I don't think there's a way to fold that hole away ( or to be more rigorous, I don't think there's a way to map every point on a solid sphere onto a punctured ball continuously ), since you fundamentally change the properties of the shape ( a ball with a hole in it doesn't have a clearly defined interior-a sphere does ).
32.
The colloquial practice of using the term " sphere " to refer to the interior of a sphere is therefore discouraged, with the interior of the sphere ( i . e ., the " solid sphere " ) being more properly termed a " ball . " " ( http : / / mathworld . wolfram . com / Sphere . html ) Preceding talk ) 03 : 50, 12 March 2013 ( UTC)
33.
Adi Setia describes the debate among Islamic scholars in the twelfth century, based on the commentary of Fakhr al-Din al-Razi about whether the celestial spheres are real, concrete physical bodies or " merely the abstract circles in the heavens traced out & by the various stars and planets . " Setia points out that most of the learned, and the astronomers, said they were solid spheres " on which the stars turn & and this view is closer to the apparent sense of the Qur'anic verses regarding the celestial orbits . " However, al-Razi mentions that some, such as the Islamic scholar Dahhak, considered them to be abstract.
34.
In the 12th century, Fakhr al-Din al-Razi participated in the debate among Islamic scholars over whether the celestial spheres or orbits ( " falak " ) are " to be considered as real, concrete physical bodies " or " merely the abstract circles in the heavens traced out year in and year out by the various stars and planets . " He points out that many astronomers prefer to see them as solid spheres " on which the stars turn, " while others, such as the Islamic scholar Dahhak, view the celestial sphere as " not a body but merely the abstract orbit traced by the stars . " Al-Razi himself remains " undecided as to which prophetic traditions . " He concludes that " astronomical models, whatever their utility or lack thereof for ordering the heavens, are not founded on sound rational proofs, and so no intellectual commitment can be made to them insofar as description and explanation of celestial realities are concerned ."
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