TED | 我们为什么要学数学？——神奇的斐波那契数列

演讲简介

2013 | 我们为什么要学数学？数学是研究规律的科学，我们通过学习它来训练逻辑思维，思辩能力，创造力。但是学校里学的数学，却激不起我们的兴趣。每当学生问起“为什么要学?”得到的答案往往是“考试要考”。有没有可能，哪怕只有一小会儿，我们研究数学仅仅因为兴趣，或是数学的优美？

 

演讲精彩片段（节选）欣赏

So why do we learn mathematics? Essentially, for three reasons: calculation, application, and last, and unfortunately least in terms of the time we give it, inspiration.

我们为什么要学数学？根本原因有三个：计算、应用、最后一个，很不幸的从时间分配来看也是最少的，激发灵感。

 

Mathematics is the science of patterns, and we study it to learn how to think logically, critically and creatively, but too much of the mathematics that we learn in school is not effectively motivated, and when our students ask, "Why are we learning this?" then they often hear that they'll need it in an upcoming math class or on a future test.

数学是研究规律的科学，我们通过学数学来训练逻辑思维能力、思辩能力以及创造力，但是我们在学校里面学到的数学，根本没有激起我们的兴趣。每当我们的学生问起 “我们为什么要学这个？” 他们得到的答案往往是考试要考，或者后续的数学课程中要用到。

 

But wouldn't it be great if every once in a while we did mathematics simply because it was fun or beautiful or because it excited the mind? Now, I know many people have not had the opportunity to see how this can happen, so let me give you a quick example with my favorite collection of numbers, the Fibonacci numbers.

有没有可能，哪怕只有那么一小会儿，我们研究数学仅仅是因为自己的兴趣，或是数学的优美，那岂不是很棒？现在我知道很多人一直没有机会来体验这一点，所以现在我们就来体验一下，以我最喜欢的数列——斐波纳契数列为例。

 

Yeah! I already have Fibonacci fans here. That's great.

太好了！看来在座的也有喜欢斐波纳契的。

 

Now these numbers can be appreciated in many different ways. From the standpoint of calculation, they're as easy to understand as one plus one, which is two. Then one plus two is three, two plus three is five, three plus five is eight, and so on.

非常好，我们可以从多种不同的角度来欣赏斐波纳契序列。从计算的角度，斐波纳契数列很容易被理解1加1，等于2。1加2等于3，2加3等于5，3加5等于8以此类推。

 

Indeed, the person we call Fibonacci was actually named Leonardo of Pisa, and these numbers appear in his book "Liber Abaci," which taught the Western world the methods of arithmetic that we use today. In terms of applications, Fibonacci numbers appear in nature surprisingly often. The number of petals on a flower is typically a Fibonacci number, or the number of spirals on a sunflower or a pineapple tends to be a Fibonacci number as well.

事实上，那个我们称呼“斐波纳契”的人真实的名字叫列昂纳多，来自比萨，这个数列出自他的书《算盘宝典》（"Liber Abaci"）这本书奠定了西方世界的数学基础，其中的算术方法一直沿用至今。从应用的角度来看，斐波纳契数列在自然界中经常神奇的出现。一朵花的花瓣数量一般是一个斐波纳契数，向日葵的螺旋，菠萝表面的凸起也都对应着某个斐波纳契数。

 

In fact, there are many more applications of Fibonacci numbers, but what I find most inspirational about them are the beautiful number patterns they display. Let me show you one of my favorites. Suppose you like to square numbers, and frankly, who doesn't?

事实上还有很多斐波纳契数的应用实例，而我发现这其中最能给人启发的是这些数字呈现出来的漂亮模式。让我们看下我最喜欢的一个。假设你喜欢计算数的平方。坦白说，谁不喜欢？