The document discusses Platonic solids, which are five specific geometric shapes - the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. These shapes were discovered by ancient Greek mathematicians and philosophers like Plato to have significance. Each shape has identical regular faces, vertices, and edges. The document provides examples of these shapes appearing in nature and architecture.
There are five regular polyhedra known as the Platonic solids. They are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The Platonic solids have identical regular polygons as faces and identical vertices. They were known to ancient Greeks like Plato and Pythagoras and have been important in fields like philosophy, art, and science through history.
The document discusses the five Platonic solids - tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Each solid is defined by the number of faces it has and the geometric shape of those faces. In ancient Greek philosophy, each solid was associated with one of the classical elements - fire, earth, air, water. The properties of the elements, like their physical characteristics, provided intuitive connections to the shapes of the matching Platonic solid. For example, fire was seen as sharp like the points of a tetrahedron and water flowed like the small balls of an icosahedron.
The document discusses the five Platonic solids, which are convex polyhedra with congruent, regular faces. These five shapes are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. According to Plato, each solid was associated with an element - the tetrahedron with fire, cube with earth, octahedron with air, icosahedron with water, and dodecahedron with the universe. The document also provides context on Plato and the origins of the term "polyhedron".
The document discusses the five Platonic solids - geometric shapes that are the only possible convex regular polyhedra. These five shapes are the tetrahedron (4 faces), cube (6 faces), octahedron (8 faces), dodecahedron (12 faces), and icosahedron (20 faces). The Platonic solids have been known since antiquity and are notable for their symmetry, with all faces being the same regular polygon and all vertices having the same configuration. They can all be inscribed in a sphere and satisfy Euler's formula relating the number of vertices, edges, and faces.
The ancient Greeks, including the Pythagoreans and mathematician Theaetetus, studied five regular polyhedra known as the Platonic solids. These shapes, which include the tetrahedron, cube, octahedron, dodecahedron, and icosahedron, were believed by the philosopher Plato to represent fundamental aspects of the physical universe.
This document provides an overview of five important Greek philosophers: Socrates, Plato, Pythagoras, Aristotle, and Empedocles. It summarizes key biographical details and contributions to philosophy for each one. Socrates is considered the father of western philosophy and was put on trial and sentenced to death. Plato founded the Academy in Athens and was a student of Socrates. Pythagoras made important contributions to mathematics and believed that numbers governed the universe. Aristotle studied under Plato and rejected his theory of forms, making significant contributions across many fields. Empedocles originated the theory of the four classical elements and proposed the forces of Love and Strife.
Aristotle was a Greek philosopher and scientist born in 384 BC who made significant contributions across many areas of knowledge. He wrote extensively on many topics, establishing the first comprehensive system of Western philosophy. Aristotle studied under Plato and later taught Alexander the Great. His works were enormously influential for over two thousand years and helped lay the foundations for many sciences and shaped Western scholarship in numerous fields including physics, biology, zoology, and logic. Though much of his original writings are now lost, Aristotle left behind one of the largest intellectual legacies of the ancient world.
The document discusses Platonic solids, which are five specific geometric shapes - the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. These shapes were discovered by ancient Greek mathematicians and philosophers like Plato to have significance. Each shape has identical regular faces, vertices, and edges. The document provides examples of these shapes appearing in nature and architecture.
There are five regular polyhedra known as the Platonic solids. They are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. The Platonic solids have identical regular polygons as faces and identical vertices. They were known to ancient Greeks like Plato and Pythagoras and have been important in fields like philosophy, art, and science through history.
The document discusses the five Platonic solids - tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Each solid is defined by the number of faces it has and the geometric shape of those faces. In ancient Greek philosophy, each solid was associated with one of the classical elements - fire, earth, air, water. The properties of the elements, like their physical characteristics, provided intuitive connections to the shapes of the matching Platonic solid. For example, fire was seen as sharp like the points of a tetrahedron and water flowed like the small balls of an icosahedron.
The document discusses the five Platonic solids, which are convex polyhedra with congruent, regular faces. These five shapes are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. According to Plato, each solid was associated with an element - the tetrahedron with fire, cube with earth, octahedron with air, icosahedron with water, and dodecahedron with the universe. The document also provides context on Plato and the origins of the term "polyhedron".
The document discusses the five Platonic solids - geometric shapes that are the only possible convex regular polyhedra. These five shapes are the tetrahedron (4 faces), cube (6 faces), octahedron (8 faces), dodecahedron (12 faces), and icosahedron (20 faces). The Platonic solids have been known since antiquity and are notable for their symmetry, with all faces being the same regular polygon and all vertices having the same configuration. They can all be inscribed in a sphere and satisfy Euler's formula relating the number of vertices, edges, and faces.
The ancient Greeks, including the Pythagoreans and mathematician Theaetetus, studied five regular polyhedra known as the Platonic solids. These shapes, which include the tetrahedron, cube, octahedron, dodecahedron, and icosahedron, were believed by the philosopher Plato to represent fundamental aspects of the physical universe.
This document provides an overview of five important Greek philosophers: Socrates, Plato, Pythagoras, Aristotle, and Empedocles. It summarizes key biographical details and contributions to philosophy for each one. Socrates is considered the father of western philosophy and was put on trial and sentenced to death. Plato founded the Academy in Athens and was a student of Socrates. Pythagoras made important contributions to mathematics and believed that numbers governed the universe. Aristotle studied under Plato and rejected his theory of forms, making significant contributions across many fields. Empedocles originated the theory of the four classical elements and proposed the forces of Love and Strife.
Aristotle was a Greek philosopher and scientist born in 384 BC who made significant contributions across many areas of knowledge. He wrote extensively on many topics, establishing the first comprehensive system of Western philosophy. Aristotle studied under Plato and later taught Alexander the Great. His works were enormously influential for over two thousand years and helped lay the foundations for many sciences and shaped Western scholarship in numerous fields including physics, biology, zoology, and logic. Though much of his original writings are now lost, Aristotle left behind one of the largest intellectual legacies of the ancient world.
The document provides information about the Orion Nebula. Some key points:
- The Orion Nebula was the first nebula discovered, seen as a star by the naked eye in 1610 using an early telescope.
- Later observations by Huygens in 1656 determined it was a compact quadruple star system rather than a single star.
- Advances in instrumentation over the 18th-19th centuries allowed determination of motion in 3D space and classification of nebulae as distant galaxies/star systems.
Sacred geometry is the study of geometric patterns and sacred numbers that appear in sacred spaces and nature. Some key concepts discussed in the document include fractals that appear throughout nature, the golden spiral and ratio, platonic solids, the flower of life, tree of life, Pythagorean symbols like the vesica piscis and pentagram, crop circles, astrological aspects, mandalas, the tesseract, sangaku puzzles, ley lines, and influences of sacred geometry and Fibonacci sequences in music. The document provides examples and descriptions of these geometric patterns found in architecture, art, nature, and other religious and cultural contexts.
This document provides an overview of the connections between Euclid's 47th proposition, Pythagoras' teachings, and Speculative Freemasonry. It discusses how Euclid established mathematical rigor through his Elements, building on postulates like parallel lines. Pythagoras founded a religious brotherhood based on principles of mathematics in nature and the transmigration of souls. His teachings influenced early Christianity and aligned with concepts of the Trinity. Speculative Freemasonry references Pythagoras and Euclid's 47th proposition as symbols representing squaring one's actions with spiritual and divine principles.
Dark matter is a mysterious form of matter that cannot be seen but accounts for most of the mass in the universe. It was first hypothesized to explain discrepancies between the observed motions of galaxies and clusters and what was predicted based on the amount of visible matter. Dark matter is thought to make up around 23% of the universe, binding galaxies together through gravity. While dark matter cannot be directly observed, its effects on visible matter provide evidence of its existence. Scientists continue searching for dark matter particles and investigating its nature to better understand how it shapes the universe.
1) Kepler discovered that the orbits of planets are ellipses with the Sun located at one of the ellipse's two focal points. This became known as Kepler's First Law of Planetary Motion.
2) Kepler also found that a line connecting a planet to the Sun sweeps out equal areas in equal intervals of time. This is Kepler's Second Law.
3) Through his analysis of Tycho Brahe's precise astronomical observations, Kepler was able to overcome the imperfect circular orbital models of earlier astronomers and establish his revolutionary elliptical model of planetary motion.
Astrobiology Comic (Issue 1)για παιδιά Γυμνασίου.pdfΜαυρουδης Μακης
This document provides a summary of the history of exobiology and astrobiology at NASA. It discusses how the fields have evolved over the past 50 years from early speculation about life on other planets to the establishment of NASA's Exobiology program in 1960 and the expanded Astrobiology Program in the 1990s. The summary also highlights some of the key figures and experiments that helped shape our understanding of the potential for life elsewhere, such as the Miller-Urey experiment which demonstrated how organic molecules could form in conditions similar to the early Earth.
Science in the 16th Century- Interactive LectureCaitlin Pala
This document discusses science in early modern Europe, including:
1) There was debate around whether there was a "Scientific Revolution" and how science related to religion. Science was created by communities of scholars, not just individuals.
2) The term "science" comes from the Latin scientia, meaning knowledge. Natural philosophy and history created knowledge about the natural world and were part of the medieval university.
3) Early modern science included organizations like the Accademia dei Lincei that brought together natural historians, as well as figures like Tycho Brahe who made important astronomical observations.
This document summarizes several ancient Greek philosophers and their ideas, including Socrates, Plato, Aristotle, and Democritus. Socrates helped lay the foundations of western philosophy through his use of inductive reasoning and belief that wrongdoing stems from ignorance. Plato was a student of Socrates and documented his teachings, founding the Academy in Athens. Aristotle studied under Plato and made contributions across many fields, including physics, biology, and optics. Democritus originated the atomic theory that the universe is composed of indivisible atoms and void.
1) The document discusses the origins and development of Newton's laws of motion and gravity, starting with ancient Greek astronomers like Hipparchus, Ptolemy, and Aristarchus.
2) It then covers the contributions of key figures like Tycho Brahe, Galileo, and Kepler, who made important observational advances and discoveries that helped displace the geocentric Ptolemaic system.
3) The document focuses on Newton's extraordinary achievements in formulating mathematical laws of motion and universal gravitation, which were grounded in the work of the great scientists that came before him.
This document provides a critique of philosophy and an argument for the pre-eminence of art in describing reality. It summarizes philosophy as promoting skepticism and confusion through overthinking. Modern physics is described as speculative and uncertain in its understanding of reality. The document argues that art such as Giorgione's "The Tempest" can retell eternal stories that language and logic cannot configure, showing art's superiority over philosophy in depicting reality.
The document discusses the geocentric theory, which was the dominant model of the universe from ancient Greece until the 16th century. It states that under the geocentric theory, Earth is at the center of the universe and all other celestial bodies revolve around it. The theory was first proposed by ancient Greek philosophers like Aristotle and Ptolemy. It was later replaced by Copernicus' heliocentric theory, which placed the Sun at the center. The document provides details on the Ptolemaic system and key figures like Galileo who provided evidence supporting the heliocentric view.
The document discusses the geocentric theory, which was the dominant model of the universe from ancient Greece until the 16th century. It held that Earth is at the center of the universe, and all other celestial bodies revolve around it. Key aspects included that planets moved in circular orbits using epicycles and deferents, and the order of orbits. The theory was eventually replaced by the heliocentric model of Copernicus, Galileo and Kepler, which placed the Sun at the center.
1. The document discusses the history and evolution of optics from ancient times to the 11th century CE. It describes how early civilizations like the Greeks, Chinese, and Phoenicians made early observations and experiments with light, lenses, mirrors, and vision.
2. The work of the ancient Greek philosophers such as Euclid, Ptolemy, and Aristotle helped develop early theories of light, but it was not until the 11th century Arab scholar Ibn al-Haytham (Alhazen) that many modern theories of vision and optics began to take hold. Through experiments with lenses, mirrors, and the camera obscura, Alhazen helped debunk earlier theories and establish that light travels in straight lines
Boyle and Vitter The Copernican Model & Kepler Laws.pptxMohammadRajihBih
The document discusses the transition from the Aristotelian to the Copernican paradigm in astronomy. It describes Nicolaus Copernicus' heliocentric model proposed in 1543's De Revolutionibus, which placed the Sun rather than Earth at the center of the universe. Though not completely displacing the Ptolemaic system, Copernicus' model was further developed by Johannes Kepler, who established his three laws of planetary motion based on Tycho Brahe's astronomical observations. Kepler's laws provided strong evidence that the Copernican model more accurately described the motions of celestial bodies.
1) Prior to the Scientific Revolution, most Europeans believed in the geocentric model that the Earth was at the center of the universe.
2) Copernicus, Kepler, Galileo and Newton helped establish the heliocentric model through observations, experiments, and mathematical laws.
3) The Scientific Revolution established the modern scientific method and fundamentally changed how people understood the universe.
This is an 1880 gouache painting by the British artist Edward Burne-Jones titled The Magic Circle. This is how
I want to introduce you to Merlin -- our gardener, mariner guide, and astronomer extraordinaire.
Anthropologists place him in all sorts of teacher guises in the stretch of history. Here Merlin shows up as a
Mariner attracted by the inner call of the astonished person on the right.
http://wynnwolfe.com
The document discusses the Fundamental Fury roller coaster. It has a fast hydraulic launch that accelerates riders to over 250 km/h in 5 seconds. The coaster passes close to other sections of track, emphasizing its extreme nature. It is themed after fundamental particles and how violently they interact. The coaster tracks are colored cyan and purple to represent scientific color terms for subatomic particles. Dense evergreen trees surround much of the ride, providing scenery.
The document provides information about the Orion Nebula. Some key points:
- The Orion Nebula was the first nebula discovered, seen as a star by the naked eye in 1610 using an early telescope.
- Later observations by Huygens in 1656 determined it was a compact quadruple star system rather than a single star.
- Advances in instrumentation over the 18th-19th centuries allowed determination of motion in 3D space and classification of nebulae as distant galaxies/star systems.
Sacred geometry is the study of geometric patterns and sacred numbers that appear in sacred spaces and nature. Some key concepts discussed in the document include fractals that appear throughout nature, the golden spiral and ratio, platonic solids, the flower of life, tree of life, Pythagorean symbols like the vesica piscis and pentagram, crop circles, astrological aspects, mandalas, the tesseract, sangaku puzzles, ley lines, and influences of sacred geometry and Fibonacci sequences in music. The document provides examples and descriptions of these geometric patterns found in architecture, art, nature, and other religious and cultural contexts.
This document provides an overview of the connections between Euclid's 47th proposition, Pythagoras' teachings, and Speculative Freemasonry. It discusses how Euclid established mathematical rigor through his Elements, building on postulates like parallel lines. Pythagoras founded a religious brotherhood based on principles of mathematics in nature and the transmigration of souls. His teachings influenced early Christianity and aligned with concepts of the Trinity. Speculative Freemasonry references Pythagoras and Euclid's 47th proposition as symbols representing squaring one's actions with spiritual and divine principles.
Dark matter is a mysterious form of matter that cannot be seen but accounts for most of the mass in the universe. It was first hypothesized to explain discrepancies between the observed motions of galaxies and clusters and what was predicted based on the amount of visible matter. Dark matter is thought to make up around 23% of the universe, binding galaxies together through gravity. While dark matter cannot be directly observed, its effects on visible matter provide evidence of its existence. Scientists continue searching for dark matter particles and investigating its nature to better understand how it shapes the universe.
1) Kepler discovered that the orbits of planets are ellipses with the Sun located at one of the ellipse's two focal points. This became known as Kepler's First Law of Planetary Motion.
2) Kepler also found that a line connecting a planet to the Sun sweeps out equal areas in equal intervals of time. This is Kepler's Second Law.
3) Through his analysis of Tycho Brahe's precise astronomical observations, Kepler was able to overcome the imperfect circular orbital models of earlier astronomers and establish his revolutionary elliptical model of planetary motion.
Astrobiology Comic (Issue 1)για παιδιά Γυμνασίου.pdfΜαυρουδης Μακης
This document provides a summary of the history of exobiology and astrobiology at NASA. It discusses how the fields have evolved over the past 50 years from early speculation about life on other planets to the establishment of NASA's Exobiology program in 1960 and the expanded Astrobiology Program in the 1990s. The summary also highlights some of the key figures and experiments that helped shape our understanding of the potential for life elsewhere, such as the Miller-Urey experiment which demonstrated how organic molecules could form in conditions similar to the early Earth.
Science in the 16th Century- Interactive LectureCaitlin Pala
This document discusses science in early modern Europe, including:
1) There was debate around whether there was a "Scientific Revolution" and how science related to religion. Science was created by communities of scholars, not just individuals.
2) The term "science" comes from the Latin scientia, meaning knowledge. Natural philosophy and history created knowledge about the natural world and were part of the medieval university.
3) Early modern science included organizations like the Accademia dei Lincei that brought together natural historians, as well as figures like Tycho Brahe who made important astronomical observations.
This document summarizes several ancient Greek philosophers and their ideas, including Socrates, Plato, Aristotle, and Democritus. Socrates helped lay the foundations of western philosophy through his use of inductive reasoning and belief that wrongdoing stems from ignorance. Plato was a student of Socrates and documented his teachings, founding the Academy in Athens. Aristotle studied under Plato and made contributions across many fields, including physics, biology, and optics. Democritus originated the atomic theory that the universe is composed of indivisible atoms and void.
1) The document discusses the origins and development of Newton's laws of motion and gravity, starting with ancient Greek astronomers like Hipparchus, Ptolemy, and Aristarchus.
2) It then covers the contributions of key figures like Tycho Brahe, Galileo, and Kepler, who made important observational advances and discoveries that helped displace the geocentric Ptolemaic system.
3) The document focuses on Newton's extraordinary achievements in formulating mathematical laws of motion and universal gravitation, which were grounded in the work of the great scientists that came before him.
This document provides a critique of philosophy and an argument for the pre-eminence of art in describing reality. It summarizes philosophy as promoting skepticism and confusion through overthinking. Modern physics is described as speculative and uncertain in its understanding of reality. The document argues that art such as Giorgione's "The Tempest" can retell eternal stories that language and logic cannot configure, showing art's superiority over philosophy in depicting reality.
The document discusses the geocentric theory, which was the dominant model of the universe from ancient Greece until the 16th century. It states that under the geocentric theory, Earth is at the center of the universe and all other celestial bodies revolve around it. The theory was first proposed by ancient Greek philosophers like Aristotle and Ptolemy. It was later replaced by Copernicus' heliocentric theory, which placed the Sun at the center. The document provides details on the Ptolemaic system and key figures like Galileo who provided evidence supporting the heliocentric view.
The document discusses the geocentric theory, which was the dominant model of the universe from ancient Greece until the 16th century. It held that Earth is at the center of the universe, and all other celestial bodies revolve around it. Key aspects included that planets moved in circular orbits using epicycles and deferents, and the order of orbits. The theory was eventually replaced by the heliocentric model of Copernicus, Galileo and Kepler, which placed the Sun at the center.
1. The document discusses the history and evolution of optics from ancient times to the 11th century CE. It describes how early civilizations like the Greeks, Chinese, and Phoenicians made early observations and experiments with light, lenses, mirrors, and vision.
2. The work of the ancient Greek philosophers such as Euclid, Ptolemy, and Aristotle helped develop early theories of light, but it was not until the 11th century Arab scholar Ibn al-Haytham (Alhazen) that many modern theories of vision and optics began to take hold. Through experiments with lenses, mirrors, and the camera obscura, Alhazen helped debunk earlier theories and establish that light travels in straight lines
Boyle and Vitter The Copernican Model & Kepler Laws.pptxMohammadRajihBih
The document discusses the transition from the Aristotelian to the Copernican paradigm in astronomy. It describes Nicolaus Copernicus' heliocentric model proposed in 1543's De Revolutionibus, which placed the Sun rather than Earth at the center of the universe. Though not completely displacing the Ptolemaic system, Copernicus' model was further developed by Johannes Kepler, who established his three laws of planetary motion based on Tycho Brahe's astronomical observations. Kepler's laws provided strong evidence that the Copernican model more accurately described the motions of celestial bodies.
1) Prior to the Scientific Revolution, most Europeans believed in the geocentric model that the Earth was at the center of the universe.
2) Copernicus, Kepler, Galileo and Newton helped establish the heliocentric model through observations, experiments, and mathematical laws.
3) The Scientific Revolution established the modern scientific method and fundamentally changed how people understood the universe.
This is an 1880 gouache painting by the British artist Edward Burne-Jones titled The Magic Circle. This is how
I want to introduce you to Merlin -- our gardener, mariner guide, and astronomer extraordinaire.
Anthropologists place him in all sorts of teacher guises in the stretch of history. Here Merlin shows up as a
Mariner attracted by the inner call of the astonished person on the right.
http://wynnwolfe.com
The document discusses the Fundamental Fury roller coaster. It has a fast hydraulic launch that accelerates riders to over 250 km/h in 5 seconds. The coaster passes close to other sections of track, emphasizing its extreme nature. It is themed after fundamental particles and how violently they interact. The coaster tracks are colored cyan and purple to represent scientific color terms for subatomic particles. Dense evergreen trees surround much of the ride, providing scenery.
M.C. Escher was a Dutch graphic artist known for his mathematically inspired woodcuts, lithographs, and mezzotints that often featured impossible constructions, explorations of infinity, and tessellations. Some of his most famous works include Waterfall, which appears to violate the law of gravity, and his lithograph Print Gallery, which depicts a never-ending staircase. His artworks explored spatial illusions, reflections, and concepts in mathematics like topology.
Acolyte Episodes review (TV series) The Acolyte. Learn about the influence of the program on the Star Wars world, as well as new characters and story twists.
04062024_First India Newspaper Jaipur.pdfFIRST INDIA
Find Latest India News and Breaking News these days from India on Politics, Business, Entertainment, Technology, Sports, Lifestyle and Coronavirus News in India and the world over that you can't miss. For real time update Visit our social media handle. Read First India NewsPaper in your morning replace. Visit First India.
CLICK:- https://firstindia.co.in/
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Essential Tools for Modern PR Business .pptxPragencyuk
Discover the essential tools and strategies for modern PR business success. Learn how to craft compelling news releases, leverage press release sites and news wires, stay updated with PR news, and integrate effective PR practices to enhance your brand's visibility and credibility. Elevate your PR efforts with our comprehensive guide.
Here is Gabe Whitley's response to my defamation lawsuit for him calling me a rapist and perjurer in court documents.
You have to read it to believe it, but after you read it, you won't believe it. And I included eight examples of defamatory statements/
An astonishing, first-of-its-kind, report by the NYT assessing damage in Ukraine. Even if the war ends tomorrow, in many places there will be nothing to go back to.
El Puerto de Algeciras continúa un año más como el más eficiente del continente europeo y vuelve a situarse en el “top ten” mundial, según el informe The Container Port Performance Index 2023 (CPPI), elaborado por el Banco Mundial y la consultora S&P Global.
El informe CPPI utiliza dos enfoques metodológicos diferentes para calcular la clasificación del índice: uno administrativo o técnico y otro estadístico, basado en análisis factorial (FA). Según los autores, esta dualidad pretende asegurar una clasificación que refleje con precisión el rendimiento real del puerto, a la vez que sea estadísticamente sólida. En esta edición del informe CPPI 2023, se han empleado los mismos enfoques metodológicos y se ha aplicado un método de agregación de clasificaciones para combinar los resultados de ambos enfoques y obtener una clasificación agregada.
1. In the figures we can see some
examples of poligons: the pyramids of
Cheope ,a ball ,but also some nature
examples like the bacteriophage in
the lower left and the cells of bees.
Platonic solid is the synonymous of regular solid and of convex
polyhedron
and is a convex polyhedron that has congruent regular
polygons for faces ( that is exactly superimposable ).
2. Platonic solids and
phylosophy
The Platonic solids are five and according to the philosophy they
were the five bases on wich rests the world.
That is, the smaller forms that organize the visible matter and
invisible. In the “TIMEO” Platon himself describes the tetrahedron
as a “force and germ "of the fire, the octahedron as air, the
icosahedron as water ,the cube as the Earth, and the
dodecahedron represents the image of the universe in its totality.
3. The origins of the solids
The cube, the pyramid (tetrahedron) and the dodecahedron are
attributed to the Pythagoreans, and the discovery of the octahedron
and the icosahedron goes back to the Theaetetus.
In particular the discovery of the dodecahedron can be traced to
the fact that in Ancient Greece (especially in Sicily) people found
easy beautiful pyrite crystals of this form.
4. Luck in the history of Platonic solids
The luck of the Platonic solids in thescientific imagination of Western culture has
been enormous.
Art and science blend in a deep, Piero Della Francesca writes
the "de Libellus quinque corporibus regularibus" and Luca Pacioli gives a vulgar
version in the "De divina proportione “. He commissioned 60 plates to Leonardo da
Vinci precisely in order to illustrate the possible variations of simple regular
polyhedra.
Science is no longer seen only as an abstraction or a purely technical but also as a
liberal art. (below you can see on the left "The Flagellation of Christ" by Piero della
Francesca, and right on "De Divina Proportione"). Is interesting to note how in the
work of Piero della Francesca the proportions and harmony are respected.
5. Astronomy, physics and mathematics
with the Platonic solids
Kepler, known for his enormous contribution to astronomy, tried to
show how the properties of the Platonic solids are closely related
with the regularity of the planetary system.
In fact, the regularity of the Platonic solids is strictly connected to
the symmetry properties of the physical world.
The regular polyhedra are also now the starting point of many fields
of research in mathematics and physics.
6. Thanks to the orbiting Hubble telescope and other new
telescopes outside the Earth's atmosphere that have
The Platonic taken more detailed pictures and clear than those from
the ground, it has been possible since 2000, creating
new maps of the sky, galaxies, galaxy clusters and
solids and super-clusters of galaxies. Using radio waves, x-rays
and other measurements, were located many galaxies
the universe are not visible. These data were combined and found
that the super-clusters are collected along known lines
and points of intersection which form at least 4
octahedra premises, which are joined to the vertices in a
kind of crystalline scheme. Among these octahedra and
within them, there are gaps related to magnetic fields
and galaxies should contain a lot of dark matter. This is
the largest structure in the Universe directly observed: