Now, let’s look at a special case of Bernoulli’s equation, known as Torricelli’s theorem.

现在，让我们看一下努利方程的一个特例， 即托里拆利定。

And we've seen this when we first learned about Bernoulli distributions.

在我们初次学习努利分布时，就曾见过一概念。

And this equation, the story goes, Bernoulli immediately recognized as the equation of a cycloid.

据说，努利立刻就个方程是摆线方程。

Newton and Bernoulli figured out the shortest  path, a straight line, isn't the shortest time.

牛顿和努利发现最短路径——直线，并不是最短时间。

We talk about Bernoulli's principle a lot on this  channel, and he's got something to say about the flow of water in a spillway.

我们在频道上经常讨论努利原，它对泄洪道中水流的情况有一些说明。

Bernoulli also came up with what we now know as Bernoulli's equation.

努利还放了什么 我们通过努利方程知道它。

1737. Swiss mathematician Daniel Bernoulli poses the St. Petersburg paradox, examining how players can evaluate options involving chance.

1737年， 瑞士数学家丹·努利提了圣彼得堡悖论，探讨了玩家如何评估涉及机会的选择。

I hope you'll recognize that if I use this as the likelihood, Instead of the version coming from the Bernoulli representation, that I would have had n choose some x here, n choose some x here.

我希望你能识到，如果我用个作为可能性，而不是来自努利表示的版本，我会让 n 在里选择一些 x，n 在里选择一些 x。

In this method, the shield tunnel is considered as a continuous beam, namely Timoshenko (TM) and Euler-Bernoulli (EB) beams, lying on the Pasternak foundation.

在种方法中，盾构隧道被为是位于帕斯捷纳克地基上的连续梁，即蒂莫申科 （TM） 和欧拉-努利 （EB） 梁。

And these are both Bernoulli distributions and we know, just because this'll be useful later on, that the means of this distribution are the same as the proportion that will vote for it.

些都是努利分布， 我们知道，因为在后面会用到，些分布的均值与投票支持的比例相同。

Nearly 60 years later, in June of 1696, Johann Bernoulli set this problem as a challenge to the best mathematicians in the world.

近 60 年后，1696 年 6 月，约翰·努利将个问题向世界上最优秀的数学家提挑战。

The key is stability, and the essence is using aerodynamics, which is fundamentally based on Bernoulli's principle.

关键是稳定性， 而本质是使用空气动力学，从根本上是基于努利原的。

Bernoulli's principle is a part of mechanics and science.

努利原是力学和科学的一部分。

Some of the X odds are going to be Bernoulli.

一些X赔率将是努利。

This is known as Bernoulli’s principle.

被称为努利原。

When Bernoulli divided that by volume, he got density times small g times height -- the potential energy density, and the third term of his equation.

当努利将其除以体积时， 他得到了密度乘以小 g 乘以高度——势能密度，以及他的方程式的第三项。

[Derek] And on the 29th of January, 1697, Newton returned home after a long day at work to find Bernoulli's challenge in the mail.

- [德里克] 1697 年 1 月 29 日，牛顿结束了一天的漫长工作回到家，在邮件中发现了努利的挑战。

Again, Bernoulli divided this form of energy by volume, to get half the fluid's density, times its velocity squared.

努利将种形式的能量分开，得到 流体密度的一半，再乘以速度的平方。

The first term in Bernoulli's equation takes that energy, and divides it by volume.

努利方程的第一项是 能量除以体积。

We see some xi's from a Bernoulli distribution.

我们从努利分布中看到了一些xi。