The Golden Mean
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The document discusses the Golden Mean (also called the Golden Ratio or Golden Section), which is a ratio of approximately 1.618 that is found throughout nature and considered aesthetically pleasing. It relates to the Fibonacci sequence and can be used to create Golden Rectangles and spirals. Many artists have incorporated the Golden Mean into their works, such as Leonardo Da Vinci in the Mona Lisa. Examples of the Golden Mean can also be found in architecture, music, and nature.
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- Face To Face
- Interlocking
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TRANSFORMATION
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one or more of a structures dimensions
are transformed
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of the Roof decreases
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shape divided into
many....
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form of the Building a
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elements are added into the design .
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change and the gaps between are giving this
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Edge to Edge
Transformation
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connecting ....
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In this Building, the roofs of the
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another...
In this Building, the floors of the
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positive) respectively...Geometry concepts in architectural design
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Mathematics is the study of topics such as quantity, structure, space, and change. It is used in many fields including science, engineering, and finance. Art includes activities that create visual works, performing arts, literature, and other media. Mathematics and art are closely related through concepts like fractals, the golden ratio, symmetry, patterns, and geometric shapes that appear in both natural and human-made works. Many artists use mathematical principles in their compositions to achieve balance, proportion and other aesthetic goals.Proportion
Proportionsmitchem
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The document discusses the golden ratio and its appearances in nature and art. It is a naturally occurring number that is represented by phi and appears in growth patterns like seashell spirals and ferns. Ancient Greeks used it in architecture for a feeling of natural order and integrity. Artists since have also used it for its aesthetically pleasing proportions. The document instructs students to choose a natural pattern using the golden ratio, like a nautilus shell or sunflower seeds, and create an original design inspired by it.medieval European mathematics
medieval European mathematicsdhayjanebananlopez
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The document discusses medieval mathematics from the 12th-14th centuries. It provides biographies of several important medieval mathematicians including Fibonacci, who introduced the Fibonacci sequence to Western Europe and studied rabbit populations. It also discusses Nicole Oresme who proved the divergence of the harmonic series and Giovanni di Casali who analyzed accelerated motion graphically. The document notes that during this time, Europeans learned mathematics from Arabic sources that had been translated to Latin.MEM RES.docx
MEM RES.docxJosePlasabas
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During the Dark Ages in Europe from the 4th to 12th centuries, mathematical study stagnated while Chinese, Indian, and Islamic mathematicians advanced the field. European knowledge was limited until the 12th century when trade with the East began spreading foreign ideas and practical needs drove more study of arithmetic. The 15th century printer furthered mathematics education, and figures like Fibonacci, Oresme, and Regiomontatus made important contributions that advanced European mathematics.MEM RES.docx
MEM RES.docxJosePlasabas
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During the Dark Ages in Europe from the 4th to 12th centuries, mathematical study stagnated while Chinese, Indian, and Islamic mathematicians advanced the field. European knowledge was limited until the 12th century when trade with the East began spreading foreign ideas and practical needs drove more study of arithmetic. The 15th century printer furthered mathematics education, and figures like Fibonacci, Oresme, and Regiomontatus made important contributions that advanced European mathematics.
Fibonacci sequence and golden ratio
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The document discusses Fibonacci numbers and the golden ratio, explaining how Fibonacci discovered the Fibonacci sequence by modeling rabbit populations and how ratios between numbers in the sequence converge on the golden ratio. It provides many examples of how the golden ratio appears frequently in nature, art, architecture, and the human body, demonstrating its aesthetic appeal and role in design.Fibonacci Sequence and Golden Ratio
Fibonacci Sequence and Golden Ratiovayappurathu
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The document discusses Fibonacci numbers and the golden ratio, explaining how Fibonacci discovered the Fibonacci sequence by modeling rabbit populations and how ratios between numbers in the sequence converge on the golden ratio. It provides many examples of how the golden ratio appears frequently in nature, art, architecture, and the human body, demonstrating its aesthetic appeal and role in design.Math, Art, and Composition
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This document discusses how mathematics, specifically geometry and the rule of thirds and golden ratio, have been used by artists throughout history to create visually pleasing compositions. The rule of thirds involves dividing the canvas into thirds and placing focal points of the artwork near the intersecting lines. The golden ratio is based on the Fibonacci sequence discovered by Leonardo Pisano, where each number is the sum of the previous two. When applied to artwork, the golden ratio highlights areas near the rule of thirds as natural focal points. Examples are given of how the golden ratio can be seen in nature and in art and architecture.Golden Mean
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this is a great bit of research examples the explain where the golden mean occurs in nature, humans, archtecture for composition.Computers in education final
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The golden ratio is a number approximately equal to 1.618 that is considered aesthetically pleasing. It arises from dividing a line into two parts where the ratio of the whole line to the longer part equals the ratio of the longer part to the shorter part. The golden ratio appears throughout nature and was used by ancient Greeks in sculptures and architecture. It relates to the Fibonacci sequence where the ratios of consecutive terms approach the golden ratio.THE_GOLDEN_RATIO_AND_ITS_APPLICATION_IN.pdf
THE_GOLDEN_RATIO_AND_ITS_APPLICATION_IN.pdfMarijaikoKuli
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The document discusses the golden ratio and its applications in design. It begins with an introduction to the golden ratio as a mathematical concept dating back to ancient Greeks. It then discusses how the golden ratio appears in nature and has been used in designs throughout history, including in things like the dimensions of the Parthenon temple and Great Pyramid of Giza. The document also explores how the golden ratio continues to be used in modern architecture and design, noting that it provides a pleasing and stable configuration for constructions.Maths in Art and Architecture Why Maths? Comenius project
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THIS EBOOK WAS PREPARED
AS A PART OF THE COMENIUS PROJECT
WHY MATHS?
by the students and the teachers from:
BERKENBOOM HUMANIORA BOVENBOUW, IN SINT-NIKLAAS ( BELGIUM)
EUREKA SECONDARY SCHOOL IN KELLS (IRELAND)
LICEO CLASSICO STATALE CRISTOFORO COLOMBO IN GENOA (ITALY)
GIMNAZJUM IM. ANNY WAZWNY IN GOLUB-DOBRZY (POLAND)
ESCOLA SECUNDARIA COM 3.尊 CICLO D. MANUEL I IN BEJA (PORTUGAL)
IES LVAREZ CUBERO IN PRIEGO DE CRDOBA (SPAIN)Recently uploaded (20)
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Principle and Practices of Animal Breeding Full Note
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Title:
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Other Link :
1.Introduction to computer network - /slideshow/lecture-notes-introduction-to-computer-network/274183454
2. Physical Layer - /slideshow/lecture-notes-unit-ii-the-physical-layer/274747125
3. Data Link Layer Part 1 : /slideshow/lecture-notes-unit-iii-the-datalink-layer/275288798
Target Audience:
Final year B.Sc. Computer Science students at Alagappa University seeking a solid foundation in Computer Network principles for academic.
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Dr. S. Murugan is Associate Professor at Alagappa Government Arts College, Karaikudi. With 23 years of teaching experience in the field of Computer Science, Dr. S. Murugan has a passion for simplifying complex concepts in Computer Network
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The Golden Mean
- 1. The Golden Mean By Susan Convery Foltz Broward College EPI 003 Technology February 8, 2009
- 2. The Golden Mean The Golden Mean is the divine proportion, or golden section, represented by the Greek letter phi 陸. It is one of those mysterious natural numbers like pi that seems to arise out of the basic structure of the universe. Phi appears clearly and regularly in the realm of things that grow and unfold in steps, especially living things, but also in art and architecture.
- 3. How to Calculate the Golden Mean: The Golden Mean is the ratio most pleasing to the eye. The ratio is the same as the ratio of the number 1 to Phi 陸 (1.6180339887) A Golden Rectangle
- 4. Fibonacci Numbers and the Golden Mean The 11th century Mathematician, Leonardo of Pisa, derived a formula for the same relationship commonly found in nature. All Fibonacci Series begin with 0, 1 and every number thereafter is the sum of the two previous numbers. 0,1,1, 2, 3, 5, 8, 13, 21, 34. As a Fibonacci rectangle grows larger it resembles the perfect proportions of the Golden Mean A Fibonacci Sequence A Golden Sequence
- 5. To Create a Golden Spiral We now draw a quarter circle on each square and bring all the squares back to where they were in the original rectangle. There then emerges a winding (logarithmic) spiral. By spinning the pinwheel in clockwise or counterclockwise direction, the spiral pattern implodes into the pole or expands outwardly.
- 6. Examples of Golden Spirals found in nature
- 7. The Golden Mean in Art When a building or artwork is designed to incorporate phi 陸 it has the purest possible proportions and is the most pleasing to the eye. Since painting and photography are most often produced on a rectangular field we can use this formula to create a Golden Rectangle and find the most harmonious location for our center of interest.
- 8. The Golden Mean in Music and Architecture The early Greeks used these formulas to produce the Parthenon Mozarts sonatas seem to divide into parts at the golden section of the total time of the work. In Beethovens 5th symphony the opening motto is repeated at exactly the golden section of the work. 油
- 9. Famous Artists and the Golden Mean Leonardo Da Vinci was a great Italian Renaissance painter, as well as a scientist and inventor, who lived in 15th century. In his art, Da Vinci carefully examined the proportions of the human body and found many occurrences of the golden ratio and golden rectangles. Follow this link for more on the Mona Lisa http:// britton.disted.camosun.bc.ca/monalisa.swf
- 10. More Artists who used the Golden Mean Georges Seurat Henri Cartier-Bresson Piet Mondrian
- 11. Your Assignment: Find 2 examples of artwork that is based on the Golden Mean Find 2 examples in a magazine of advertising which uses the Golden Mean Find 2 examples in nature of the Golden Mean Create a work of art based on the Golden Mean. References: http://www.bgpu.ru/intel/Material/mc_04/master/shelli/photojournalism/Photographs%20before/student_samples/student_presentation/Golden_Mean.ppt http://www.mlahanas.de/Greeks/GoldenSection.htm http://www.freemasonry.bcy.ca/symbolism/golden_ratio/index.htm http://techcenter.davidson.k12.nc.us/ruth/math/mathconnect2.ppt http://britton.disted.camosun.bc.ca/monalisa.swf http://www.princetonol.com/groups/iad/lessons/high/Grace-golden.htm http://community.middlebury.edu/~harris/Humanities/TheGoldenMean.html