The document discusses ancient Greek concepts of harmony, proportion, and aesthetics. It describes how the ancient Greek architect Vitruvius observed proportional relationships between parts of the human body, and how these influenced ideas of ideal proportions in architecture. Later, Plato expanded on Pythagoras' theory that mathematics describes the harmonious order of the universe.
The document discusses ancient Greek concepts of harmony, proportion, and aesthetics. It describes how the ancient Greek architect Vitruvius observed proportional relationships between parts of the human body, and how these influenced ideas about ideal architectural proportions. Later, Plato expanded on Pythagoras' theory that mathematics describes the harmonious order of the universe.
The document discusses concepts of recursion, symmetry, and variation in nature through various examples and imagery. It explores recursion through self-reference loops and cloning. Symmetry is examined through artistic renderings and patterns in nature. Variation is seen as important for survival and evolution. Big ideas around the interconnectedness of man, nature, and the universe are presented.
The document discusses Aristotle's theory of tragedy from his work Poetics. It outlines the six key aspects of Greek tragedy according to Aristotle: catharsis, hamartia, universality, artful diction, unity of action, and spectacle. For each aspect, the document provides explanations and examples from Greek tragedies like Oedipus Rex to illustrate Aristotle's concepts. It also discusses how these tragic elements can be connected to elements of contemporary culture.
The document provides an overview of a course on ancient Greek philosophy and theater. The goals are to understand the historical context of Theban plays, factors influencing ancient Greek society, and the influence of Greek philosophy on Western thought. It discusses how asking fundamental questions has propelled civilization and discusses the six branches of philosophy, including aesthetics, epistemology, politics, and metaphysics.
The document discusses logic and reasoning, including valid and invalid arguments. It defines several common fallacies of reasoning such as ad hominem circumstantial, ad hominem tu quoque, appeal to belief, burden of proof, appeal to ridicule, and bandwagon. It also provides examples of each fallacy. The document then discusses the 1957 film 12 Angry Men and tasks the reader with identifying examples of fallacious reasoning in the film used to proclaim the accused boy guilty.
Dante's Divine Comedy describes his journey through the spheres of heaven. In Paradiso, Dante ascends through nine celestial spheres with Beatrice, representing increasing perfection. Each sphere corresponds to a virtue and contains souls exemplifying that virtue. The spheres are nested within each other according to medieval cosmology, with the earth at the center and God in the Empyrean, the highest heaven beyond the moving spheres. In the Empyrean, Dante experiences a vision of God as a blinding light.
The Divine Comedy by Dante Alighieri is divided into three sections - Inferno, Purgatorio, and Paradiso. Inferno describes Dante's journey through the nine circles of Hell guided by Virgil. Purgatorio details his ascent up the Mountain of Purgatory in seven terraces. In Paradiso, Dante is guided by Beatrice through the nine spheres of Heaven and one Empyrean, seeing blessed souls and angels. The poem discusses the theological concepts of sin, redemption, and the nature of the afterlife through Dante's journey to understand God and achieve spiritual fulfillment.
1) Dante's Divine Comedy is an allegorical poem about a journey through Hell, Purgatory and Heaven. It uses these realms and characters within them to represent moral truths and ultimately to help readers prepare for the afterlife.
2) The poem is composed of 100 cantos divided into three parts, following Dante's journey. He passes through nine circles of Hell housing different types of sinners. Purgatory cleanses souls over seven terraces. Heaven is depicted as nine celestial spheres containing angels and the souls of the righteous.
3) The work had a profound influence on Christian thought and literature and aimed to guide people to salvation through vividly depicting the consequences of sin and virtue.
The document discusses ancient Greek concepts of harmony, proportion, and aesthetics. It describes how the ancient Greek architect Vitruvius observed proportional relationships between parts of the human body, and how these influenced ideas about ideal architectural proportions. Later, Plato expanded on Pythagoras' theory that mathematics describes the harmonious order of the universe.
The document discusses concepts of recursion, symmetry, and variation in nature through various examples and imagery. It explores recursion through self-reference loops and cloning. Symmetry is examined through artistic renderings and patterns in nature. Variation is seen as important for survival and evolution. Big ideas around the interconnectedness of man, nature, and the universe are presented.
The document discusses Aristotle's theory of tragedy from his work Poetics. It outlines the six key aspects of Greek tragedy according to Aristotle: catharsis, hamartia, universality, artful diction, unity of action, and spectacle. For each aspect, the document provides explanations and examples from Greek tragedies like Oedipus Rex to illustrate Aristotle's concepts. It also discusses how these tragic elements can be connected to elements of contemporary culture.
The document provides an overview of a course on ancient Greek philosophy and theater. The goals are to understand the historical context of Theban plays, factors influencing ancient Greek society, and the influence of Greek philosophy on Western thought. It discusses how asking fundamental questions has propelled civilization and discusses the six branches of philosophy, including aesthetics, epistemology, politics, and metaphysics.
The document discusses logic and reasoning, including valid and invalid arguments. It defines several common fallacies of reasoning such as ad hominem circumstantial, ad hominem tu quoque, appeal to belief, burden of proof, appeal to ridicule, and bandwagon. It also provides examples of each fallacy. The document then discusses the 1957 film 12 Angry Men and tasks the reader with identifying examples of fallacious reasoning in the film used to proclaim the accused boy guilty.
Dante's Divine Comedy describes his journey through the spheres of heaven. In Paradiso, Dante ascends through nine celestial spheres with Beatrice, representing increasing perfection. Each sphere corresponds to a virtue and contains souls exemplifying that virtue. The spheres are nested within each other according to medieval cosmology, with the earth at the center and God in the Empyrean, the highest heaven beyond the moving spheres. In the Empyrean, Dante experiences a vision of God as a blinding light.
The Divine Comedy by Dante Alighieri is divided into three sections - Inferno, Purgatorio, and Paradiso. Inferno describes Dante's journey through the nine circles of Hell guided by Virgil. Purgatorio details his ascent up the Mountain of Purgatory in seven terraces. In Paradiso, Dante is guided by Beatrice through the nine spheres of Heaven and one Empyrean, seeing blessed souls and angels. The poem discusses the theological concepts of sin, redemption, and the nature of the afterlife through Dante's journey to understand God and achieve spiritual fulfillment.
1) Dante's Divine Comedy is an allegorical poem about a journey through Hell, Purgatory and Heaven. It uses these realms and characters within them to represent moral truths and ultimately to help readers prepare for the afterlife.
2) The poem is composed of 100 cantos divided into three parts, following Dante's journey. He passes through nine circles of Hell housing different types of sinners. Purgatory cleanses souls over seven terraces. Heaven is depicted as nine celestial spheres containing angels and the souls of the righteous.
3) The work had a profound influence on Christian thought and literature and aimed to guide people to salvation through vividly depicting the consequences of sin and virtue.
The document provides an overview of Dante Alighieri's Divine Comedy, one of the greatest poems of European literature. It discusses Dante's life and inspiration for writing the poem, as well as the structure and allegorical nature of the poem as a journey through Hell, Purgatory, and Heaven. The summary focuses on key details like the poem being divided into 100 cantos structured around religious numerology, and its depiction of sins and their punishments divided across 9 circles of Hell.
The document provides background information on Dante Alighieri and an overview of the structure and content of his epic poem Divine Comedy. It describes the poem's three sections - Inferno, Purgatorio, and Paradiso - and how Inferno is structured into 9 circles of Hell containing sinners who are punished for different sins. It summarizes several Cantos from Inferno, describing the circles and the people or monsters encountered in each circle.
Aristotle was a Greek philosopher from the 4th century BC who made seminal contributions to many fields including metaphysics, logic, ethics, politics, and literary criticism. He wrote Poetics, considered the first work of literary theory, which analyzed Greek tragedy and established principles for understanding dramatic art. In Poetics, Aristotle defines tragedy as an imitation of action that arouses pity and fear through catharsis. He identifies six elements of tragedy - plot, character, diction, thought, melody, and spectacle - and describes how they work together to achieve the desired emotional effect. Aristotle's analysis of tragedy set the standard for dramatic criticism for centuries.
Dante Alighieri is considered the father of Italian literature. His masterpiece, the Divine Comedy, is widely regarded as the greatest literary work composed in the Italian language. Written between 1308 and 1321, the Divine Comedy is an epic poem that follows Dante on an allegorical journey through Hell (Inferno), Purgatory (Purgatorio), and Paradise (Paradiso). Through this journey, Dante establishes the Tuscan language as the standardized Italian and influences many other important writers around the world.
Aristotle's Poetics c. 335 BCE is the earliest surviving work of dramatic theory and the first extant philosophical treatise to focus on literary theory
Plato believed that the physical world we perceive with our senses is imperfect and filled with error. There exists a more perfect, eternal realm populated by abstract concepts like goodness, equality, and beauty. Plato's most fundamental distinction was between these abstract forms which things in the physical world imitate or copy. Nearly all of Plato's works were devoted to defining these abstract forms and discussing how we can achieve understanding of them through reasoning.
The document provides an overview of the structure and contents of Dante's Divine Comedy. It is composed of three parts (Inferno, Purgatorio, Paradiso) with 33 cantos each, totaling 100 cantos. The poem describes Dante's journey through Hell, Purgatory and Heaven, guided by Virgil and later Beatrice. Hell is organized into 9 circles punishing different types of sins in order of severity. The circles and their punishments are described, including lust, gluttony, heresy and violence against others.
The Divine Comedy by Dante Alighieri depicts his allegorical journey through Hell, Purgatory and Paradise. It begins when Dante, lost in a dark wood, is met by the Roman poet Virgil who will guide him through Hell. They enter through the gates of Hell and descend through its nine circles, witnessing the eternal damnation of sinners based on the sins they committed in life. Upon exiting, Virgil then leads Dante up the mountain of Purgatory where souls purge themselves of sins before entering Paradise.
Dante and Virgil witness the arrival of the Angel of God in a small boat carrying over 100 souls. As the Angel docks, the souls chant from Psalms and disembark, gazing at their new surroundings. The sun has now risen over the Mountain of Purgatory, illuminating the new arrivals.
The document provides an overview of key concepts for analyzing theatrical texts, including plays, scripts, and other works meant for performance. It defines what a text can include and discusses how plays are incomplete on the page but meant to be performed. The document also summarizes Aristotle's six elements of drama - plot, character, thought, diction, music, and spectacle - and how they are used to analyze plays. Different genres of theatre like tragedy and comedy are also mentioned.
The document provides an overview of Dante Alighieri's epic poem Divine Comedy. It discusses the poem's structure, which is divided into three sections - Inferno, Purgatorio, and Paradiso - representing Hell, Purgatory, and Heaven. It also summarizes the content of each section, with Inferno depicting Dante's journey through the nine circles of Hell, guided by the Roman poet Virgil. The circles are organized by the types of sins punished in each, such as lust, gluttony, heresy, and violence.
Differences and similarities of sculptures 1irbaaz
Roman sculptures often depicted animals and beasts, whereas Renaissance sculptures usually featured nude human figures. Roman sculptures emphasized accurate details in portraits, while Renaissance sculptures focused more on emphasizing the sculptures themselves. Both Roman and Renaissance sculptures were influenced by Greek art, though Romans copied Greek styles directly while Renaissance artists adapted Greek styles.
Classical Greek humanism placed man at the center and valued human reason above all else. Education was individualized for males and focused on household management for females. Art and architecture glorified human proportions and perfection through symmetry and mathematics. Literature included histories by Herodotus and fables by Aesop, as well as tragedies by Sophocles like Oedipus Rex. Greek philosophy used abstract thought to explore life's big questions, with Sophists rejecting single truths and emphasizing civic duty and excellence. Major philosophers included Socrates, his student Plato who wrote The Republic, and Aristotle who tutored Alexander.
Socrates, Plato, and Aristotle formed a great triumvirate of classical Greek philosophers. Socrates used questioning to teach virtue, Plato was his student and wrote dialogues featuring Socrates, and Aristotle was Plato's student who went on to tutor Alexander the Great and founded his own school. Together, they laid the fundamentals of Western philosophy through Socrates' teachings, Plato's dialogues and ideas of forms, and Aristotle's writings on logic, happiness, and moderation.
A slideshow connected to a lecture of Greek Art available at Art History Teaching Resources (http://arthistoryteachingresources.org/), written by Alexis Culotta.
The document discusses the historical foundations of education during the Renaissance and Reformation periods. It describes Humanism as a movement that began in the 14th-16th centuries marked by a revival of classical Roman and Greek influences. Italian or individual Humanism stressed personal culture and development of elites, while Northern Humanism aimed to reform society through education accessible to all. The Reformation sought religious and moral reform through returning to biblical beliefs and promoting family values.
The document provides an overview of ancient Egyptian art from the Predynastic and Early Dynastic Periods through the New Kingdom. It describes the major historical periods of ancient Egypt and highlights several key works that exemplify artistic conventions like composite view, hieratic scale, and registers. The document discusses the relationship between art, architecture, and expressions of power and authority. It also examines ideals of idealization versus naturalism and how the human form was depicted over time in ancient Egyptian art.
This document provides an overview and questions for a proposed TED Talk on the integration of mathematics, music, and geometry in the works of historical figures like Da Vinci, Pythagoras, and Plato. It discusses how their understanding of harmonic design has been lost over time, replacing ancient concepts like rational numbers and proportions with modern systems like decimals and the chromatic scale. The talk aims to visualize these old concepts and principles through examples like the Vitruvian Man and designs for a Pythagorean guitar.
Here are some questions you could develop around your topic of improving reading comprehension and critical thinking skills for middle school students:
1. What specific reading comprehension and critical thinking skills are important for middle school students to continue developing beyond 6th grade?
2. How can reading instruction in 7th and 8th grade focus on applying reading skills across other subject areas like science, history, math, etc.?
3. What instructional strategies and activities have been shown to effectively build reading comprehension and critical thinking for middle school students?
4. How much dedicated class time per week is needed in 7th and 8th grade to sufficiently practice and develop these skills without being an elective?
5. What assessments or measures
Pythagoras was a Greek philosopher and mathematician born on the island of Samos in the 6th century BC. He founded a secretive religious society called the Pythagoreans that was focused on mathematics and music. The Pythagoreans believed that numbers underpinned the order of the universe and discovered that consonant musical intervals could be expressed as simple numerical ratios. They theorized that the movement of celestial bodies produced a harmonic "music of the spheres" inaudible to human ears.
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.
Pythagoras was a 6th century BC Greek philosopher and mathematician who founded a secretive group. He is most famous for discovering mathematical relationships between musical intervals and string lengths. Pythagoras believed that mathematics described the harmony of the universe and that numbers held mystical properties. His followers studied mathematics, lived communally, and believed music could cure illness through its mathematical harmonies.
The document provides an overview of Dante Alighieri's Divine Comedy, one of the greatest poems of European literature. It discusses Dante's life and inspiration for writing the poem, as well as the structure and allegorical nature of the poem as a journey through Hell, Purgatory, and Heaven. The summary focuses on key details like the poem being divided into 100 cantos structured around religious numerology, and its depiction of sins and their punishments divided across 9 circles of Hell.
The document provides background information on Dante Alighieri and an overview of the structure and content of his epic poem Divine Comedy. It describes the poem's three sections - Inferno, Purgatorio, and Paradiso - and how Inferno is structured into 9 circles of Hell containing sinners who are punished for different sins. It summarizes several Cantos from Inferno, describing the circles and the people or monsters encountered in each circle.
Aristotle was a Greek philosopher from the 4th century BC who made seminal contributions to many fields including metaphysics, logic, ethics, politics, and literary criticism. He wrote Poetics, considered the first work of literary theory, which analyzed Greek tragedy and established principles for understanding dramatic art. In Poetics, Aristotle defines tragedy as an imitation of action that arouses pity and fear through catharsis. He identifies six elements of tragedy - plot, character, diction, thought, melody, and spectacle - and describes how they work together to achieve the desired emotional effect. Aristotle's analysis of tragedy set the standard for dramatic criticism for centuries.
Dante Alighieri is considered the father of Italian literature. His masterpiece, the Divine Comedy, is widely regarded as the greatest literary work composed in the Italian language. Written between 1308 and 1321, the Divine Comedy is an epic poem that follows Dante on an allegorical journey through Hell (Inferno), Purgatory (Purgatorio), and Paradise (Paradiso). Through this journey, Dante establishes the Tuscan language as the standardized Italian and influences many other important writers around the world.
Aristotle's Poetics c. 335 BCE is the earliest surviving work of dramatic theory and the first extant philosophical treatise to focus on literary theory
Plato believed that the physical world we perceive with our senses is imperfect and filled with error. There exists a more perfect, eternal realm populated by abstract concepts like goodness, equality, and beauty. Plato's most fundamental distinction was between these abstract forms which things in the physical world imitate or copy. Nearly all of Plato's works were devoted to defining these abstract forms and discussing how we can achieve understanding of them through reasoning.
The document provides an overview of the structure and contents of Dante's Divine Comedy. It is composed of three parts (Inferno, Purgatorio, Paradiso) with 33 cantos each, totaling 100 cantos. The poem describes Dante's journey through Hell, Purgatory and Heaven, guided by Virgil and later Beatrice. Hell is organized into 9 circles punishing different types of sins in order of severity. The circles and their punishments are described, including lust, gluttony, heresy and violence against others.
The Divine Comedy by Dante Alighieri depicts his allegorical journey through Hell, Purgatory and Paradise. It begins when Dante, lost in a dark wood, is met by the Roman poet Virgil who will guide him through Hell. They enter through the gates of Hell and descend through its nine circles, witnessing the eternal damnation of sinners based on the sins they committed in life. Upon exiting, Virgil then leads Dante up the mountain of Purgatory where souls purge themselves of sins before entering Paradise.
Dante and Virgil witness the arrival of the Angel of God in a small boat carrying over 100 souls. As the Angel docks, the souls chant from Psalms and disembark, gazing at their new surroundings. The sun has now risen over the Mountain of Purgatory, illuminating the new arrivals.
The document provides an overview of key concepts for analyzing theatrical texts, including plays, scripts, and other works meant for performance. It defines what a text can include and discusses how plays are incomplete on the page but meant to be performed. The document also summarizes Aristotle's six elements of drama - plot, character, thought, diction, music, and spectacle - and how they are used to analyze plays. Different genres of theatre like tragedy and comedy are also mentioned.
The document provides an overview of Dante Alighieri's epic poem Divine Comedy. It discusses the poem's structure, which is divided into three sections - Inferno, Purgatorio, and Paradiso - representing Hell, Purgatory, and Heaven. It also summarizes the content of each section, with Inferno depicting Dante's journey through the nine circles of Hell, guided by the Roman poet Virgil. The circles are organized by the types of sins punished in each, such as lust, gluttony, heresy, and violence.
Differences and similarities of sculptures 1irbaaz
Roman sculptures often depicted animals and beasts, whereas Renaissance sculptures usually featured nude human figures. Roman sculptures emphasized accurate details in portraits, while Renaissance sculptures focused more on emphasizing the sculptures themselves. Both Roman and Renaissance sculptures were influenced by Greek art, though Romans copied Greek styles directly while Renaissance artists adapted Greek styles.
Classical Greek humanism placed man at the center and valued human reason above all else. Education was individualized for males and focused on household management for females. Art and architecture glorified human proportions and perfection through symmetry and mathematics. Literature included histories by Herodotus and fables by Aesop, as well as tragedies by Sophocles like Oedipus Rex. Greek philosophy used abstract thought to explore life's big questions, with Sophists rejecting single truths and emphasizing civic duty and excellence. Major philosophers included Socrates, his student Plato who wrote The Republic, and Aristotle who tutored Alexander.
Socrates, Plato, and Aristotle formed a great triumvirate of classical Greek philosophers. Socrates used questioning to teach virtue, Plato was his student and wrote dialogues featuring Socrates, and Aristotle was Plato's student who went on to tutor Alexander the Great and founded his own school. Together, they laid the fundamentals of Western philosophy through Socrates' teachings, Plato's dialogues and ideas of forms, and Aristotle's writings on logic, happiness, and moderation.
A slideshow connected to a lecture of Greek Art available at Art History Teaching Resources (http://arthistoryteachingresources.org/), written by Alexis Culotta.
The document discusses the historical foundations of education during the Renaissance and Reformation periods. It describes Humanism as a movement that began in the 14th-16th centuries marked by a revival of classical Roman and Greek influences. Italian or individual Humanism stressed personal culture and development of elites, while Northern Humanism aimed to reform society through education accessible to all. The Reformation sought religious and moral reform through returning to biblical beliefs and promoting family values.
The document provides an overview of ancient Egyptian art from the Predynastic and Early Dynastic Periods through the New Kingdom. It describes the major historical periods of ancient Egypt and highlights several key works that exemplify artistic conventions like composite view, hieratic scale, and registers. The document discusses the relationship between art, architecture, and expressions of power and authority. It also examines ideals of idealization versus naturalism and how the human form was depicted over time in ancient Egyptian art.
This document provides an overview and questions for a proposed TED Talk on the integration of mathematics, music, and geometry in the works of historical figures like Da Vinci, Pythagoras, and Plato. It discusses how their understanding of harmonic design has been lost over time, replacing ancient concepts like rational numbers and proportions with modern systems like decimals and the chromatic scale. The talk aims to visualize these old concepts and principles through examples like the Vitruvian Man and designs for a Pythagorean guitar.
Here are some questions you could develop around your topic of improving reading comprehension and critical thinking skills for middle school students:
1. What specific reading comprehension and critical thinking skills are important for middle school students to continue developing beyond 6th grade?
2. How can reading instruction in 7th and 8th grade focus on applying reading skills across other subject areas like science, history, math, etc.?
3. What instructional strategies and activities have been shown to effectively build reading comprehension and critical thinking for middle school students?
4. How much dedicated class time per week is needed in 7th and 8th grade to sufficiently practice and develop these skills without being an elective?
5. What assessments or measures
Pythagoras was a Greek philosopher and mathematician born on the island of Samos in the 6th century BC. He founded a secretive religious society called the Pythagoreans that was focused on mathematics and music. The Pythagoreans believed that numbers underpinned the order of the universe and discovered that consonant musical intervals could be expressed as simple numerical ratios. They theorized that the movement of celestial bodies produced a harmonic "music of the spheres" inaudible to human ears.
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.
Pythagoras was a 6th century BC Greek philosopher and mathematician who founded a secretive group. He is most famous for discovering mathematical relationships between musical intervals and string lengths. Pythagoras believed that mathematics described the harmony of the universe and that numbers held mystical properties. His followers studied mathematics, lived communally, and believed music could cure illness through its mathematical harmonies.
The document discusses the mathematical connections between music and art, focusing on the golden ratio. It provides background on the golden ratio, including its relationship to the Fibonacci sequence and its prevalence in nature, architecture, and the human body. Examples are given of how the golden ratio is incorporated into musical structures like time signatures and note lengths. In art, the golden ratio is seen in famous works like the Mona Lisa and influences techniques like composition.
The film Bend It Like Beckham explores themes of cultural identity and gender roles through the story of Jess Bhamra, an Indian girl living in England who has a passion for soccer but faces resistance from her traditional parents. The movie depicts the tension Jess feels between her interest in the individual pursuit of soccer and the expectations of her close-knit, hierarchical Indian family culture which emphasizes the roles of women in maintaining family traditions. Through Jess' journey, the film examines how cultural norms can influence identity and opportunities for men and women differently.
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.
Mathematics was invented by humans to describe patterns and quantities in the real world. Some key points:
- Early humans developed counting as a practical tool for tasks like tracking food supplies and trade goods. Counting led to the development of basic arithmetic operations and the first written number systems.
- Properties of numbers, geometry, algebra, calculus, etc. were conceptualized by mathematicians over thousands of years through observing patterns and designing logical systems to model physical phenomena. Different cultures developed unique systems for writing and representing numbers.
- While mathematics describes inherent patterns in nature, the specific symbols, notations, definitions, and branches we use today are all human constructs. The rules and structures of mathematics have evolved significantly over the course of history
The document discusses Pythagorean views of time and eternity. It explores how Pythagoras saw musical harmony as embodied in simple numerical ratios and the monochord instrument. Time was seen as a moving image of changeless eternity, connected through the medium of number. The work Harmonia attempts to musically express this paradoxical relationship between time and eternity using harmonics of sound and geometric constructions.
The document provides an overview of different types of fallacies in logic. It discusses semantic fallacies, which are errors due to ambiguity or incorrect construction of language. Examples of semantic fallacies given are equivocation, composition, and division. It also discusses material fallacies, which stem from issues with the subject matter itself. Examples of material fallacies provided are accident and confusing absolute and qualified statements. The document aims to define different logical fallacies and provide examples of each.
The document discusses a story called "Tut's Revenge" about workers in Luxor, Egypt who become mysteriously ill. It provides background information about Luxor's location and climate. Students are tasked with investigating possible causes of illness by considering factors like contaminated food, water, air or direct contact with toxic materials. A scientific approach is emphasized, involving forming hypotheses and gathering evidence to solve the medical mystery.
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.
Pythagoras was a Greek philosopher, mathematician, and founder of the Pythagorean movement. He made important contributions to mathematics, discovering the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Pythagoras also studied properties of numbers, geometry, music, and astronomy. He believed that numbers underlie all things and that mathematical relations exist in music, discovering musical intervals based on whole number ratios between string lengths. Pythagoras made many advances in geometry as well, constructing regular polygons and the five regular solids.
1. The document discusses the history of how numbers and mathematics have been integral to art and civilization. It traces the earliest uses of counting on artifacts like the Ishango bone from 20,000 years ago through ancient civilizations like Sumeria, Egypt, Greece, and more.
2. A key point is that the Sumerians developed one of the earliest writing systems based on accounting with clay tokens that represented amounts and quantities of goods. This led to the development of basic arithmetic.
3. Pythagoras believed that numbers represented the essence of all things in the universe and that harmony in music and aesthetics could be explained by mathematical principles and ratios. He saw mathematics as fundamental to understanding areas like music, geometry
1. The document discusses the history of the relationship between numbers and art from ancient times to today. It explores how civilizations like the Sumerians, Egyptians, Greeks, and others incorporated mathematics into art and design.
2. A key figure discussed is Pythagoras, who believed that numbers were the essence of all things and that harmony in music and nature could be explained by mathematical ratios and proportions. He is credited with discovering relationships like octaves and discovering platonic solids.
3. The document also discusses the "Golden Section" or "Golden Ratio" of approximately 1.618, which appeared in designs from the Egyptians to the Greeks and Leonardo Da Vinci. It was considered
Pythagoras and the Birth of Western Musicmatthewlovett
Pythagoras believed that mathematics and musical harmony were intrinsically linked. He discovered that consonant musical intervals had simple whole number frequency ratios, like octaves being 2:1 and perfect fifths being 3:2. Pythagoras used the first four whole numbers and their sum to represent this harmony in the symbolic figure of the tetractys, showing how unity emerges from the infinite through mathematical order and progression. This linked music, mathematics and the cosmos in a harmonic whole.
This document provides an overview of art appreciation and defines what art is. It discusses art as representation, mimesis, and how art replicates subjects faithfully. Art as expression of emotional content during the Romantic movement is covered, as well as art as form based on its formal qualities. The purposes and functions of art in transforming ideas into physical works that can be comprehended and responded to emotionally are presented. Assumptions about art being timeless, universal, and involving experience are discussed. Examples of famous artworks are provided to illustrate key points.
A PowerPoint presentation that I created for the University of Exeter's EXESESO MA in Western Esotericism. It's not really intended for viewing without any verbal explanations, but it might be of interest to some of you.
This document outlines an academic integrity policy for a school district. It defines expectations for trustworthy and responsible student behavior. The document discusses the pillars of character and aims to foster ethical decision making and respect among students. It describes cheating and plagiarism, as well as procedures for handling suspected violations. Consequences are outlined for offenses ranging from failing assignments to suspension from school. The goal is to promote honesty and integrity through clear guidelines and a fair investigative process.
This document outlines an academic integrity policy for a school district. It defines expectations for trustworthy and responsible student behavior. The document discusses the pillars of character and aims to foster good citizenship among students. It describes cheating and plagiarism, potential consequences, and procedures for handling suspected violations in a fair and uniform manner.
Short story starters (incongruent juxtaposition photos)greepie
This document provides instructions for using incongruent juxtapositions in photographs and freewriting to generate ideas for short stories. Participants will view photographs presenting unlike things in unexpected ways and freewrite without stopping to allow ideas to emerge. They are advised to view photos in different ways and write repetitive or unrelated thoughts until relevant ideas appear. After freewriting, participants will reread their work and circle ideas that could be developed into unique short story concepts. The goal is to use tension created by incongruous visual elements and an open-minded freewriting process to inspire new narrative ideas.
The document provides an overview of key plot points and characters in Emily Brontë's novel Wuthering Heights. It summarizes Heathcliff's journey from a mysterious orphan adopted by the Earnshaws to a bitter, vengeful man. The narrative also explores Catherine Earnshaw's love for Heathcliff and her eventual marriage to Edgar Linton due to social expectations. The complex narrative structure involving multiple narrators, including Nelly Dean and Mr. Lockwood, is highlighted.
The document provides guidance on how to structure an analytical essay, including how to write an effective introduction, body, and conclusion. It recommends that the introduction include a hook, occasion, pivot point, thesis statement, and projected organization. The body should have three sections that align with the projected organization, using topic sentences and evidence to support each point. The conclusion restates the thesis and proofs, reverses the pivot point, completes the occasion, and leaves a final thought.
The document summarizes findings from a commissioner's review of an education system. It identifies deficiencies in curriculum alignment, access and fairness, and data usage. It recommends developing a district-wide data policy to determine data collection, responsibilities, and review processes. It also recommends a professional development plan including training on examining student work, universal design, rubrics, and aligning curricula to standards using data.
The document summarizes findings from a commissioner's review of an education system. It identifies deficiencies in curriculum alignment, access and fairness, and data usage. It recommends developing a district-wide data policy to determine data collection, responsibilities, and review processes. It also recommends a professional development plan including training on examining student work, universal design, rubrics, and aligning curricula to standards using data.
This document provides background information on Shakespeare's play The Merchant of Venice. It discusses the main characters, plotlines involving bonds and obligations around money, prejudice, and breaking rules. It also analyzes the historical context for including a Jewish antagonist and addressing issues of prejudice, money lending, and challenging social norms during the Renaissance period in Venice.
The document discusses various topics related to the Vietnam War including different military groups involved in the war such as the Viet Cong guerrillas and the North Vietnamese Regular Army. It provides photos and descriptions of key events like the My Lai massacre and the Kent State shootings. The document also includes terminology used in the war and discusses the intense pain caused by napalm burns.
The document provides an overview of Dante's Divine Comedy and its place within the epic tradition. It discusses the work's structure including its division into the Inferno, Purgatorio, and Paradiso sections. Key details are provided on the poem's terza rima rhyme scheme, use of hendecasyllabic meter, and inclusion of allegorical and classical references. Background information is given on Dante the author and the political context of 14th century Florence.
You know you're an adult when every check-up gets you down. View What Going to the Doctor is Like as an Adult and more funny posts on salty vixen stories & more-saltyvixenstories.com
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Jason Kozup is a versatile figure whose impact spans numerous sectors. From the realms of entertainment and security, he has thrived as a producer, actor, stuntman, model, and aerospace defense contractor, showcasing excellence across the board.
Tom Cruise Daughter: An Insight into the Life of Suri Cruisegreendigital
Tom Cruise is a name that resonates with global audiences for his iconic roles in blockbuster films and his dynamic presence in Hollywood. But, beyond his illustrious career, Tom Cruise's personal life. especially his relationship with his daughter has been a subject of public fascination and media scrutiny. This article delves deep into the life of Tom Cruise daughter, Suri Cruise. Exploring her upbringing, the influence of her parents, and her current life.
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Introduction: The Fame Surrounding Tom Cruise Daughter
Suri Cruise, the daughter of Tom Cruise and Katie Holmes, has been in the public eye since her birth on April 18, 2006. Thanks to the media's relentless coverage, the world watched her grow up. As the daughter of one of Hollywood's most renowned actors. Suri has had a unique upbringing marked by privilege and scrutiny. This article aims to provide a comprehensive overview of Suri Cruise's life. Her relationship with her parents, and her journey so far.
Early Life of Tom Cruise Daughter
Birth and Immediate Fame
Suri Cruise was born in Santa Monica, California. and from the moment she came into the world, she was thrust into the limelight. Her parents, Tom Cruise and Katie Holmes. Were one of Hollywood's most talked-about couples at the time. The birth of their daughter was a anticipated event. and Suri's first public appearance in Vanity Fair magazine set the tone for her life in the public eye.
The Impact of Celebrity Parents
Having celebrity parents like Tom Cruise and Katie Holmes comes with its own set of challenges and privileges. Suri Cruise's early life marked by a whirlwind of media attention. paparazzi, and public interest. Despite the constant spotlight. Her parents tried to provide her with an upbringing that was as normal as possible.
The Influence of Tom Cruise and Katie Holmes
Tom Cruise's Parenting Style
Tom Cruise known for his dedication and passion in both his professional and personal life. As a father, Cruise has described as loving and protective. His involvement in the Church of Scientology, but, has been a point of contention and has influenced his relationship with Suri. Cruise's commitment to Scientology has reported to be a significant factor in his and Holmes' divorce and his limited public interactions with Suri.
Katie Holmes' Role in Suri's Life
Katie Holmes has been Suri's primary caregiver since her separation from Tom Cruise in 2012. Holmes has provided a stable and grounded environment for her daughter. She moved to New York City with Suri to start a new chapter in their lives away from the intense scrutiny of Hollywood.
Suri Cruise: Growing Up in the Spotlight
Media Attention and Public Interest
From stylish outfits to everyday activities. Suri Cruise has been a favorite subject for tabloids and entertainment news. The constant media attention has shaped her childhood. Despite this, Suri has managed to maintain a level of normalcy, thanks to her mother's efforts.
Morgan Freeman is Jimi Hendrix: Unveiling the Intriguing Hypothesisgreendigital
In celebrity mysteries and urban legends. Few narratives capture the imagination as the hypothesis that Morgan Freeman is Jimi Hendrix. This fascinating theory posits that the iconic actor and the legendary guitarist are, in fact, the same person. While this might seem like a far-fetched notion at first glance. a deeper exploration reveals a rich tapestry of coincidences, speculative connections. and a surprising alignment of life events fueling this captivating hypothesis.
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Introduction to the Hypothesis: Morgan Freeman is Jimi Hendrix
The idea that Morgan Freeman is Jimi Hendrix stems from a mix of historical anomalies, physical resemblances. and a penchant for myth-making that surrounds celebrities. While Jimi Hendrix's official death in 1970 is well-documented. some theorists suggest that Hendrix did not die but instead reinvented himself as Morgan Freeman. a man who would become one of Hollywood's most revered actors. This article aims to delve into the various aspects of this hypothesis. examining its origins, the supporting arguments. and the cultural impact of such a theory.
The Genesis of the Theory
Early Life Parallels
The hypothesis that Morgan Freeman is Jimi Hendrix begins by comparing their early lives. Jimi Hendrix, born Johnny Allen Hendrix in Seattle, Washington, on November 27, 1942. and Morgan Freeman, born on June 1, 1937, in Memphis, Tennessee, have lived very different lives. But, proponents of the theory suggest that the five-year age difference is negligible and point to Freeman's late start in his acting career as evidence of a life lived before under a different identity.
The Disappearance and Reappearance
Jimi Hendrix's death in 1970 at the age of 27 is a well-documented event. But, theorists argue that Hendrix's death staged. and he reemerged as Morgan Freeman. They highlight Freeman's rise to prominence in the early 1970s. coinciding with Hendrix's supposed death. Freeman's first significant acting role came in 1971 on the children's television show "The Electric Company," a mere year after Hendrix's passing.
Physical Resemblances
Facial Structure and Features
One of the most compelling arguments for the hypothesis that Morgan Freeman is Jimi Hendrix lies in the physical resemblance between the two men. Analyzing photographs, proponents point out similarities in facial structure. particularly the cheekbones and jawline. Both men have a distinctive gap between their front teeth. which is rare and often highlighted as a critical point of similarity.
Voice and Mannerisms
Supporters of the theory also draw attention to the similarities in their voices. Jimi Hendrix known for his smooth, distinctive speaking voice. which, according to some, resembles Morgan Freeman's iconic, deep, and soothing voice. Additionally, both men share certain mannerisms. such as their calm demeanor and eloquent speech patterns.
Artistic Parallels
Musical and Acting Talents
Jimi Hendrix was regarded as one of t
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Taylor Swift: Conquering Fame, Feuds, and Unmatched Success | CIO Women MagazineCIOWomenMagazine
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The Midnight Sculptor.pdf writer by Ali alsiadali345alghlay
The city of Ravens burg was known for its gothic architecture, fog-covered streets, and an eerie silence that seemed to hang over the town like a shroud.
How OTT Players Are Transforming Our TV Viewing Experience.pdfGenny Knight
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The cats, Sunny and Rishi, are brothers who live with their sister, Jessica, and their grandmother, Susie. They work as cleaners but wish to seek other kinds of employment that are better than their current jobs. New career adventures await Sunny and Rishi!
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Unlocking the Secrets of IPTV App Development_ A Comprehensive Guide.pdfWHMCS Smarters
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2. " Man is the Measure of all Things ." Protagoras Click for Vitruvian Man interview
3. Influenced by the Greeks, the Ancient Roman architect VITRUVIUS wrote that in the human body:
4. Influenced by the Greeks, the Ancient Roman architect VITRUVIUS wrote that in the human body: a palm is the width of four fingers a foot is the width of four palms a cubit is the width of six palms a man's height is four cubits (and thus 24 palms) a pace is four cubits the length of a man's outspread arms is equal to his height the distance from the hairline to the bottom of the chin is one-tenth of a man's height the distance from the top of the head to the bottom of the chin is one-eighth of a man's height the distance from the hairline to the top of the breast is one-seventh of a man's height the distance from the top of the head to the nipples is one-fourth of a man's height the maximum width of the shoulders is one-fourth of a man's height the distance from the elbow to the tip of the hand is one-fifth of a man's height the distance from the elbow to the armpit is one-eight of a man's height the length of the hand is one-tenth of a man's height the distance from the bottom of the chin to the nose is one-third of the length of the face the distance from the hairline to the eyebrows is one-third of the length of the face the length of the ear is one-third of the length of the face
16. What did Bodhi Tree say upon attaining enlightenment and realizing he was merely a green, fruit-bearing sphere atop a brown, bark-covered cylinder?
17. Ge-om-e-try What did Bodhi Tree say upon attaining enlightenment and realizing he was merely a green, fruit-bearing sphere atop a brown, bark-covered cylinder?
20. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats The Greeks perfected the use of Geometry
21. The Greeks wished to maintain ideal proportions when building any room or like structure from the ground up.
22. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats The Golden Rectangle
23. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats Q: Given a flat rectangle,
24. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats what is its most aesthetically pleasing height?
25. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats What Does that “ MEAN” ?
26. The arithmetic mean occurs when the length of the sides of a square whose PERIMETER is the same as the rectangle. ( L + W ) / 2 ( 12 + 6 ) / 2 = 9 9 exceeds 6 by 3, which is the same amount by which 12 exceeds 9. LOGIC
27. The geometric mean is the nth root of the product of the variables (sides). Here n = 2. The arithmetic mean occurs when the length of the sides of a square* whose AREA is the same as the rectangle. 9 X 4 = 36 The square root of 36 is 6 * 6 x 6
28. The harmonic mean is the number of variables (sides) divided by the sum of each side’s reciprocal. Here n=2 and the sides are 12 and 6. 1/12 + 1/6 = 3/12, or ¼. 2 divided by ¼ equals 8
30. Leon Battista Alberti, Florentine Architect (1407-1472) "We shall therefore borrow all our Rules for the Finishing our Proportions, from the MUSICIANS, who are the greatest Masters of this Sort of Numbers, and from those Things wherein Nature shows herself most excellent and complete."
31. Music, Numbers and the Universe ? "Seek truth and beauty together; you will never find them apart." Pythagoras of Samos
32. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats Big Idea: Mathematics is the language of nature. LOGIC
39. SUPERIMPOSED MIRRORED MOTIFS IN ART Bach 1685-1750 Baroque Period M.C. Escher (1898 - 1972) Modern Period Recursion in Art Recursion in Art Recursion in Art
71. Diatonic Scale H W W W H W W Step 256:243 9:8 9:8 9:8 256:243 9:8 9:8 Intra-Ratio A to B 243:128 G to A 27:16 E to F 4:3 F to G 3:2 B to C D to E C to D Tone 2:1 81:64 9:8 1:1 Tonic
80. Filling in the Gaps The harmonic mean is the number of variables (notes) divided by the sum of each side’s reciprocal. Here n=2 and the sides are 12 and 6. TASK: Calculate the harmonic mean for the numbers 1 and 2…
81. Filling in the Gaps The harmonic mean is the number of variables (notes) divided by the sum of each side’s reciprocal. Here n=2 and the sides are 12 and 6. ANSWER: For 1 and 2… 1/1 + 1/2 = 3/2 . 2 divided by 3/2 equals 4/3
85. And since harmony is reducible to number, perfection is likewise reducible to number . The universe is harmonious, so it follows that the universe as a whole can be explained in terms of number . Pythagoras of Samos LOGIC
86. I perfected the logical syllogism as a method for discovering TRUTH . Aristotle says, AGAIN…
93. Q : Which ancient Greek philosopher took Pythagoras’ theory of the universe and “shaped” it further?
94. Q : Which ancient Greek philosopher took Pythagoras’ theory of the universe and “shaped” it further? HINT : He expanded the scale of the musical scale AND the scale of the universe. PLAY
96. Plato, through Timaeus, reasoned in reverse stating that the creator made the world soul out of various ingredients, and formed it into a long strip… The strip was then marked out into intervals… Plato
97. “ First [the creator] took one portion from the strip (1st unit) and next a portion double the first (2nd unit) a third portion half again as much as the second (3rd unit) the fourth portion double the second (4th unit) the fifth three times the third (9th unit) the sixth eight times the first (8th unit) and the seventh 27 times the first (27th unit) ” They give the seven integers; 1, 2, 3, 4, 8, 9, 27. These contain the monad, source of all numbers, the first even and first odd, and their squares and cubes. Plato LAMBDA
109. LAMBDA They give the seven integers; 1, 2, 3, 4, 8, 9, 27. These contain the monad, source of all numbers, the first even and first odd, and their squares and cubes.
110. But my system wasn’t exactly perfect… Pythagoras of Samos
111. But first, let’s C who knows what the word ENHARMONIC means. HINT: If you answer correctly, you must really B#.
113. Allusion Trivia Following their final live performance atop a rooftop in 1969, which band’s musician quipped, “ I'd like to say thank you very much on behalf of the group and myself and I hope we passed the audition” ?
127. by Lorreen Pelletier in sky apple a la mode cherry or humble shoo fly pie mulberry mud or pumpkin chocolate pecan oh ruin your appetite by Lorreen Pelletier Pie. I like a peach blueberry or banana cream and lemon meringue raspberry rhubarb mincemeat pie
128. Poe, E. Near a Raven Midnights so dreary, tired and weary. Silently pondering volumes extolling all by-now obsolete lore. During my rather long nap - the weirdest tap! An ominous vibrating sound disturbing my chamber's antedoor . "This", I whispered quietly, "I ignore". Perfectly, the intellect remembers: the ghostly fires, a glittering ember . Inflamed by lightning's outbursts, windows cast penumbras upon this floor. Sorrowful, as one mistreated, unhappy thoughts I heeded : That inimitable lesson in elegance - Lenore - Is delighting, exciting...nevermore . Ominously, curtains parted (my serenity outsmarted), And fear overcame my being - the fear of "forevermore". Fearful foreboding abided, selfish sentiment confided, As I said, "Methinks mysterious traveler knocks afore. A man is visiting, of age threescore."
129. Simpler Pi Poems Did I tell a witty wisecrack? (3.14159) Yes, I love a green grassland. (3.14159) Boy, I want a glass half-full of Sprite. (3.1415926) From Paul’s Page of Pi: http://www.escape.com/~paulg53/math/pi/poems.html
161. Aristotle The truth can be found by analyzing nature (breaking in to parts).
162. … so the hotdog guy makes the hotdog with everything on it. The monk exchanges a $20 for the hotdog and waits for his change. When no change is forthcoming, the monk asks, "Hey, where's my change?" The hotdog guy replies, "Change must come from within."
164. … and the hotdog guy replies… Hey, where's my change?" The hotdog guy replies, "Change must come from within."
165. “ Sorry, but you should already know… Change comes from within."
166. Aristotle BIG IDEA : “Moral virtue is a state of character lying in a mean between two extremes . ” ETHICS
167. Aristotle’s GOLDEN MEAN ACTION Deficiency Goodness/Mean Excess Fear cowardice courage rashness/foolhardy Drinking/Eating insensible temperate self-indulgent Truth telling modesty/ truthful self-deprecation Lending $$ stingy liberality prodigality Amusement boring ready wit buffoonery “ Moral virtue is a state of character lying in a mean between two extremes . ”
170. GOLDEN SECTION Standard sized credit cards are 54mm x 86mm, creating a ratio of 0.628, less than a millimeter from a perfect golden section of 0.618. http://goldennumber.net/classic/fibonser.htm
171. the Fibonacci Series 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . http://goldennumber.net/classic/fibonser.htm
172. GOLDEN SECTION: PHI Starting with 0 and 1, each new number in the series is simply the sum of the two before it. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . . The ratio of each successive pair of numbers in the series approximates phi (1.618. . .) , as 5 divided by 3 is 1.666..., and 8 divided by 5 is 1.60. The ratios of the successive numbers in the Fibonacci series quickly converge on Phi or Φ. After the 40th number in the series, the ratio is accurate to 15 decimal places. 1.618033988749895 . . . http://goldennumber.net/classic/fibonser.htm
173. the GOLDEN MEAN Musical scales are based on Fibonacci numbers The Fibonacci series appears in the foundation of aspects of art, beauty and life. Even music has a foundation in the series, as: There are 13 notes in the span of any note through its octave. A scale is comprised of 8 notes, of which the 5th and 3rd notes create the basic foundation of all chords, and are based on whole tone which is 2 steps from the root tone, that is the 1st note of the scale. Note too how the piano keyboard scale of C to C above of 13 keys has 8 white keys and 5 black keys, split into groups of 3 and 2. http://goldennumber.net/classic/fibonser.htm
175. the GOLDEN MEAN The Fibonacci series appears in the foundation of aspects of art, beauty and life. Even music has a foundation in the series, as: There are 13 notes in the span of any note through its octave. A scale is comprised of 8 notes, of which the 5th and 3rd notes create the basic foundation of all chords, and are based on whole tone which is 2 steps from the root tone, that is the 1st note of the scale.
194. "My new Hypothesis: If we're built from Spirals while living in a giant Spiral, then is it possible that everything we put our hands to is infused with the Spiral?" -- Max Cohen in the motion picture PI
195.
196. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats The Golden Rectangle
197. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats The Golden Rectangle
200. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats What is the difference between…
201. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats What is the difference between… the truth and
202. “ Beauty is Truth and Truth Beauty, That is All Ye Know on Earth and All Ye Need to Know.” Keats What is the difference between… the truth and T ruth ?
203. The eternal paradox of literature: Art always tells the Truth
204. John Malkovich as himself in Being John Malkovich 1999 The eternal paradox of literature: Art always tells the Truth even when it’s lying.
205. The eternal paradox of literature: What’s T rue need not be true.
206. The eternal paradox of literature: Although a story is fictional… Its THEME is always True.
Ancient Greek Aesthetics: Harmony & Proportion Vitruvian Man Vitruvian Man Leonardo da Vinci , c. 1490 pen, ink and watercolour over metalpoint , 34.3 × 24.5 cm Gallerie dell'Accademia , Venice The Vitruvian Man is a famous drawing with accompanying notes by Leonardo da Vinci made around the year 1490 in one of his journals. It depicts a naked male figure in two superimposed positions with his arms apart and simultaneously inscribed in a circle and square. The drawing and text are sometimes called the Canon of Proportions . According to Leonardo's notes in the accompanying text, which are mirror writing , it was made as a study of the proportions of the (male) human body as described in a treatise by the Ancient Roman architect Vitruvius , who wrote that in the human body: a palm is the width of four fingers a foot is the width of four palms a cubit is the width of six palms a man's height is four cubits (and thus 24 palms) a pace is four cubits the length of a man's outspread arms is equal to his height the distance from the hairline to the bottom of the chin is one-tenth of a man's height the distance from the top of the head to the bottom of the chin is one-eighth of a man's height the distance from the hairline to the top of the breast is one-seventh of a man's height the distance from the top of the head to the nipples is one-fourth of a man's height the maximum width of the shoulders is one-fourth of a man's height the distance from the elbow to the tip of the hand is one-fifth of a man's height the distance from the elbow to the armpit is one-eight of a man's height the length of the hand is one-tenth of a man's height the distance from the bottom of the chin to the nose is one-third of the length of the face the distance from the hairline to the eyebrows is one-third of the length of the face the length of the ear is one-third of the length of the face Leonardo is clearly illustrating Vitruvius De Architectura 3.1.3 which reads: The navel is naturally placed in the centre of the human body, and, if in a man lying with his face upward, and his hands and feet extended, from his navel as the centre, a circle be described, it will touch his fingers and toes. It is not alone by a circle, that the human body is thus circumscribed, as may be seen by placing it within a square. For measuring from the feet to the crown of the head, and then across the arms fully extended, we find the latter measure equal to the former; so that lines at right angles to each other, enclosing the figure, will form a square. The rediscovery of the mathematical proportions of the human body in the 15th century by Leonardo and others is considered one of the great achievements leading to the Italian Renaissance . Note that Leonardo's drawing combines a careful reading of the ancient text, combined with his own observation of actual human bodies. In drawing the circle and square he correctly observes that the square cannot have the same center as the circle, the navel, but is somewhat lower in the anatomy. This adjustment is the innovative part of Leonardo's drawing and what distinguishes it from earlier illustrations. The drawing itself is often used as an implied symbol of the essential symmetry of the human body, and by extension, to the universe as a whole. It may be noticed by examining the drawing that the combination of arm and leg positions actually creates sixteen different poses. The pose with the arms straight out and the feet together is seen to be inscribed in the superimposed square. On the other hand, the "spread-eagle" pose is seen to be inscribed in the superimposed circle. This illustrates the principle that in the shift between the two poses, the apparent center of the figure seems to move, but in reality, the navel of the figure, which is the true center of gravity , remains motionless. From Wikipedia, the free encyclopedia.