The geometry of the Universe mathematically describes its overall curvature, the shape of space on the largest scales of all.

宇宙几何学在数学上描述它整体曲率，形状在所有中最大尺度。

You'll see the curvature of the Earth but the sky will still be black.

你会看到地球曲率，但天仍然是黑色。

All these objects have a strong curvature of space.

所有这些物体都有很强曲率。

At the top of the mountain, you know, you can almost kind of make out and see the curvature of the Earth.

在山顶上时，你几乎可以看出地球曲率。

But a slightly deeper issue is, the discovery is, that we've been looking at the fingerprints — perhaps we're missing a lot of information because we were overlooing things like curvature, and things that AI suggests are actually very meaningful.

但一个稍微深入问题是，这一发现表明，我们一直在研究指纹——也许我们错过很多信息，因为我们忽视像曲率这样东西，而人工智能表明这些信息实际上是非常有意义。

The reason it's harder to pluck on instruments that have a curvature versus on a guitar where you actually have a flat plane, it's a little harder to pick and actually pluck with the same rapidity that you can on a guitar.

为什么相比于平坦吉他而言，在有曲率乐器上弹奏更难，这是因为你要想以在吉他上演奏速度在大提琴上弹拨会更难。

In the 60s, Stephen Hawking and Roger Penrose predicted that an even denser star would contract into a point of infinite density and hence spacetime curvature, a point where all known laws of physics break down.

在60年代，斯蒂芬·霍金和罗杰·彭罗斯预测，密度更大会收缩成一个无限密度点，此处时曲率也无限大，在这个点上所有已知物理定律都将失效。

None of it really escapes my attention, and then, from a sonar perspective, the size of the room, the curvature of the audience around the stage, it's the height of the room.

从声呐视角，它们都在我注意力之内，房大小，观众绕讲台曲率，房高度。

One, we cannot just grab the displacements and shove them onto a different model, because it can potentially look different, have different curvatures and sizes.

第一，我们没法直接把表面纹理抓取下来放到一个不同模型上，因为这些模型有可能看起来就不一样，有不一样表面曲率、不一样大小等等。

The light from the more distant galaxies is literally bent by the curvature of space caused by stars and dark matter in its path.

从更遥远系发出光，由于其路径上和暗物质造成曲率，实际上是弯曲。

Curvature; increase of curvature of cornea or lens causes light rays to be focused in front of retina and hence Myopia occurs.

曲率；角膜或晶状体曲率增加会导致光线聚焦在视网膜前方，从而发生近视。

All of these seemingly different phenomena can be described by one idea: curvature of space or spacetime.

或时曲率。

The surface of the Earth looks pretty flat to us because we really can't see the curvature locally.

地球表面看起来对我们来说是相当平坦，因为我们不能在局部看到它曲率。

If you're drawing a small enough triangle on the beach, you won't notice the curvature of the earth.

如果你只是在海滩上画一个很小三角形，是不会注意到地球曲率。

And due to the curvature of the Earth, the sun will shine for 40 minutes longer there than on the floors that are lower down.

由于地球曲率，太阳在那里照耀时要比在较低地板上多40分钟。

Are you sure you measured the universe's curvature with infinite precision?

你确定你能无限精确地测量宇宙曲率吗？

It would probably be a challenge on the beach to draw it big enough that you would be able to notice the curvature of the earth.

要想发现大地曲率，就要在沙滩上画一个足够大三角形，这可不是件容易事。

It's very possible that the universe has curvature just inside the uncertainty range of the best measurements to date.

很可能，宇宙曲率正好在迄今为止最佳测量不确定范围内。

The key is to make the curvature more obvious — by drawing the biggest triangle you can.

最关键是，要想让曲率看上去更明显——就要尽你所能画一个最大三角形。

These curves are going to be subtle, more subtle than the curvature of the earth.

弯曲度也是极其细微，比地球曲率更细微。