Following Aristotle, al-Fârâbî taught that the world has no beginning in the past and that the celestial spheres, for instance, move from pre-eternity.
The ultimate source of the falâsifa's knowledge about God's nature, the human soul, or about the heavenly spheres, for instance, are the revelations given to early prophets such as Abraham and Moses.
A sphere, for instance, has rotational symmetry; rotate it about its center and its appearance stays the same.
Oddly, "Better Homes" doesn't really address technology in the domestic sphere — for instance, the rise of the alone-together family gathering, with individuals united around a dinner table but distracted by their individual screens.
In fact, when we do a cut on a sphere, for instance in the n = 1 case, what we are doing is the following: take a manifold and remove a ball B3 from it, then take the same manifold, reverse the orientation, carve a ball B3, and identify the boundaries between the two.
Yet, when acting on a metric space, or simply on a manifold or a bounded domain, there is an extra constraint on y: the point y must be the middle point of a geodesic between (x^tau _k) and a point x (on a sphere, for instance, this means that if (x^tau _k) is the North Pole, then y must lie in the northern hemisphere).
The most efficient way to do this is to exploit the sampling theorem on the Earth's sphere (see for instance Schaeffer, 2013 and references therein).
We now know more about the female sphere in which, for instance, Sappho lived, beyond the erotic shards of her verse that strike like thunderbolts across two and a half millennia.
Because the icosahedron has such high symmetry it is closer to a sphere than is, for instance, a cube the sound speeds turn out to be independent of the direction of propagation.
It surely matters that in European countries, where the centre-right has thrived, it can tap into traditions of conservatism that reject all-out liberalism in the economic sphere.German Christian Democracy, for instance, mixes a commitment to the welfare state with quiet conservatism on social and cultural matters.
Analogues of the direct and converse theorems in the case of approximation on the sphere are given, for instance, by Pawelke [71] and Lizorkin and Rustamov [35].
