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The whole set of the goddess is coming soon! Don't worry, it's not all about math. :)
The Golden Spiral, Fibonacci Spiral, & Golden Rectangle and Phi Grid in Fine Art Photography! Nikon D810 & 50mm Sigma Art Lens!
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The Birth of Venus! Bikini swimsuit model goddess striding forth from the sea!
The golden spiral is defined by the fact that after every quarter turn it advances by the golden ratio! :)
The phi grid is defined by golden rectangles from which the larger golden rectangle is constructed from! The golden rectangles can be found at the four corners. :)
You can see how the rule of thirds is not so far off from the Phi grid! Phi is the golden ratio, or 1.6180339887498948 and on and on! It is the least rational number! :)
I am having fun writing a book on all this called Chasing Beauty! I love where math, science, and art intersect! :)
Do you prefer the Phi grid or the rule of thirds in your own work?
Aerial photograph of intersecting highways, SR 826, the north-south Palmetto Expressway (a toll road), and SR 836, the east-west Dolphin Expressway (also a toll road), Miami, Florida. In this view to the south one can see at least five levels of freeway and quite heavy traffic headed southward. Along the right edge of the image (in mid-distance) is the Mall of the Americas.
your loop, my loop, they intersected for a second, and then we split and headed our separate ways, until we encounter our destinies again, and somehow we dismissed them as deja vu.
Aerial photograph of reflections of clouds, with intersecting waves; the wave sets appear at approximately 90 degrees to each other, Trinity Lake, east of Trinity Center, Trinity County, California.
While crossing the streets of Bushwick, Brooklyn I was intrigued by the mass activity in the air. I looked up noticing, various architecture, streets signs, street lights & intersecting wires. Once you go past this intersection, you can find much inspirational work by street & graffiti artists - Swoon, Chris Stain & Robots Will Kill.
Bigger View:
The Galleria Vittorio Emanuele II is a covered double arcade formed of two glass-vaulted arcades at right angles intersecting in an octagon; it is prominently sited on the northern side of the Piazza del Duomo in Milan, and connects to the Piazza della Scala. Named after Vittorio Emanuele II, the first king of united Italy, it was originally designed in 1861 and built by Giuseppe Mengoni between 1865 and 1877.
The street is covered over by an arching glass and cast iron roof, a popular design for nineteenth-century arcades, such as the Burlington Arcade, London, which was the prototype for larger glazed shopping arcades, beginning with the Saint-Hubert Gallery in Brussels (opened 1847) and the Passazh in St Petersburg, (opened 1848) and including the Galleria Umberto in Naples (opened 1890).
The central octagonal space is topped with a glass dome. The Milanese Galleria was larger in scale than its predecessors and was an important step in the evolution of the modern glazed and enclosed shopping mall, of which it was the direct progenitor. It has inspired the use of the term galleria for many other shopping arcades and malls.
The Galleria connects two of Milan's most famous landmarks: The Duomo and the Teatro Alla Scala.
More than 120 years after its inauguration, the four-story arcade includes elegant shops selling most things from haute couture to books, as well as restaurants, cafés and bars. Directly connected to the Galleria Vittorio Emanuele II is Milan's ultra-luxurious Town House Galleria hotel, offering the city's most luxurious (and most expensive) rooms and facilities.
The Galleria is the site for many luxury goods' shops, like Gucci, Prada, Louis Vuitton. (from Wikipedia)
see it LARGER
Explore Feb 17, 2009 #106
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CANON EOS 400D EXIF 1/400 8 70-300mm ISO 200 HDR
Bolas & Sombras - Port Forum - Barcelona - Spain
Balls & Shadows - Port Forum - Barcelona - Spain
Una sombra es una región de oscuridad donde la luz es obstaculizada. Una sombra ocupa todo el espacio de detrás de un objeto opaco con una fuente de luz frente a él. La sección eficaz de una sombra es una silueta bidimensional o una proyección invertida del objeto que bloquea la luz.
Cuanto mayor es el ángulo entre la dirección de la luz y un objeto alargado que la obstaculice, más corta será su sombra. Por otro lado, cuanto menor sea el ángulo entre la dirección de la luz y la superficie en la que aparece la sombra, más larga será ésta. Si el objeto está cerca de la fuente luminosa, la sombra será mayor que si el objeto se encuentra lejos. Si la superficie está curvada, habrá más distorsiones.
Cuando la fuente de luz no es puntual, la sombra se divide en umbra y penumbra. Cuanto más ancha es la fuente de luz, más difuminada o borrosa será la sombra.
Si hay múltiples fuentes luminosas, habrá múltiples sombras, con las partes solapadas más oscuras, o con una combinación de colores. Cuando una persona o un objeto está en contacto con la superficie, como una persona sentada en el suelo o un poste clavado, las sombras convergen al punto de contacto.
Si sólo existe una fuente de luz, las sombras arrojadas por aquella serán siempre grises, sea cual sea el color de la fuente. En cambio, si existen dos fuentes de luz de distintos colores, supongamos rojo y azul, las sombras proyectadas por cada una de ellas serán del color de la otra fuente de luz, y sólo la intersección de ambas sombras será gris. Es decir, la sombra de la luz roja será azul, pues está iluminada por la fuente azul, y viceversa. En el caso de que existan más fuentes de luz, cada sombra será del color resultante de la adición de las fuentes que aún iluminan esa zona, permaneciendo en gris las zonas donde intersecten las sombras de todas las fuentes luminosas.
A shadow is a region of darkness where light is obstructed. A shadow occupies all the space behind an opaque object with a light source in front of him. The effective section of a shadow is a two-dimensional silhouette, or reverse projection of the object that blocks light.
The bigger the angle between the direction of light and an elongated object that obstructs, his shadow will be shorter. On the other hand, the smaller the angle between the direction of the light and the surface on which the shadow, it will be longer. If the object is near the light source, the shadow will be greater than if the object is far away. If the surface is curved, there will be distortions.
When the light source is not punctual, is divided into the shadow umbra and penumbra. The more wide is the light source is more faded or blurred shadow.
If there are multiple light sources, there will be multiple shadows, with overlapping parts darker, or a combination of colors. When a person or object is in contact with the surface, like a person sitting on the floor or a pole stuck, shadows converge to the point of contact.
If there is only one source of light, the shadows thrown by that will always be gray, whatever the color of the source. However, if there are two sources of light of different colors, say red and blue shadows for each of them will be the color of another light source, and only the intersection of the two is gray shadows. Ie, the shadow of the red light will be blue, because the source is illuminated by blue and vice versa. In case there are more sources of light, each shade of color is a result of the addition of the sources that illuminate the area still remains gray areas intersecting the shadows of all light sources.
Une vue au coucher de soleil à partir de l’intersection de l’avenue de la Cathédrale et de la route N102. L'édifice présente une étrange façade ouest faite de lave polychrome et de parements mosaïquées au style roman mêlé d'influences orientales. Remplaçant un sanctuaire païen, les origines de l'édifice actuel remonte au 10e s. mais nécessita plusieurs agrandissements, le chœur est sur le roc mais quatre travées supplémentaires furent construites aux 11e et 12e s. dans le vide pour rattraper un dénivelé de 17 m grâce à d'imposants piliers chargés de soutenir les hautes arcades, véritables prouesses à l'époque.
La cathédrale est un monument majeur de l'art roman et de l'Occident chrétien. Elle a été érigée en basilique mineure par un bref apostolique de Pie IX, le 11 février 1856. Elle a été inscrite en 1998 sur la liste du patrimoine mondial par l'UNESCO (WHL-868) au titre des chemins de Saint-Jacques-de-Compostelle en France. Une Vierge noire, objet de nombreux pèlerinages au cours des siècles, trône sur un maître-autel baroque. Les légendes locales du Puy-en-Velay évoluent autour d'un dolmen qui occupait depuis plusieurs millénaires, sans doute, l'emplacement actuel de la cathédrale.
Capitale historique du Velay dans la partie sud-est du Massif central, Puy-en-Velay est réputée pour sa fabrication de la dentelle du Puy, la culture de la lentille verte du Puy et la production de Verveine du Velay. Elle est aussi connue pour être le départ de la Via Podiensis, un des quatre chemins de Compostelle français. Entourée de plateaux volcaniques, la ville du Puy occupe le centre d'un bassin géologique complexe qui porte son nom. Ce bassin, où se rejoignent deux cours d'eau avant leur confluence avec la Loire toute proche est ponctué de deux éminences volcaniques : le rocher d'Aiguilhe, un piton volcanique surmonté de l'église Saint-Michel d'Aiguilhe, sur la commune du même nom, et le rocher Corneille (757 m) surmontée de la sculpture de la Vierge, contre lequel s'appuie le centre historique du Puy-en-Velay. Enchâssée dans ce cadre verdoyant où l’eau et le feu ont sculpté des décors naturels et où l’homme a fait triompher la beauté de l’art, la ville est appelé fréquemment le «Mont St Michel des Terres».
L'Hallgrimskirkja est située à l’extrémité sud de Skólavörðuholti, juste en face de l’intersection avec les rues Eiríksgata et Frakkastígur, au centre de Reykjavík, capitale d’Islande.
Le décor intérieur de l’église Hallgrimskirkja est moderne très sobre. Son orgue, construit par le facteur allemand Johannes Klais Orgelbau, à traction mécanique et commandes électriques, possède 5275 tuyaux pour 72 jeux. Il est haut de 15 mètres et pèse 25 tonnes. Il a été achevé en 1992.
Cette église luthérienne, la plus grande d'Islande, est devenue l'édifice-symbole de Reykjavík. Sa façade blanche rappelle les glaciers. Ses courbes dynamiques imitent les orgues basaltiques d'origine volcanique présents en grand nombre en Islande. Elle doit son nom au poète et pasteur Hallgrímur Pétursson (1614-74) qui écrivit le célèbre livre d'hymnes "Passion Hymns", un texte majeur dans l'histoire de la littérature islandaise. Dessinée par Gudjón Samúelsson (1887-1950), l'architecte islandais le plus renommé du 20e s., elle fut construite à partir de 1946 et a ouvert progressivement de 1974 à 1986.
Du haut de la flèche-fusée (73 m), visible à 20 km à la ronde, la vue sur la capitale est superbe.
Theme 'Intersecting' - My 15th shot of 2014 for this 52 week group. London SW1 Selbourne House.
Another out of the window image some turn out well due to the angles.
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mostly SOOC in-camera double exposure. I adjusted the levels slightly and reduced the resolution before uploading.
My one inch sea shell piercing the 50 light year in diameter Sombrero Galaxy.
Distance to Earth: 29.35 million light years
Radius: 25,000 light years
Galaxy photo: Hubble telescope
Shell photo: me
Shell length: 3 cm
The Sombrero Galaxy (Messier Object 104, M104) is one of the most unusual looking barred spiral galaxies visible from Earth. Its bright nucleus, large central bulge and spiral arms threaded through with a thick dust lane make it look a little like a hat from Mexico. The dust lane is a ring that circles the bulge of the galaxy, and it is rich with gas, dust, and hydrogen gas. Because it has all the elements needed for star formation, it’s not surprising that astronomers have found many sites of star formation inside.
The Sombrero Galaxy may not be part of a formal galaxy group, but could be a member of a string of galaxies that extends away from the Virgo Cluster.
As many as 2,000 globular clusters swarm around the core of the Sombrero Galaxy, and the number could be related to the size of the central bulge.
The Sombrero has a central supermassive black hole at its heart. Observations of star motions near the black hole suggest it could have the mass of a billion Suns, perhaps the most massive of any black hole found so far at the heart of a galaxy.
The Sombrero Galaxy is a favorite target for well-equipped amateur astronomers. If you have a good dark-sky sight, it can be spotted through binoculars; those with large telescopes can spot the dust lane. The Sombrero is a spring and early summer observing object half-way between the constellations Virgo and Corvus.
NASA’s Hubble Space Telescope and Spitzer Space Telescope have been used to study the Sombrero in visible and infrared light. The starbirth regions stand out in infrared wavelengths are are mostly located along the outer rim of the dust ring surrounding the galaxy’s core.
The Sombrero Galaxy looks as it does partly because we are viewing it “edge on” from our point of view here on Earth.
Korsika / Bastanisee
seen on the descent from Monte Renoso
gesehen beim Abstieg vom Monte Renoso
Situated at the foot of the Punta Bacinello, facing Monte Renosu, the Lac de Bastani is one of the highest lakes in Corsica (2,092m).
The Lac de Bastani is situated less than 500m to the north of Monte Renoso (2,352m) and less than a kilometre to the north-west of the Lac de Nielluccio.
This path begins at an altitude of 1,586m, above Ghisoni and near the Capannelle refuge and shepherds' huts on the GR20 long-distance footpath. Leave the GR20 to follow the path leading up to the Petraniella ski-lift. At around 1,725m, the path leaves the small skiing area to follow a wide ridge. After a few fairly steep sections, which are intersected by a small grassy plateau and various pools and peat bogs, the well-marked path arrives a few dozen metres above the Lac de Bastani, situated at an altitude of 2,090m. The walk to this point should take between 1hr 30min and 2hr. This heart-shaped lake is a truly magnificent sight and is considered to be one of the most beautiful mountain lakes in Corsica.
(visit-corsica.com)
Le lac de Bastani situé au pied de la Punta Bacinello, face au Monte Renoso (2 352 m), est l'un des lacs les plus hauts de Corse (2 092 m). Il est dans le bassin versant du fleuve Fiumorbo.
Le lac de Bastani est situé à l'est du Monte Renoso et de la Punta Bacinello (2 247 m) sur la commune de Ghisoni dans le département de la Haute-Corse.
Il se trouve dans le Fium'Orbu, un « territoire de vie » du parc naturel régional de Corse et est situé à moins de 500 mètres au nord du Monte Renoso ainsi qu'à moins d'un kilomètre au nord-ouest du lac de Nielluccio.
Le lac de Bastani, comme son voisin le lac de Nielluccio, a pour émissaire le ruisseau de Casso qui se jette dans le fleuve Fiumorbo.
Le lac de Bastiani fait partie d'une zone naturelle d'intérêt écologique, faunistique et floristique de deuxième génération nommée ZNIEFF940004171 Cirques et lacs glaciaires du Monte Renoso. Cette ZNIEFF d'une superficie de 2 018 Ha, s'étend sur les communes de Bastelica, Bocognano et Ghisoni, à une altitude variant entre 1 600 m et 2 352 m.
(Wikipedia)
Dieser See am Fuße der "Punta Bacinello", gegenüber dem Monte Renosu ist mit 2352 m einer der höchstgelegenen Seen von Korsika, nur 500 m nördlich des Berges und kaum einen Kilometer nord-westlich vom See Nielluccio. Der Weg zu ihm beginnt in 1586 m Höhe oberhalb von Ghisoni, in der Nähe der Schutzhütte und der Schafställe von Capanelle am Wanderweg GR 20. Man verlässt unmittelbar hier den GR 20, um den Weg nach oben zu nehmen, der zum Schlepplift von Petraniella führt, mit dem man schnell auf 1725 m gelangt, wo man die kleine Zone des Skisports verlässt und mehr oder weniger einem der Gipfel folgt... Nach einigen etwas steileren Passagen, unterbrochen von einem großen Gras-Plateau mit kleinen Quellen und sumpfig-moorigen Grasflächen, öffnet sich der sehr gut beschilderte Weg 50, 60 m oberhalb des Sees von Bastani. Sie erreichen diesen Punkt in etwa 1,5 bis 2 Stunden. Der See ist ein wahres Schmuckstück, nicht zuletzt durch seine Herzform... einer der schönsten in Korsikas Bergwelt.
(visit-corsica.com)
Although the geology of the western canyons is very often simple layers overlying each other the variations in colour and the action of water and wind have created wonderful geometrical lines within the landscape.
Bryce Canyon, Utah, USA
Railway tracks have amused me since childhood. I associate the tracks with both Joy and Sorrow at the same time. They make loved ones meet and separate very much like the tracks in this image.
Shot somewhere on the Maharashtra-Chattisgarh Border on my return journey from Sambalpur to Pune