And since the volume of a parallelepiped (that's a 3D parallelogram) doesn't depend at all on its slant, then no matter how fast you're moving horizontally the same amount of rain will land on top of you each second.

由于棱柱（即平形对应的立体模型）的体积并不受它倾斜的角度决定，不管你在水平方向上跑得多快，每秒你头顶上都会淋到等量的雨。

The kinds of things you need to learn in seventh grade math, sure, they're hard: ratios, decimals, the area of a parallelogram.

比率，小数，还要算平形的面积。

A circle actually has infinite axis of symmetry, except poor Mr. Parallelogram, no access for you.

圆实际上有无限的对称轴，除可怜的平形先生，你无路可走。

How do you calculate the square footage of a parallelogram?

如何计算平形的面积？

Stephen lay watching the Great Bear; Elfride was regarding a monotonous parallelogram of window blind.

史蒂芬躺在那里看着大熊。 Elfride 正在考虑单调的平形百叶窗。

If they would, for example, praise the beauty of a woman, or any other animal, they describe it by rhombs, circles, parallelograms, ellipses, and other geometrical terms, or by words of art drawn from music, needless here to repeat.

如果他们要赞美女人或其他动物的美丽，他们会用菱形、圆形、平形、椭圆等几何术语，或者从音乐中提取的专业词汇来描述，这里就不列举。

Sure enough, there's a miniscule gap between the triangles and trapezoids, forming a parallelogram that stretches the entire length of the board and accounts for the missing square.

果然，三角形和梯形之间有微小的间隙，形成平形，延伸整板的长度并弥补缺失的正方形。

The area of this parallelogram is its base, 1, times the height perpendicular to that base, which is the y-coordinate of our input vector.

这平形的面积是其底，1， 乘以垂直于该底的高度，即输入向量的y坐标。

This gives us the area of a parallelogram spanned out by those two vectors, with the possibility of being negative depending on the orientation of the vectors.

这就得到由这两向量张成的平形的面积 根据向量的方向有可能是负的。

When one hundred and fifty passengers who were destined to be its burden, were on board, they stood like a solid parallelogram, without a possibility of moving; and they were up to their waists in water.

当百五十名注定要成为它的负担的乘客上船时，他们像实心的平形样站着，没有移动的可能;他们在水里没到腰部。

The servants cut our bread into cones, cylinders, parallelograms, and several other mathematical figures.

仆人们把我们的面包切成圆锥、圆柱、平形和其他几种数学图形。

A circle actually has infinite axis of symmetry, except poor Mister Parallelogram, no access for you.

圆圈实际上具有无限的对称轴, 除可怜的平形先生, 你无法进入。

Well, this is the transformed version of that parallelogram we were looking at earlier, whose area was the y-coordinate of the mystery input vector.

好吧， 这是之前我们看到的那平形的变换版本，其面积就是神秘输入向量的y坐标。

Where before you had a nice rectangular-looking book, now you have more of a … parallelogram.

以前，这本书是长方形的。 现在它更像平形。

For example, if you look the parallelogram spanned by the vector where your first basis vector lands, which is the first column of the matrix, and the transformed version of [x; y], what is its area?

例如，如果你查看由基向量的第落点（矩阵的第列）和[x; y]向量的变换版本所张成的平形，它的面积是多少？

The cross product of VNW, written with the X shaped multiplication symbol, is the area of this parallelogram.

VNW的叉乘 用X形乘法符号表示 就是这平形的面积。

We'll start in two dimensions. If you have two vectors V and W, think about the parallelogram that they span out.

我们从二维开始 如果有两向量V和W 想想它们张成的平形。

Actually, to be more accurate, you should think of the signed area of this parallelogram, in the sense described by the determinant video.

实际上， 为更准确地理解， 你应该考虑这平形的有符号面积，就像列式视频中描述的那样。

After the transformation, that square gets turned into the parallelogram that we care about.

变换之后 这正方形就变成我们关心的平形。

Its length equals the area of the parallelogram defined by vn W.

它的长度等于用vnw定义的平形的面积。