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The basic idea is, you take a guess and you -- whoops -- and you find the tangent of that guess.
首先取个猜想数,然后，嗯,去取猜想数那儿的切线。
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Let's say you have to go through three or four operations to get a final number, well, do it algebraically.
让我们说,你不得不通过3-4个操作,才能得到最终的数，好吧，用代数方法求解。
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And frankly it would be incredibly time-consuming and tedious for me, to count this room full of people old school style-- 1, 2, 3 and so forth.
坦白说，按学校的老办法一个人一个人的数,1个，2个，3个……,对我来说极其费时费力。
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So let's go to a second clicker question here and try one more. So why don't you tell me how many possible orbitals you can have in a single atom that have the following two quantum numbers?
让我们来看下一道题目,你们来告诉我,有多少个可能的轨道,含有这些量子数呢？
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Well, I could look at the value here, and compare it to the value I'm trying to find, and say the following; if the value I'm looking for is bigger than this value, where do I need to look? Just here.
然后把它和目标数做个比较，然后做出如下的判断：,如果目标值大于这个值;,那么我应该去哪找呢？对，应该在这里,对不对？不可能在那儿。
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This adds on several hours to my work week.
这给我增加了数个小时的工作时间。
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Claire Elise is going to get her own vote plus 1, 2, 3, 4, 5, 6, 7, 8, 8 votes and Beatrice is getting 1, 2, 3, 4, 5, 6, 7, how did I end up with eight, I thought I had an odd number. 1, 2, 3, 4, 5, 6, 7 there must have been an odd number before.
克莱尔·伊莉斯将获得自己的选票加上,12345678 8张选票,而比阿特丽斯获得1234567,我怎么数出8个来的,我想应该是个奇数,1234567,之前也应该是个奇数
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The Republic is also a utopia, a word that Plato does not use, was not coined until many, many centuries later by Sir Thomas More.
理想国》也是乌托邦，一个柏拉图不使用的词汇，直到数个世纪之后,才由Sir，Thomas，More，杜撰出来。
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So now we're just counting up our orbitals, an orbital is completely described by the 3 quantum numbers.
所以现在我们只要把这些轨道加起来，一个轨道是由３个量子数完全确定的。
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The reason there are three quantum numbers is we're describing an orbital in three dimensions, so it makes sense that we would need to describe in terms of three different quantum numbers.
我们需要，3个量子数的原因,是因为我们描述的是一个，三维的轨道，所以我们需要，3个不同的量子数,来描述它。
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So what do you do when you're a kid and you want 3 to count a little faster than 1 and 2 and 3 and 4 what is the simplest thing you do?
因此当你还是个孩子的时候,你想数得比1，2，3，4快一些3,最简单的方法是什么？
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All right, so hopefully if you see any other combination of quantum numbers, for example, if it doesn't quickly come to you how many orbitals you have, you can actually try to write out all the possible orbitals and that should get you started.
所以希望你们如果遇到,任何其它的量子数组合的问题，如果你们不能马上想到有多少个轨道，可以试着先写出所有的轨道,这是个不错的切入点。
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And then the number of pairs at month n is the number of pairs at month n - 1 plus the number of pairs at month n - 2.
我们让第一个月的兔子数是1对,第n个月的兔子对数,是第n-1个月的兔子对数。
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- We know from Wednesday if -- briefly -- that there's this thing called a "char" or "char," depending on how you want to pronounce it, which is just a single character but where there's also an int.
我们知道从周三起--简单说下-,我们有个叫做“char“或“char“,看你们怎么读它了，那代表一个单一的字符,但那里会有个整型数与之对应。
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And I just want to point out that now we have these three quantum numbers.
我想指出的是,现在我们有了，这3个量子数。
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And we also, when we solved or we looked at the solution to that Schrodinger equation, what we saw was that we actually needed three different quantum numbers to fully describe the wave function of a hydrogen atom or to fully describe an orbital.
此外，当我们解波函数,或者考虑薛定谔方程的结果时，我们看到的确３个不同的量子数,完全刻画了氢原子,的波函数或者说轨道。
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How many different orbitals can you have that have those two quantum numbers in them?
有多少个轨道是,含有这两个量子数的？
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We know we need to divide by 266, 266 but what we need you to help us with is to figure out this top number here and see how many particles are going to backscatter. So if the TAs can come up and quickly hand out 1 particle to everyone.
知道背散射的概率就可以了，我们知道要除以,但还需要你们来搞清楚,分子上的数是多少，有多少个发生背散射的粒子,助教们请过来,把这些球分给同学们。
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And we can generalize to figure out, based on any principle quantum number n, how many orbitals we have of the same energy, n and what we can say is that for any shell n, there are n squared degenerate orbitals.
我们可以总结出来，在，主量子数为n的情况下，同一个能量上，有多少个轨道，我们可以说，对任何壳层，有n平方个简并轨道。
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