Posts filled under #iaafworlds

We this! Smile for the ca

We this! Smile for the camera and get right back in beast mode! #Repost @usatf (@get_repost) After winning Gold in the women's 400m hurdles, @thekorimonster became quite popular......not only for her performance, but for her introduction. And from there, #TheKoriCarter was born. Over the last few days, #TeamUSATF has been practicing. #iaafworlds #teamusa #usatf #track #tracknation #trackandfield #hurdles @justingatlin @pretty_quinn1908 @b1ghomie_ @kerronclement @amhurdlestar @rcrouser @philly_phyl88 @_coleman2 @teejay_holmes

@Regrann from @iten_kenya

@Regrann from @iten_kenya - "I will be shifting to the 5,000m race but that doesnt mean I will exit the 1,500m. In fact, it will be good for me since I will be using it in my speed work that helps an athlete in the final lap in long distances, said Kiprop. Asbel Kiprop has announced that he will be shifting focus to 5000M event. Kiprop said he would start his build up for the longer race after running 1,500m in the two remaining Diamond League meets Birmingham and Zurich. #diamondleague #birminghumdl . . . . #iaafworldchampionships2017 #runningisfun #athletes #iaafworlds #iaafworlds2017 #running #kenya #golden #run #runner #running #globalchampionships #runners #photooftheday #rellofollowboost #gainwithcarlz #flotrack #iaaf #gainwithspikes #athletics #trackandfield #scienceofrunning #tracknation #londonmarathon #iaafworldchampionships #corredores #gainwithxtiandela #landenfollowtrain

An extract on #iaafworlds

The Platonic solids have been known since antiquity. Carved stone balls created by the late Neolithic people of Scotland lie near ornamented models resembling them, but the Platonic solids do not appear to have been preferred over less-symmetrical objects, and some of the Platonic solids may even be absent. Dice go back to the dawn of civilization with shapes that predated formal charting of Platonic solids. The ancient Greeks studied the Platonic solids extensively. Some sources (such as Proclus) credit Pythagoras with their discovery. Other evidence suggests that he may have only been familiar with the tetrahedron, cube, and dodecahedron and that the discovery of the octahedron and icosahedron belong to Theaetetus, a contemporary of Plato. In any case, Theaetetus gave a mathematical description of all five and may have been responsible for the first known proof that no other convex regular polyhedra exist. The Platonic solids are prominent in the philosophy of Plato, their namesake. Plato wrote about them in the dialogue Timaeus c.360 B.C. in which he associated each of the four classical elements (earth, air, water, and fire) with a regular solid. Earth was associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron. There was intuitive justification for these associations: the heat of fire feels sharp and stabbing (like little tetrahedra). Air is made of the octahedron; its minuscule components are so smooth that one can barely feel it. Water, the icosahedron, flows out of one's hand when picked up, as if it is made of tiny little balls. By contrast, a highly nonspherical solid, the hexahedron (cube) represents "earth". These clumsy little solids cause dirt to crumble and break when picked up in stark difference to the smooth flow of water. Moreover, the cube's being the only regular solid that tessellates Euclidean space was believed to cause the solidity of the Earth. Of the fifth Platonic solid, the dodecahedron, Plato obscurely remarks, "...the god used [it] for arranging the constellations on the whole heaven". Aristotle added a fifth element, aithr (aether in Latin, "ether" in English) and postulated that the heavens were made of this element, but he had no interest in matching it with Plato's fifth solid. Euclid completely mathematically described the Platonic solids in the Elements, the last book (Book XIII) of which is devoted to their properties. Propositions 1317 in Book XIII describe the construction of the tetrahedron, octahedron, cube, icosahedron, and dodecahedron in that order. For each solid Euclid finds the ratio of the diameter of the circumscribed sphere to the edge length. In Proposition 18 he argues that there are no further convex regular polyhedra. Andreas Speiser has advocated the view that the construction of the 5 regular solids is the chief goal of the deductive system canonized in the Elements. Much of the information in Book XIII is probably derived from the work of Theaetetus. In the 16th century, the German astronomer Johannes Kepler attempted to relate the five extraterrestrial planets known at that time to the five Platonic solids. In Mysterium Cosmographicum, published in 1596, Kepler proposed a model of the Solar System in which the five solids were set inside one another and separated by a series of inscribed and circumscribed spheres. Kepler proposed that the distance relationships between the six planets known at that time could be understood in terms of the five Platonic solids enclosed within a sphere that represented the orbit of Saturn. The six spheres each corresponded to one of the planets (Mercury, Venus, Earth, Mars, Jupiter, and Saturn). The solids were ordered with the innermost being the octahedron, followed by the icosahedron, dodecahedron, tetrahedron, and finally the cube, thereby dictating the structure of the solar system and the distance relationships between the planets by the Platonic solids. In the end, Kepler's original idea had to be abandoned, but out of his research came his three laws of orbital dynamics, the first of which was that the orbits of planets are ellipses rather than circles, changing the course of physics and astronomy. He also discovered the Kepler solids. In the 20th century, attempts to link Platonic solids to the physical world were expanded to the electron shell model in chemistry by Robert Moon in a theory known as the "Moon model".

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