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 正在考虑一个单调平行四边形百叶窗。

He drew parallelogram and parabola up to par.

他画平行四边形和抛物线都是达到标准。

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

把我们面包切成圆锥体、圆柱体、平行四边形和其他几种数学图形。

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。 在它更像一个平行四边形。

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，还要算平行四边形面积。

Take the parallelogram defined by the 1st basis factor I had, and the mystery input vector X-Y.

取由第一个基因子平行四边形 以及未知输入向量X-Y。

Look at the parallelogram we defined earlier, which encodes the excordinate of the mystery input vector spanned by that vector.

看看我们之前平行四边形 它编码了神秘输入向量由该向量张成横坐标。

Well, as you apply some sort of matrix transformation, the areas of these parallelograms, well, they don't stay the same.

当你进行某种矩阵变换时 这些平行四边形面积 它们不会保持不变。

So the area of that parallelogram is a sort of screwy, roundabout way to describe the vector's Y cordon.

所以平行四边形面积是一种扭曲 迂回方式来描述矢量Y线。

At least, if you think of I had as, in some sense, being the 1st out of these two vectors defining the parallelogram.

至少 如果你把它看做 在某种意上 是这两个向量中第一个平行四边形。

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

它长度等于用vnw平行四边形面积。

That way, a vector with a negative Y coordinate, I would correspond to a negative area for this parallelogram.

这样 一个Y坐标为负向量 就对应了这个平行四边形负面积。

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

VNW叉乘 用X形乘法符号表示 就是这个平行四边形面积。

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一个微小间隙，形成了一个平行四边形，延伸了整个板长度并弥补了缺失正方形。

Just as before, we're still going to consider the parallelogram defined by the two vectors that were crossing together.

就像以前一样 我们仍然要考虑平行四边形由两个相交向量。

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 如果有两个向量V和W 想想它们张成平行四边形。

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

变换之后 这个正方形就变成了我们关心平行四边形。

The area of this parallelogram is the base one times the height perpendicular to that base, which is the Y coordinate of that input vector.

这个平行四边形面积等于底1乘以垂直于底高 也就是输入向量Y坐标。

The parallelogram that they define in this simple example is actually a square.

这个简单例子中平行四边形实际上是一个正方形。

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

这是我们之前看到平行四边形变换后版本 它面积是未知输入向量Y坐标。