Golden Ratio The Idea Behind It Have a try yourself (use the slider): Beauty This rectangle has been made using the Golden Ratio, Looks like a typical frame for a painting, doesn't it? Some artists and architects believe the Golden Ratio makes the most pleasing and beautiful shape. Do you think it is the "most pleasing rectangle"? Maybe you do or don't, that is up to you! Many buildings and artworks have the Golden Ratio in them, such as the Parthenon in Greece, but it is not really known if it was designed that way. The Actual Value The Golden Ratio is equal to: 1.61803398874989484820... The digits just keep on going, with no pattern. Calculating It You can calculate it yourself by starting with any number and following these steps: A) divide 1 by your number (=1/number) B) add 1 C) that is your new number, start again at A With a calculator, just keep pressing "1/x", "+", "1", "=", around and around. It is getting closer and closer! Drawing It Here is one way to draw a rectangle with the Golden Ratio: Pentagram
ANCIENT EGYPT : The Ten Keys of Hermes Trismegistos I, King Pepi, am THOTH, the mightiest of the gods ... Pyramid Texts, § 1237. I, said he, am POIMANDRES, the Mind of the Sovereignty. "Do You not know that You have become a God, and son of the One, even as I have ?" 1 The mental origin of the world and of man. 2 Corresponding harmonics. 3 Dynamics of alternation. 4 Bi-polarity and complementarity. 5 Cyclic repolarisation. 6 Cause and effect. 7 Gender. 8 The astrology of the Ogdoad. 9 The magic of the Ennead. 10 The alchemy of the Decad. "Content is Atum, father of the gods. With this great and might word, which issued from the mouth of THOTH for Osiris, the Treasurer of Life, Seal-bearer of the gods, Anubis, who claims hearts, claims Osiris King Pepi ... Hear O THOTH, in whom is the peace of the gods ... Abstract The religion of Ancient Egypt has been reconstructed by the Greeks (in the Hermetica), by the Abrahamic tradition (in their Scriptures) and by the Western Mystery Tradition (Hermeticism). Introduction ► the Zohar "In 1612, G.
Pi Day Activity- Make Pi Art! Happy Pi Day everyone! I remember thinking this holiday was really cool when I was younger. We let out our inner nerds, drank soda, and ate a pizza pie in class. Earlier this week I whetted your mathy appetite when I shared how I turned Pi into wearable art. My super easy and colorful Pi Day Bracelets were made by stringing different colored beads according to the digits in Pi. Today I'm celebrating Pi Day with two colorful and geometric pieces of Pi Day Inspired Artwork. "Easy As Pi" Artwork! And if you have younger preschool aged children, check out my 5 easy ways to celebrate Pi Day with Preschoolers! Now let's celebrate your inner nerd and create some fun artwork to brighten up your wall. Materials Needed to Make Pi Artwork: Paper (I used Watercolor)MarkersPencilRulerSomething with a long straight edgeEraserProtractor Large circular objectPrintout of Pi's digits Color codes (To relate Pi's digits to specific colors) Draw Polka Dot Pi Inspired Artwork: 1. Draw Pi As a Colorful Network: 1.
Golden Ratio The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron. It is denoted , or sometimes The designations "phi" (for the golden ratio conjugate ) and "Phi" (for the larger quantity ) are sometimes also used (Knott), although this usage is not necessarily recommended. The term "golden section" (in German, goldener Schnitt or der goldene Schnitt) seems to first have been used by Martin Ohm in the 1835 2nd edition of his textbook Die Reine Elementar-Mathematik (Livio 2002, p. 6). ("phi") was apparently first used by Mark Barr at the beginning of the 20th century in commemoration of the Greek sculptor Phidias (ca. 490-430 BC), who a number of art historians claim made extensive use of the golden ratio in his works (Livio 2002, pp. 5-6). is an abbreviation of the Greek tome, meaning "to cut." giving for the line segment
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Matematyka w architekturze. by Max Lyszkowski on Prezi Sezione aurea di un segmento Sezione aurea di un segmento ( A cura di Nannelli Lorenzo) La sezione aurea di un segmento, per definizione, è la parte del segmento che risulta media proporzionale tra l’intero segmento e la parte dello stesso che rimane sottraendo al segmento la sua parte aurea. Nella figura a lato è indicato il segmento AB ed è indicato il punto P interno ad esso. , affinché il segmento AP sia la parte aurea del segmento AB la misura x (positiva) deve verificare la seguente proporzione Osserviamo che , quindi la sezione aurea di un segmento rappresenta quasi il 62% del segmento. Teorema: il lato del decagono regolare è uguale alla sezione aurea del raggio della circonferenza in cui è inscritto. Dimostrazione Per dimostrare ciò si deve considerare un triangolo isoscele avente l’angolo al vertice di 36° (e conseguentemente i due angoli alla base di misura 72°) e far vedere che la base del triangolo rappresenta la sezione aurea del lato. dalla quale emerge che si può anche scrivere
Polygon art and golden ratio inspired by Piet mondrian SEZIONE AUREA prof Giuseppe Spina H o apprezzato molto questo lavoro del prof. Giuseppe Spina docente di matematica - fisica e vicario del Liceo Artistico Statale di Cosenza sul rapporto fra le grandezze con specifica focalizzazione sulla “Sezione aurea del segmento”. gusto nel sapere trasferire agli altri nozioni e concetti, frutto anche della sua ultra trentennale esperienza di docente. ormai pregiudizialmente rifiutano l’autorità costituita così come ogni apprendimento che viene loro imposto. innovative e pressanti di pratiche informatiche sempre più egemonizzanti. potremmo chiosare che il prof. come elemento di equilibrio, in quanto rispetta armoniosamente le proporzioni tra il tradizionale ed il modulare . Si dice sezione aurea di un segmento quella parte del segmento (la maggiore), che è media proporzionale fra l’intero segmento e la rimanente parte ( la minore). Se il punto E divide il segmento AB in due parti tali che si abbia: diremo che AE è la sezione aurea del segmento AB. C e D. sostituendo si ha :
Making Art with the Golden Ratio « Math Craft :: WonderHowTo You can do some pretty cool stuff with the golden ratio. The image above is made from taking each quarter-circle in the golden spiral and expanding it into a full circle. In the second image, the spiral and the golden rectangles are overlaid on the the first image, showing how it works. The length of the radius of the nth circle is 1/phi^(n-1). The image above is made by connecting the the center of one circle to the center of the circle in the next iteration (or the corner of one square to the corner of the next), using it for the side of a pentagon which is then turned into a star. Anyway, there's some really awesome stuff you can do with the Golden Ratio and these are just a couple of them.