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I know you're bugged by my bad humor, but too bad. Maybe you're bugged by this, saying wait a minute, how does this thing stop? This is the kind of definition that your high school geometry teacher would have rapped your knuckles over.
我也知道你可能觉得我的冷笑话很烦，但是很不幸，可能你会觉得这个很烦,你会想等等,这个程序怎么停下来呢？,这就是你们高中几何。
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And the geometry, which I didn't ask you, is going to be bent for this molecule.
几何形状，虽然我没有问你们，对于这个分子是折线型。
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If we add one to the return, then you've got a number that's never negative and we can then use geometric returns.
然后加上1,你永远也得不到一个负数,然后我们对这个值求几何平均
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And I am going to call this whole geometric factor here, I am going to put it into one number, and I am going to denote that the Madelung constant.
接下来我将会称这一部分为几何因子，我将把它们整合在一个数字里，我将会标注它为马德隆常数。
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So an easy thing to do in planar geometry is I want to make a line segment.
在平面几何里比较容易的一件事,就是做一个线段。
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So, for instance,you will see references to words like proto-geometric.
所以 举例来说,你会看到,参照的术语有像"原几何"
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A seed,a strength,a virtue,a competence that other teachers did not see, because they did not ask this question; because they asked,metaphorically speaking, ?" "how many geometric shapes do you see on the screen?"
潜能，优点，品德，能力,这些是其他老师没看到的，因为他们没提出这个问题;,打个比方，他们只会问，“你在屏幕上看到多少个几何图案“
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Jeremy says in the text that the geometric return is always lower than the arithmetic return unless all the numbers are the same.
杰里米在书里说几何平均,总是比算术平均小,当然如果所有数字都一样,两个均值相等
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Jeremy Siegel says that in finance we should be using geometric and not arithmetic averages.
杰里米·西格尔认为在金融上应该用几何平均,而不是算术平均
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It's a geometric factor that's unique for each crystal structure.
特有的几何参数,对不同晶型而言。
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The Madelung constant is simply the geometric factor.
马德隆常数也就是几何因子。
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The other kind of average is called the geometric average.
这种均值叫做几何平均
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There is a geometric constraint.
受到了几何限制。
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The length of a line segment?
好，几何学是怎么说的来着？
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So, we should use that, but people in finance resist using that because it's a lower number and when you're advertising your return you want to make it look as big as possible.
所以我们应该用这个指标,但金融界反感使用几何平均,因为它比其他平均数都来得小,他们为自己的收益率做广告时,当然希望数字越大越好
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It's a less optimistic version.
几何平均相比算术平均更加严谨
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In class on Monday, we did go over the geometries, and the geometries themselves are very straightforward, once you know what the Lewis structure is, but remember, you can't just always look at a molecule and automatically know the Lewis structure.
在周一的课上，我们讲过了几何形状，一旦你们知道了Lewis结构，这些几何形状是十分直接的，但记住，你不能总是仅仅看一眼,分子就知道它的Lewis结构。
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To calculate the expected utility of your wealth, you might also have to look at the expected return, or the geometric expected return, or the standard deviation.
要计算你财富的期望效用,你也许还要研究预期收益曲线,或几何预期收益率,或是标准差
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This is called the geometric average and it's used only for positive numbers.
这种平均叫几何平均,只能用于正的数值
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