned.

19 Activity 1. Take out a sheet of paper. 2. Find the artwork you used during the Beautiful Activity. 3. Take one transparency. See if you can find a pattern in the artwork that matches part or all of the grid. Note any patterns. 4. Switch transparencies with another student with a different grid. Note any patterns. 5. How many of you found that the artists were following the golden mean to design their artwork?

20 Quick Write Take out a sheet of paper. Take out a sheet of paper. Take out your Anticipation Guide hand out. Take out your Anticipation Guide hand out. Pick one statement you agree or disagree with. Pick one statement you agree or disagree with. Write one or more paragraphs describing why you agree or disagree with the statement. Write one or more paragraphs describing why you agree or disagree with the statement. Use evidence from your experience with the Beautiful Activity, Golden Mean Activity, and reading of Beauty is Truth to support your agreement or disagreement. Use evidence from your experience with the Beautiful Activity, Golden Mean Activity, and reading of Beauty is Truth to support your agreement or disagreement. When youre done, put your name, period, and date on your sheet of paper and turn it in. When youre done, put your name, period, and date on your sheet of paper and turn it in.


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