A Mars-sized planet, given the unofficial name Theia, slammed into our young planet, but it wasn't a head-on impact; it was a grazing collision.

个火星大小行星，它有个非正式名字 Theia，撞上了我们年轻星球，但不是正面撞击，而是沿切线掠射。

If I add my next tangent line up here, it is around 0.5.

如果我在这上面加上我切线，它值大约是0.5。

You can’t see the big picture or even recall your last epiphany because you’re caught up in the momentum of a particular idea and your neurons keep firing until a new idea takes hold and you go off on a new tangent.

你无法看到大局，甚至无法回忆起你上次顿悟，因为你被某个特定想法动力所吸引，你神经元直在燃烧，直到个新想法生根发芽，你开始了新切线。

What a grown up movie tells you that it is okay to make mistakes because we can use the mistakes in the music of our life to find a lovely tangent to meander into.

部长大电影告诉你， 犯错误是可， 因为我们可利用生活中音乐中错误来找到个可爱切线来蜿蜒曲折。

The setup for this problem is that we have three different circles, just in two-dimensional space, and what we're going to do is draw the external tangents to each pair of them.

这个问题设定是我们有三个不同圆，都在二维空间中， 我们要做是画出每对圆外切线。

What we now call functions mathematical functions, which are Continuous that is that are not formed out of a discrete sets like the counting numbers for instance Newton there were already

我们现在称之为函数数学函数，它们是， 也就是说，它们不是由像计数数字那样离散集合构成。 举例来说，在牛顿时代， 已经存在些方法来解决涉及诸如求曲线面积和曲线切线等问题， 但这些方法仅适用于某些特定且有限曲线类型。

I literally didn't understand a lot of it, kind of, won't go off on my crypto tangent, but I don't understand.

我确实不太理解其中很多内容，有点， 不会偏离我加密切线，但我不明白。

Since the angles here are so small, you can just assume that the tangent of an angle is roughly equal to the angle itself.

由于这里角度非常小，您 可假设角度切线 大致等于角度本身。

And this is really where you get into the graffiti side of things because you look at these boxes and they're just all over the place and there's no real tangents going in the same direction.

这确实是你进入涂鸦方面地方，因为你看这些盒子，它们遍布整个地方，并且没有真正切线朝同方向延伸。

Unfortunately, the term " essential to national defense" can be—and has been—stretched to include products only remotely, tangentially, or fictitiously, related to military defense.

不幸是，“对国防至关重要”词可能而且已经被延伸到仅包括与军事防御远程、切线或虚构相关产品。

Oh, pointless meanders and superfluous tangents.

哦，毫无意义曲折和多余切线。

There's another benefit you get by shifting the focus to the center of similarity rather than describing these points as the intersection of external tangents.

将焦点转移到相似中心而不是描述这些点为外切线交点，你会得到另个好处。

And the calculations of tangents to curves are reciprocal to one another and the procedures that he develops is a particular form of the calculus.

曲线切线计算与面积计算互为逆运算，而他所发展方法是种特殊微积分形式。

And in a ray diagram, you can see that the tangent of the first angle, theta, is the height of the real image over the focal length of the objective lens.

在射线图中，您可看到 第个角度切线 theta 是真实图像 在物镜焦距上高度。

And you can also see examples of overlapping and parallel tangents in this single piece.

您还可在这件作品中看到重叠和平行切线示例。

My pointless meanders and superfluous tangents do go more ovular around, oval around, around, oval around.

我毫无意义蜿蜒和多余切线确实变得更加卵形，椭圆形，椭圆形，椭圆形。

No, that's not stuffing; there's pointless meanders and superfluous tangents and stuff… yeah, and there's… I have pockets full of stuffing, as well.

不，那不是填充物；那里有无意义曲折和多余切线等等… … 是，还有… … 我口袋里也装满了填充物。

I claim that that line also passes through the intersection point between the external tangents of the circles that we care about.

我声称那线也经过我们关心圆外切线交点。

And the new things that he begins to do leads him to a recognition that the calculations of areas

而他开始新探索使他认识到，面积计算与曲线切线计算是相互对应，他发展这些方法正是微积分种特殊形式。

I didn't expect it to, didn't understand what he meant by pointless meanders and superfluous tangents, but eventually, yeah, I realized I've been looking for a podcast like this my whole life.

我没想到会这样，不明白他所说无意义漫无目闲聊和多余切线是什么意思，但最终，是，我意识到我生都在寻找这样播客。