The spell grew geometrically, as it rippled through the air.

咒语在空气中扩散，呈几何级数增长着。

This paper is about designing and creating furniture with pieces that are geometrically interlocked.

这篇论文是关于设计和创造由几何互锁部件构成的家具的。

Here nature had done her work geometrically, with square and compass and plummet.

在这里，大自然以几何方式完成了她的工作， 用直角尺、指南针和垂直线。

" But even so, the art of living demonstrated geometrically" ?

“但即便如此，生活的艺术却以几何方式展现”？

And this is one of hundreds of ways in which this typeface was designed to look geometrically perfect, even though it's mathematically not.

这是这种字体被设计成几何学上完美的几百种方式中的一种，尽管它在数学上并不完美。

The important part here is to know what that cross product vector geometrically represents.

这里重要的部分是知道叉乘向量在几何上表示什么。

So the answer that we found earlier computationally, using that special notational trick, must correspond geometrically to this vector.

所以我们之前计算得到的答案 用那个特殊的符号技巧 一定在几何上对应于这个向量。

There's no nonsense with basis factors stuck in a matrix or anything like that, just an ordinary determinant returning a number geometrically.

在矩阵中没有基因子之类的废话 只是一个普通的行列式几何上返回一个数。

Geometrically, this matrix transforms our grid into jennifer's grid, but numerically it's translating a vector described in her language to our language.

几何上 这个矩阵将我们的网格转换成jennifer的网格 但从数字上讲 它将用她的语言描述的向量转换成我们的语言。

But several commenters have asked about non square matrices, so I thought I'd take a moment to just show what those mean geometrically.

但是有几个评论者问了关于非方阵的问题 所以我想我应该花点时间来说明这些矩阵在几何上的含义。

But thinking geometrically, we can deduce that this dual vector must be perpendicular to VMW with a length equal to the area of the parallelogram spanned out by those two vectors.

但从几何角度考虑 我们可以推导出这个对偶向量必须垂直于VMW 其长度等于由这两个向量张成的平行四边形的面积。

Geometrically, each system has some kind of linear transformation associated with it, and when that transformation has an inverse, you can use that inverse to solve your system otherwise.

几何上 每个系统都有某种线性变换与之相关 当这个变换有逆函数时 你可以用它的逆函数来解方程组。

Geometrically, the meaning of this function is that for any input vector X-Y-Z, you consider the parallelopyped defined by this vector, V and W, then you return its volume with a plus or minus sign, depending on orientation.

几何上 这个函数的意义是 对于任何输入向量X-Y-Z 你考虑由这个向量V和W定义的平行体 然后你返回它的体积 根据方向带正号或负号。

And as you know from Chapter five, geometrically, this would give you the volume of a parallellapiped spanned out by those three vectors, with a plus or min assigned depending on the right hand rule orientation of those three vectors.

在第五章中 从几何上讲 这就得到了由这三个向量张成的平行四边形的体积 加号或最小值取决于这三个向量的右手定则方向。