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| {{Unreferenced|date=December 2009}}
| | Dalton is what's written on his birth certificate even so he never really enjoyed reading that name. The widely used hobby for him and / or his kids is you will need but he's been ingesting on new things not too lengthy ago. Auditing is where his primary income derives from. Massachusetts is where it and his wife stay. He's not godd at design but locate want to check his / her website: http://Circuspartypanama.com<br><br>[https://Www.Flickr.com/search/?q=Feel+free Feel free] to surf to my web blog - [http://Circuspartypanama.com clash Of clans unlimited gems apk] |
| The idea of a '''sphere-world''' was constructed by [[Henri Poincaré]] who, while pursuing his argument for [[conventionalism]] (see [[philosophy of space and time]]), offered a [[thought experiment]] about a [[sphere]] with strange properties.
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| Poincaré asks us to imagine a sphere of radius ''R''. The temperature of the sphere decreases from its maximum at the center to absolute zero at its extremity such that a body’s temperature at a distance ''r'' from the center is proportional to <math>R^2-r^2</math>.
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| In addition, all bodies have the same [[coefficient of thermal expansion|coefficient of dilatation]] so every body shrinks and expands in similar proportion as they move about the sphere. To finish the story, Poincaré states that the [[refractive index|index of refraction]] will also vary with the distance ''r'', in [[inverse proportion]] to <math>R^2-r^2</math>.
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| How will this world look to inhabitants of this sphere?
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| In many ways it will look ''normal''. Bodies will remain intact upon transfer from place to place, as well as seeming to remain the same size (the Spherians would shrink along with them). The geometry, on the other hand, would seem quite different. Supposing the inhabitants were to view rods believed to be rigid, or measure [[distance]] with [[light ray]]s. They would find that a [[geodesic]] is not a straight line, and that the ratio of a circle’s circumference to its radius is greater than <math>2\pi</math>.
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| These inhabitants would in fact determine that their universe is not ruled by [[Euclidean geometry]], but instead by [[hyperbolic geometry]].
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| ==See also== | |
| * [[Flatland]]
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| * [[sphere world]] - a mathematical concept in robotics
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| {{DEFAULTSORT:Sphere-World}}
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| [[Category:Thought experiments]] | |
| [[Category:Spheres]]
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Latest revision as of 08:16, 17 October 2014
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