Golden ratio
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The document discusses the Golden Ratio and its applications. It begins by defining the Golden Ratio mathematically and describing the Fibonacci sequence. It then explains how the Golden Ratio appears in nature and has been used by artists, architects, and designers to achieve aesthetic proportions. Examples mentioned include the proportions of the human body, seashells, and plant structures, as well as applications in photography through the Rule of Thirds composition technique.
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PowerPoint Presentation on Golden Ratio
The document is a presentation on the golden ratio. It defines the golden ratio as an irrational number approximated to 1.618, often denoted by Greek letters tau or phi. It describes two quantities being in a golden ratio if the ratio between their sum and the larger quantity equals the ratio between the larger and smaller quantities. The golden ratio is used in architecture, painting, book design, nature, aesthetics, and perceptual studies. A golden triangle is an isosceles triangle where the smaller side is in golden ratio to the adjacent side, and they can be found in pentagrams and stellated polyhedra.
Golden ratio
The document discusses the golden ratio, also known as the divine proportion or golden mean. It is a number approximately equal to 1.618 characterized by the property that the ratio between the whole and the larger part is the same as the ratio between the larger part and the smaller part. The golden ratio is found throughout nature and is considered aesthetically pleasing in art and architecture. It can be constructed geometrically and is exhibited in the proportions of the human body as well as structures like seashells, snowflakes, and spirals in flowers. Famous artists like Leonardo Da Vinci incorporated the golden ratio into their works and structures like the Parthenon exhibit it in their dimensions.
The golden ratio
The Golden Ratio is a mathematical constant approximately equal to 1.618 that is found in art, architecture, and nature. It describes a proportion where a line is divided such that the ratio of the whole line to the longer segment is the same as the ratio of the longer segment to the shorter segment. The Golden Ratio was used by ancient Greeks and Egyptians to achieve beauty and balance in their structures. It also appears in the Fibonacci sequence of numbers and is believed to influence what humans perceive as aesthetically pleasing in faces and bodies.
Golden ratio
The document discusses the golden ratio. It defines the golden ratio mathematically as two quantities where the ratio of the sum to the larger quantity equals the ratio of the larger to the smaller quantity. This value is approximately 1.618. The golden ratio has appeared throughout history in art and architecture believed to be aesthetically pleasing. It also appears in nature. Mathematicians have further explored its properties. The use of the golden ratio can be traced back to ancient Egyptians and Greeks and it continued to be used and studied by many famous mathematicians and artists throughout history.
Golden Ratio: Definitions and Applications on Graphical Representations
This document discusses the golden ratio and its applications in various fields. It begins by defining the golden ratio and relations of size. It then discusses how the golden ratio can be found in geometry like the golden rectangle and pentagram. It also discusses its relationship to the Fibonacci sequence. The document notes that the golden ratio is found throughout nature and in proportions of the human body. It provides many examples of how the golden ratio has been used and can be found in architecture, art, photography, design grids, and more. It suggests this is why the golden ratio is so appreciated in these fields.
Golden ratio
The golden ratio is a proportion where the ratio of the longer part to the whole is equal to the ratio of the shorter part to the longer part. Many artists and architects have used the golden ratio in their works believing it creates aesthetically pleasing designs. Structures like the Parthenon, Taj Mahal, Pyramids of Giza, and UN Secretariat Building incorporate the golden ratio in aspects of their design like column heights, window widths, and geometric floor plans. The golden ratio is also found in patterns in nature like pinecones, shells, and the human face.
Golden ratio
The golden ratio is a mathematical constant approximately equal to 1.6180339887. It is the ratio between two quantities where the ratio of the whole to the larger part is equal to the ratio of the larger part to the smaller part. The golden ratio is found throughout nature and is considered aesthetically pleasing in architecture and art. It appears in structures like the Parthenon and in works by Leonardo Da Vinci. Fibonacci numbers approach the golden ratio as the numbers increase. While not always precise, the golden ratio approximates proportions found in plants, shells, the human body, and other biological systems.
Golden ratio
1) The document discusses the golden ratio and its prevalence in architecture throughout history.
2) Key examples discussed include the Egyptian pyramids, the Parthenon, Notre Dame Cathedral, the Eiffel Tower, the Taj Mahal, the UN Building, and the CN Tower, all of which incorporate proportions based on the golden ratio.
3) The golden ratio is a number that arises from divisions of lines according to specific proportions, and many architects have incorporated it into designs believing it creates pleasing aesthetics that reflect principles of harmony found in nature.
Recommended
PowerPoint Presentation on Golden Ratio
The document is a presentation on the golden ratio. It defines the golden ratio as an irrational number approximated to 1.618, often denoted by Greek letters tau or phi. It describes two quantities being in a golden ratio if the ratio between their sum and the larger quantity equals the ratio between the larger and smaller quantities. The golden ratio is used in architecture, painting, book design, nature, aesthetics, and perceptual studies. A golden triangle is an isosceles triangle where the smaller side is in golden ratio to the adjacent side, and they can be found in pentagrams and stellated polyhedra.
Golden ratio
The document discusses the golden ratio, also known as the divine proportion or golden mean. It is a number approximately equal to 1.618 characterized by the property that the ratio between the whole and the larger part is the same as the ratio between the larger part and the smaller part. The golden ratio is found throughout nature and is considered aesthetically pleasing in art and architecture. It can be constructed geometrically and is exhibited in the proportions of the human body as well as structures like seashells, snowflakes, and spirals in flowers. Famous artists like Leonardo Da Vinci incorporated the golden ratio into their works and structures like the Parthenon exhibit it in their dimensions.
The golden ratio
The Golden Ratio is a mathematical constant approximately equal to 1.618 that is found in art, architecture, and nature. It describes a proportion where a line is divided such that the ratio of the whole line to the longer segment is the same as the ratio of the longer segment to the shorter segment. The Golden Ratio was used by ancient Greeks and Egyptians to achieve beauty and balance in their structures. It also appears in the Fibonacci sequence of numbers and is believed to influence what humans perceive as aesthetically pleasing in faces and bodies.
Golden ratio
The document discusses the golden ratio. It defines the golden ratio mathematically as two quantities where the ratio of the sum to the larger quantity equals the ratio of the larger to the smaller quantity. This value is approximately 1.618. The golden ratio has appeared throughout history in art and architecture believed to be aesthetically pleasing. It also appears in nature. Mathematicians have further explored its properties. The use of the golden ratio can be traced back to ancient Egyptians and Greeks and it continued to be used and studied by many famous mathematicians and artists throughout history.
Golden Ratio: Definitions and Applications on Graphical Representations
This document discusses the golden ratio and its applications in various fields. It begins by defining the golden ratio and relations of size. It then discusses how the golden ratio can be found in geometry like the golden rectangle and pentagram. It also discusses its relationship to the Fibonacci sequence. The document notes that the golden ratio is found throughout nature and in proportions of the human body. It provides many examples of how the golden ratio has been used and can be found in architecture, art, photography, design grids, and more. It suggests this is why the golden ratio is so appreciated in these fields.
Golden ratio
The golden ratio is a proportion where the ratio of the longer part to the whole is equal to the ratio of the shorter part to the longer part. Many artists and architects have used the golden ratio in their works believing it creates aesthetically pleasing designs. Structures like the Parthenon, Taj Mahal, Pyramids of Giza, and UN Secretariat Building incorporate the golden ratio in aspects of their design like column heights, window widths, and geometric floor plans. The golden ratio is also found in patterns in nature like pinecones, shells, and the human face.
Golden ratio
The golden ratio is a mathematical constant approximately equal to 1.6180339887. It is the ratio between two quantities where the ratio of the whole to the larger part is equal to the ratio of the larger part to the smaller part. The golden ratio is found throughout nature and is considered aesthetically pleasing in architecture and art. It appears in structures like the Parthenon and in works by Leonardo Da Vinci. Fibonacci numbers approach the golden ratio as the numbers increase. While not always precise, the golden ratio approximates proportions found in plants, shells, the human body, and other biological systems.
Golden ratio
1) The document discusses the golden ratio and its prevalence in architecture throughout history.
2) Key examples discussed include the Egyptian pyramids, the Parthenon, Notre Dame Cathedral, the Eiffel Tower, the Taj Mahal, the UN Building, and the CN Tower, all of which incorporate proportions based on the golden ratio.
3) The golden ratio is a number that arises from divisions of lines according to specific proportions, and many architects have incorporated it into designs believing it creates pleasing aesthetics that reflect principles of harmony found in nature.
Golden mean
This document discusses the golden ratio and its applications. It begins by explaining the history of the golden ratio in mathematics and its use by ancient Egyptians and Leonardo Da Vinci. It then discusses why objects containing the golden ratio are pleasing to the human eye. Several examples are given of the golden ratio appearing in nature, including plant growth patterns, spiral shells, and the human face and body. Architectural examples like the Great Pyramid are also discussed. The relationship between the golden ratio and Fibonacci sequence is explained. The document concludes that extensive examples of the golden ratio can be found throughout nature, art, architecture and more.
The Golden Ratio
Golden ratio, golden proportion, golden rule, Fibonacci rule, rule of thirds, golden spiral, proportion
Golden ratio
The golden ratio is a number approximately equal to 1.618 that is found throughout nature and is considered aesthetically pleasing to humans. It is exhibited in things like DNA spirals, heart rhythms, musical scales, architecture like the Parthenon and Taj Mahal, artwork like the Mona Lisa, the proportions of the human face, and even logos of companies like Apple and Pepsi. The Fibonacci sequence, which has numbers that approach the golden ratio, is also found in patterns in nature like pinecones and sunflower seeds.
The fibonacci sequence
The Fibonacci sequence is a sequence where each number is the sum of the two preceding numbers. This sequence appears frequently in nature, such as the spiral patterns of shells, flowers, pine cones, and galaxies. The golden ratio is the number approximately equal to 1.6180 that results from dividing any number in the Fibonacci sequence by its predecessor. Both the Fibonacci sequence and golden ratio are found in architecture, like the Parthenon, as well as in music scales.
Golden Mean in Design
The Golden Ratio or Golden Mean or Divine Proportion is said to be the key to artistic design. It includes frame design sequence, often it logo design, website interface or brochure, on a set series of ratio equivalent to the value of Phi i.e. 1.618.....
In ancient era, Egyptians applied the Golden Ratio to design constructive magnificence into Egyptian pyramids. Still now a day, golden ratio can be observed in modern potraiet, design, sculpture, architecture and human anatomy. We have add together this short but informative presentation for your deliberation in which you shall find a number of logo design examples that deliver the conclusive global value of stability and magnificence. Have a glance and let us know of your sentiment!
Call us for design a <a>harmonized Logo</a>.
mathematics in architecture
The document discusses various architectural structures from around the world and through history that incorporate principles of geometry, mathematics, and the golden ratio. Many famous structures like the Parthenon, Taj Mahal, and Notre Dame used proportions and dimensions based on the golden ratio or other mathematical concepts. City planning in ancient India also incorporated mandalas and geometric patterns rooted in cosmological principles. Overall, the document shows how mathematics and principles of structure have long been applied in architectural design around the world.
Fractals
Fractals are irregular patterns that are self-similar across different scales. They are a branch of mathematics concerned with shapes found in nature that have non-integer dimensions. Some early contributors to fractal concepts included Leibiz, Cantor, and Hausdorff, but it was Mandelbrot who coined the term "fractal" and brought greater attention to the field. One of the most basic and important fractals is the Mandelbrot set, which is a set of complex numbers that fulfill certain recursive conditions. Fractals can also be classified based on their level of self-similarity, from exact to statistical self-similarity. Fractals are found throughout nature and have applications in fields like astrophysics
Mathematics and Art
Mathematics and art have a long historical relationship. The Golden ratio, Geometric patterns, Fractals are all fascinating mathematical ideas that have inspired artists and architects for centuries, I am just exploring these ideas in this presentation
Golden ratio
Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.
It is the ratio of a line segment cut into two pieces of different lengths such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment.
Application of pi golden ratio
The document discusses the prevalence and applications of the golden ratio, also known as phi, in mathematics, nature, art, architecture, music, and the human body. Some key points include:
- The golden ratio is approximately 1.618 and can be seen in the proportions of flowers, shells, galaxies, DNA, and the human face/body.
- It has been used intentionally in architecture for centuries, appearing in structures like the Parthenon and pyramids of Giza.
- The Fibonacci sequence is related to the golden ratio and can be observed in patterns in nature as well as the piano keyboard.
- Artists, architects and designers continue to find inspiration from the golden ratio's
Fi̇bonacci̇ sequence
The document discusses the Fibonacci sequence and its properties. It defines the Fibonacci sequence as a sequence where each number is the sum of the previous two, starting with 0 and 1 or 1 and 1. It then provides examples of where the Fibonacci sequence and golden ratio appear in nature, such as spiral galaxies, DNA molecules, seed heads, tree branches, and fingers. It also discusses applications of the Fibonacci sequence in mathematics, pseudorandom number generation, and software development estimation techniques.
The fibonacci sequence and the golden ratio #Scichallenge2017
#SciChallenge2017
In this presentation I would like to show how important mathematics is. It is shows up in everyday life through nature.
"In order to understand the Universe you must know the language which it is written and that is Mathematics." /Galileo Galilei/
GOLDEN RATIO - "The Divine Proportion"
The golden ratio is about 1.618, and represented by the Greek letter phi.
The golden ratio is sometimes called the "divine proportion," because of its frequency in the natural world.
The Golden Mean
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.
Golden ratio new
The golden ratio appears frequently in nature, art, architecture, and other areas. It is approximately equal to 1.618. The golden ratio is related to the Fibonacci sequence, where each number is the sum of the previous two numbers. Many examples can be found where the proportions of objects relate to the golden ratio, such as spiral shells, hurricanes, plant structures, and more. Artists and architects have also incorporated the golden ratio into their works to achieve a pleasing aesthetic, as seen in pieces by Da Vinci, Michelangelo, and designs of buildings like the Parthenon. Music also demonstrates connections to the golden ratio through compositions, instrument structures, and musical scales/octaves.
Maths in Art and Architecture Why Maths? Comenius project
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 WAZÓWNY IN GOLUB-DOBRZYŃ (POLAND)
ESCOLA SECUNDARIA COM 3.º CICLO D. MANUEL I IN BEJA (PORTUGAL)
IES ÁLVAREZ CUBERO IN PRIEGO DE CÓRDOBA (SPAIN)
Golden ratio and Fibonacci series
In this presentation, we see that how golden ratio and Fibonacci series are calculated or working? and What is the problem faced by Fibonacci in Fibonacci series.
The beauty of mathematics
This document provides an overview of mathematics and its relationship to concepts of beauty, architecture, and human life. It discusses how mathematical patterns like the golden ratio and Fibonacci sequence are found in nature and influence concepts of beauty. It also explores how mathematics influenced ancient architecture and how geometry guides both fields. Additionally, it examines how mathematicians think and how numbers are fundamental to mathematics, similar to how words are to language. The document aims to convey the breadth of mathematics and its applications beyond numerical calculations.
Fibonacci series and Golden ratio
The document discusses the Fibonacci sequence and the golden ratio. It begins by introducing the Fibonacci sequence of numbers: 1, 1, 2, 3, 5, 8, etc., where each number is the sum of the previous two. It then explains that the ratios of successive numbers in the sequence converge on the golden ratio, approximately 1.618. The golden ratio is found throughout nature, such as in the proportions of the human body and in vegetation. The document also provides methods for constructing a golden rectangle using squares and diagonals, with a final ratio matching the golden ratio.
Fibonacci Sequence and Golden Ratio
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.
Golden ratio
The document discusses the golden ratio, including its definition as a ratio where the whole is to the longer part as the longer part is to the shorter part. It provides the formula for calculating the golden ratio as (1+√5)/2, which evaluates to approximately 1.618. The document also provides a brief history of the golden ratio, suggesting it was potentially used in designs like the Great Pyramids and Parthenon by early civilizations like the Egyptians and Greeks.
Golden Ratio
Golden Ratio
How this ratio is used in our daily work....??
It is especially used for aesthetics purposes for beauty of things.
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Golden mean
This document discusses the golden ratio and its applications. It begins by explaining the history of the golden ratio in mathematics and its use by ancient Egyptians and Leonardo Da Vinci. It then discusses why objects containing the golden ratio are pleasing to the human eye. Several examples are given of the golden ratio appearing in nature, including plant growth patterns, spiral shells, and the human face and body. Architectural examples like the Great Pyramid are also discussed. The relationship between the golden ratio and Fibonacci sequence is explained. The document concludes that extensive examples of the golden ratio can be found throughout nature, art, architecture and more.
The Golden Ratio
Golden ratio, golden proportion, golden rule, Fibonacci rule, rule of thirds, golden spiral, proportion
Golden ratio
The golden ratio is a number approximately equal to 1.618 that is found throughout nature and is considered aesthetically pleasing to humans. It is exhibited in things like DNA spirals, heart rhythms, musical scales, architecture like the Parthenon and Taj Mahal, artwork like the Mona Lisa, the proportions of the human face, and even logos of companies like Apple and Pepsi. The Fibonacci sequence, which has numbers that approach the golden ratio, is also found in patterns in nature like pinecones and sunflower seeds.
The fibonacci sequence
The Fibonacci sequence is a sequence where each number is the sum of the two preceding numbers. This sequence appears frequently in nature, such as the spiral patterns of shells, flowers, pine cones, and galaxies. The golden ratio is the number approximately equal to 1.6180 that results from dividing any number in the Fibonacci sequence by its predecessor. Both the Fibonacci sequence and golden ratio are found in architecture, like the Parthenon, as well as in music scales.
Golden Mean in Design
The Golden Ratio or Golden Mean or Divine Proportion is said to be the key to artistic design. It includes frame design sequence, often it logo design, website interface or brochure, on a set series of ratio equivalent to the value of Phi i.e. 1.618.....
In ancient era, Egyptians applied the Golden Ratio to design constructive magnificence into Egyptian pyramids. Still now a day, golden ratio can be observed in modern potraiet, design, sculpture, architecture and human anatomy. We have add together this short but informative presentation for your deliberation in which you shall find a number of logo design examples that deliver the conclusive global value of stability and magnificence. Have a glance and let us know of your sentiment!
Call us for design a <a>harmonized Logo</a>.
mathematics in architecture
The document discusses various architectural structures from around the world and through history that incorporate principles of geometry, mathematics, and the golden ratio. Many famous structures like the Parthenon, Taj Mahal, and Notre Dame used proportions and dimensions based on the golden ratio or other mathematical concepts. City planning in ancient India also incorporated mandalas and geometric patterns rooted in cosmological principles. Overall, the document shows how mathematics and principles of structure have long been applied in architectural design around the world.
Fractals
Fractals are irregular patterns that are self-similar across different scales. They are a branch of mathematics concerned with shapes found in nature that have non-integer dimensions. Some early contributors to fractal concepts included Leibiz, Cantor, and Hausdorff, but it was Mandelbrot who coined the term "fractal" and brought greater attention to the field. One of the most basic and important fractals is the Mandelbrot set, which is a set of complex numbers that fulfill certain recursive conditions. Fractals can also be classified based on their level of self-similarity, from exact to statistical self-similarity. Fractals are found throughout nature and have applications in fields like astrophysics
Mathematics and Art
Mathematics and art have a long historical relationship. The Golden ratio, Geometric patterns, Fractals are all fascinating mathematical ideas that have inspired artists and architects for centuries, I am just exploring these ideas in this presentation
Golden ratio
Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.
It is the ratio of a line segment cut into two pieces of different lengths such that the ratio of the whole segment to that of the longer segment is equal to the ratio of the longer segment to the shorter segment.
Application of pi golden ratio
The document discusses the prevalence and applications of the golden ratio, also known as phi, in mathematics, nature, art, architecture, music, and the human body. Some key points include:
- The golden ratio is approximately 1.618 and can be seen in the proportions of flowers, shells, galaxies, DNA, and the human face/body.
- It has been used intentionally in architecture for centuries, appearing in structures like the Parthenon and pyramids of Giza.
- The Fibonacci sequence is related to the golden ratio and can be observed in patterns in nature as well as the piano keyboard.
- Artists, architects and designers continue to find inspiration from the golden ratio's
Fi̇bonacci̇ sequence
The document discusses the Fibonacci sequence and its properties. It defines the Fibonacci sequence as a sequence where each number is the sum of the previous two, starting with 0 and 1 or 1 and 1. It then provides examples of where the Fibonacci sequence and golden ratio appear in nature, such as spiral galaxies, DNA molecules, seed heads, tree branches, and fingers. It also discusses applications of the Fibonacci sequence in mathematics, pseudorandom number generation, and software development estimation techniques.
The fibonacci sequence and the golden ratio #Scichallenge2017
#SciChallenge2017
In this presentation I would like to show how important mathematics is. It is shows up in everyday life through nature.
"In order to understand the Universe you must know the language which it is written and that is Mathematics." /Galileo Galilei/
GOLDEN RATIO - "The Divine Proportion"
The golden ratio is about 1.618, and represented by the Greek letter phi.
The golden ratio is sometimes called the "divine proportion," because of its frequency in the natural world.
The Golden Mean
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.
Golden ratio new
The golden ratio appears frequently in nature, art, architecture, and other areas. It is approximately equal to 1.618. The golden ratio is related to the Fibonacci sequence, where each number is the sum of the previous two numbers. Many examples can be found where the proportions of objects relate to the golden ratio, such as spiral shells, hurricanes, plant structures, and more. Artists and architects have also incorporated the golden ratio into their works to achieve a pleasing aesthetic, as seen in pieces by Da Vinci, Michelangelo, and designs of buildings like the Parthenon. Music also demonstrates connections to the golden ratio through compositions, instrument structures, and musical scales/octaves.
Maths in Art and Architecture Why Maths? Comenius project
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 WAZÓWNY IN GOLUB-DOBRZYŃ (POLAND)
ESCOLA SECUNDARIA COM 3.º CICLO D. MANUEL I IN BEJA (PORTUGAL)
IES ÁLVAREZ CUBERO IN PRIEGO DE CÓRDOBA (SPAIN)
Golden ratio and Fibonacci series
In this presentation, we see that how golden ratio and Fibonacci series are calculated or working? and What is the problem faced by Fibonacci in Fibonacci series.
The beauty of mathematics
This document provides an overview of mathematics and its relationship to concepts of beauty, architecture, and human life. It discusses how mathematical patterns like the golden ratio and Fibonacci sequence are found in nature and influence concepts of beauty. It also explores how mathematics influenced ancient architecture and how geometry guides both fields. Additionally, it examines how mathematicians think and how numbers are fundamental to mathematics, similar to how words are to language. The document aims to convey the breadth of mathematics and its applications beyond numerical calculations.
Fibonacci series and Golden ratio
The document discusses the Fibonacci sequence and the golden ratio. It begins by introducing the Fibonacci sequence of numbers: 1, 1, 2, 3, 5, 8, etc., where each number is the sum of the previous two. It then explains that the ratios of successive numbers in the sequence converge on the golden ratio, approximately 1.618. The golden ratio is found throughout nature, such as in the proportions of the human body and in vegetation. The document also provides methods for constructing a golden rectangle using squares and diagonals, with a final ratio matching the golden ratio.
Fibonacci Sequence and Golden Ratio
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.
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The fibonacci sequence and the golden ratio #Scichallenge2017
The fibonacci sequence and the golden ratio #Scichallenge2017
Maths in Art and Architecture Why Maths? Comenius project
Maths in Art and Architecture Why Maths? Comenius project
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Golden ratio
The document discusses the golden ratio, including its definition as a ratio where the whole is to the longer part as the longer part is to the shorter part. It provides the formula for calculating the golden ratio as (1+√5)/2, which evaluates to approximately 1.618. The document also provides a brief history of the golden ratio, suggesting it was potentially used in designs like the Great Pyramids and Parthenon by early civilizations like the Egyptians and Greeks.
Golden Ratio
Golden Ratio
How this ratio is used in our daily work....??
It is especially used for aesthetics purposes for beauty of things.
Golden ratio
The document discusses various topics in theoretical computer science including:
1) Fibonacci numbers and their recurrence relation. Fibonacci numbers appear in patterns in nature like pinecones and flower petals.
2) Polynomial division and how it relates to geometric series and Fibonacci numbers. The power series expansion of x/(1-x-x^2) equals the Fibonacci sequence.
3) Other mathematical concepts like continued fractions, the golden ratio, and their connections to algorithms and computer science problems.
Proportion
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.
Fibonacci and the Golden Ratio
The document discusses the Fibonacci sequence and the Golden Ratio. It provides a table that lists Fibonacci ratios, their calculated frequencies based on A=440 Hz, tempered frequencies, the associated note in the musical scale, and the musical relationship between notes. It shows that many musical intervals correspond to Fibonacci ratios and their approximations in the tempered scale.
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The Lotus Temple in Delhi, India is designed in the form of a lotus flower, which is sacred in Hinduism. It consists of 27 free-standing marble "petals" arranged in clusters of three, which are repeated nine times to form the structure. The central prayer hall sits under a high domed ceiling and can seat over 1,200 people. Design elements like radial symmetry, hierarchy, rhythm and repetition, scale, and proportion are used to create a harmonious and sacred space.
Marvellous 'Baha'i Temple' or ' Lotus Temple'
The document summarizes the design, construction, and components of the Baha'i House of Worship in New Delhi, India. It describes the architect's design evolution of a symmetrical half-open lotus flower structure and the complex analysis and construction process. Key aspects included the reinforced concrete shells and domes, white marble cladding, and specialized construction techniques needed to complete the intricate geometric design. The completed structure was hailed as an architectural and engineering marvel.
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Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Golden ratio
- 1. THE GOLDEN RATIO… AN ENGINEER’S PERSPECTIVE…
- 2. WHAT IS IT? 1+ 5 j= 2 2
- 3. FIBONACCI… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 3
- 4. FIBONACCI… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 4
- 5. FIBONACCI… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 5
- 6. FIBONACCI… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 6
- 7. FIBONACCI… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 7
- 8. FIBONACCI… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765… 8
- 9. FIBONACCI… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 9
- 10. FIBONACCI… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 10
- 11. FIBONACCI… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 11
- 12. FIBONACCI… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 12
- 13. GOLDEN RATIO… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 1 13
- 14. GOLDEN RATIO… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 65… 2 14
- 15. GOLDEN RATIO… 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 67 3 65… = 1.5 2 15
- 16. GOLDEN RATIO… 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 1,2, , , , , , , , , , , , , , , , , , 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 1+ 5 j= 2 j = 1.61803... 16
- 17. WHY IS IT USEFUL? 17
- 18. PHOTOGRAPHY… 18
- 19. RULE OF THIRDS? 19
- 20. RULE OF THIRDS? 20
- 21. RULE OF THIRDS? 21
- 22. RULE OF THIRDS? 22
- 23. RULE OF THIRDS? 23
- 24. RULE OF THIRDS? 24
- 25. RULE OF THIRDS? 25
- 26. RULE OF THIRDS? 26
- 27. NEAR ENOUGH?.. 27
- 28. SO WHAT! 28
- 29. Courtesy of Flickr - Kyri Sarantakos Licensed under GREEKS… 29
- 30. Courtesy of Flickr - Kyri Sarantakos Licensed under PROPORTIONS… 1.0 1.61803 30
- 31. PLATONIC SOLIDS… Dodecahedron Octahedron Icosahedron Cube 31 Tetrahedron
- 32. BUCKY FULLER… Courtesy of Flickr - caribb Licensed under 32
- 33. NATURE… Courtesy of Flickr - eEditor Licensed under 33
- 34. NATURE… 34
- 35. BIOMIMETICS… Courtesy of Flickr - kibuyu Licensed under 35
- 36. THANK YOU… 36