To understand the poincare conjecture, start by thinking of any object existing in a three-dimensional world.
要理解庞加莱猜想，当始于对三维世界存在的一切物体的认识。
The mind (" I ") which discerns the three dimensional world around us, orders it by dividing it in separate objects, locating them spatially.
能感知我们周围的三维世界的心(“我”)，把这个世界分为不同的物体，把它们放在空间的不同位置。
For the holographic universe to hold true, information must be encoded in the outermost reaches of the universe and it is projected into our 3 dimensional world.
为了让全息的宇宙保持真实，信息必须能在宇宙的最远处被编码，并被投射到我们的三维世界。
His conjecture, made in 1904, was that in this four-dimensional world, all closed three-dimensional surfaces that are simply connected could be transformed to look like a three-dimensional sphere.
他在1904年就提出猜想：在四维空间，所有单连通的封闭三维面都能转化为一个三维球体。
We live in a colorful, three-dimensional world.
我们住在一个多姿多彩的立体的世界里。
These concepts make up the two-dimensional and three dimensional world.
这些概念构成二维和三维世界。
Theatre starts in the three-dimensional world wherein both performer and spectator join.
剧院是一个三维的世界，表演者和观众都身处其中。
It will appear to be a normal three dimensional world, an exact copy, indistinguishable from reality.
它会看上去像一个平常的三维世界，一个相同的拷贝，与现实毫无二致。
We live in a three dimensional world. Our mind tries to convert a two dimensional object into a 3d one.
我们住在一个三维的世界里，所以我们的意识总是期待把一个二维的物体转换成一个三维的物体。
Straight lines in the three dimensional world must project to straight lines in the image plane, if the distortion is compensated effectively.
在畸变得到有效校正的前提下，三维空间中的直线投影到图像平面上应该是直线。
Straight lines in the three dimensional world must project to straight lines in the image plane, if the distortion is compensated effectively.
在畸变得到有效校正的前提下，三维空间中的直线投影到图像平面上应该是直线。
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