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

伯努利还提出了我们现在所知的伯努利。

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

在我们初次学习伯努利分布时，就曾见过这一概念。

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

据说，伯努利立刻就认出这个是摆线。

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

牛顿和伯努利发现最短路径——直线，并不是最短时间。

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

伯努利的第一项是 能量除以体积。

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

伯努利原理是力学和科学的一部分。

We see some xi's from a Bernoulli distribution.

我们从伯努利分布中看到了一些xi。

Some of the X odds are going to be Bernoulli.

一些X赔率将是伯努利。

This is known as Bernoulli’s principle.

这被称为伯努利原理。

And then the variance of this Bernoulli distribution is going to be these two proportions multiplied.

然后这个伯努利分布的差就是这两个样本比例的乘积。

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

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

That's called the kinetic energy density, and it's the second term of Bernoulli's equation.

这称为动能密度， 它是伯努利的第二项。

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

伯努利中的第一项取该能量， 并将其除以体积。

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，这从根本上是基于伯努利原理的。

So Gottfried Leibniz, a friend of Bernoulli's, persuaded him to extend the deadline to give foreigners a chance.

因此伯努利的朋友戈特弗里德·莱布尼茨说服他延长最后期限，以便给外国人一个机会。

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

伯努利将这种形式的能量分开，得到 流体密度的一半，再乘以速度的平。

This is known as Bernoulli's principle.

这被称为伯努利定律。

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

伯努利还放了什么 我们通过伯努利知道它。

That’s called the kinetic energy density, and it’s the second term of Bernoulli’s equation.

这就是所谓的动能密度， 它是伯努利的第二项。

And we saw this many many videos ago when we learned about Bernoulli distributions.

我们在很久以前学习伯努利分布的中见过这个。