What this app does is in three dimensional space, it actually places you right over where our excavation occurs.

“这个应用呈现的是一个三维空间，能够让人们看到我们挖掘化石的地方。

So moving stuff in three dimensional space, it's always useful.

因此在三维空间中移动东西总是很有用的。

Basically putting things into three dimensional space.

基本上将事物放入三维空间中。

According to some theories, the university experience is just for dimensional surface in a ten or eleven dimensional space.

根据一些理论 大学经历只是在十维或十一维空间中的一个维度表面。

That tip will trace out some kind of flat sheet cutting through the origin of three dimensional space.

这个尖端会勾勒出某种平面 穿过三维空间的原点。

The idea of span gets a lot more interesting if we start thinking about vectors in three dimensional space, e.g.

张成空间的概念变得有趣得多 如果我们开始考虑三维空间中的向量 例如。

One dimensional space is really just the number line, so transformation like this takes into de vectors and spits out numbers.

一维空间实际上就是数轴 所以像这样的变换会得到向量 然后得到数字。

So for a span example, the span of most pairs of vectors ends up being the entire infinite sheet of two dimensional space.

对于张成空间的例子 大多数向量对张成的空间最终是整个二维空间的无限平面。

And once again, we're just using our mental abilities of perspective type stuff and three dimensional space in order to just eyeball that.

再说一次，我们只是利用透视类型的东西和三维空间的心理能力来观察它。

So I want each one to be 3D or at least have a drop shadow to really sell it that it's, you know, in three dimensional space.

所以我希望每一个都是 3D 的， 或者至少有一个投影来真正推销它，你知道，在三维空间中。

Much more than a box, which is kind of the standard thing you might use when you're first learning art to practice drawing things in three dimensional space.

不仅仅是一个盒子，这是当你第一次学习艺术以练习在三维空间中绘画时可能会使用的标准东西。

This fifth dimensional space, this basic universe of reality of which I speak, expands constantly in terms of intensity and quality and value, in a way that has nothing to do with your idea of space.

这第五维空间，这个我所说的实相的基本宇宙，在强度、特性和值上不断地扩展，这种扩展方式与你们的空间观念毫无关系。

But for this video, will limit our view to the case of a non zero determinant, meaning the outputs of this transformation still span the full dimensional space that it started in.

但是在这个视频中 我们将把视野限制在非零行列式的情况下 这意味着这个变换的输出仍然张成了它开始时所在的全维空间。

Or rather, I should say p orbitals, because we're talking about 3 dimensional space here, so there can be one on the x axis, and one on the y axis, and one on the z axis.

或者更确切地说， 我应该说 p 轨道，因为我们在这里谈论的是 3 维空间， 所以可以有一个在 x 轴上，一个在 y 轴上， 一个在 z 轴上。

We can visualize this by smashing around all the points in three dimensional space, as represented by a grid, in such a way that keeps the grid lines parallel and evenly spaced, and which fixes the origin in place.

我们可以把三维空间中的所有点都打碎 用网格表示 使网格线保持平行和均匀间隔 并固定原点。