Any object with a simply connected surface can be smoothed out to look like a sphere.

任何具有单连通表面的物体都能简化成一个球体。

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The equation smoothes out the irregularities of an object, transforming it mathematically into something that looks like a uniform three-dimensional sphere.

这个方程能消除物体间的差异，并能把物件精确的变形为一个统一的三维球体。

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These object are so dense that nothing, not even light, escapes once inside a sphere of influence known as an event horizon.

这些东西的密度是那样大，以至于在它们的势力范围——也就是黑洞表面——之内，任何东西，甚至光线，都不能逃离。

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Any object with a simply connected surface can be smoothed out to look like a sphere.

ECONOMIST: Proof of the truth of the Poincar�� conjecture

The equation smoothes out the irregularities of an object, transforming it mathematically into something that looks like a uniform three-dimensional sphere.

ECONOMIST: Proof of the truth of the Poincar�� conjecture

Richard Hamilton of Columbia University had previously realised the usefulness of this heat-flow model but became unstuck when he found that, under this transformation, the object may stretch out to form singularities spikes that could not be easily manipulated into a sphere.

ECONOMIST: Proof of the truth of the Poincar�� conjecture