But at least I'd got the squared paper or I'd have had problems drawing it all to scale.

不过好在我带的方格纸，不然想要全部按规定比例画出来就太困难了。

So does it sort of look like graph paper, but dark?

所以它看起来有点像深色的方格纸吗？

But before you waste a ton of graph paper, you should know that a true Hamiltonian path isn't possible with these end points.

在你浪费大量方格纸之前，你应该知道真正的哈密顿路径对这些端点不可能的。

" Let us see, " said Caleb, taking up a pen, examining it carefully and handing it, well dipped, to Fred with a sheet of ruled paper.

凯勒布说，拿起一支笔， 仔查了一下， 然后把笔蘸好， 连同一张方格纸递给弗雷德。

So not only are they a little hard to depict and solve on graph paper, but we believe they're even out of the reach of a quantum computer.

因此， 它们不仅有点难以在方格纸上描绘和解决，而且我们相信它们甚至超出了量子计算机的范围。

Now I encourage you to get some graph paper out and to actually plot this vector, and think about how it relates to this vector right over here.

现在我鼓励你拿出一些方格纸， 实际绘制这个向量，并考虑它与这里的这个向量有什么关系。

Now, unlike those two- and three-dimensional geometric problems that we used to have to try to solve with pen and graph paper in high school, most of these problems are defined in well over 500 dimensions.

现在，与我们过去在高中时必须尝试用笔和方格纸解决的那些二维和三维几何问题不同， 这些问题中的大多数都在 500 多个维度中定义。