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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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I once counted the number of times he used the word the letter--O--in that poem, and I quit counting.
我曾经数过他到底在诗里用了多少个"啊",最后我放弃了
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So we have a total of 2, 4, 6, 8, 10 valence electrons, so I'll make sure I count to 10 as we fill up our molecular orbitals here.
我们一共有2，4，6，8，10个价电子，所以我一边填一边要确认,我数到10。
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What's the biggest number you can represent with three decimal digits? Pardon?
你们想用这3个十进制数表示什么？,请再说一遍？
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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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Yeah. So we have two orbitals, or four electrons that can have that set of quantum numbers.
嗯，有我们有两个轨道，也就是４个电子可以有这套量子数。
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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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Well, if intuitively the problem is the result of dividing an int by an int, surely a solution is: "Don't do that," right?
好的，直观地看,如果那个问题的原因是因为整型数除以整型数的话,无疑有个解决方案是：“不要那样做“，是吗？
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So carbon 12. We know that it has the proton number, by definition, is 6. And the neutron number, 6 from 12 is 6. So it has 6 protons and 6 neutrons.
所以碳12，我们知道它有质子数，根据定义，那就是6，而电子数，12减6等于6，所以它有6个中子。
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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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Two significant digits is good enough.
个有效数应该绰绰有余了。
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Is this a real or a float?
看看到底是个实数还是个浮点数？
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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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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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- 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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So similarly, as we now move up only one more atom in the table, 3 so to an atomic number of three or lithium, now we're going from six variables all the way to nine variables.
类似地就像我们现在,移动到周期表中仅仅多一个电子的情况，移动到一个原子数为，或者锂元素,现在我们从6个变量到了9个变量。
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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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So, those are our three quantum numbers.
这就是，3个量子数。
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So we can completely describe an orbital with just using three quantum numbers, but we have this fourth quantum number that describes something about the electron that's required for now a complete description of the electron, and that's the idea of spin.
所以我们可以用３个,量子数完全刻画轨道，但我们有这第四个量子数,来完整的,描述电子，这就是自旋的概念。
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And I said I'm giving you three decimal digits.
我说给你们3个10进制数。
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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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m And the third one is called m, l it's also m sub l.
第三个量子数叫做，也叫做m小标。
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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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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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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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