TED | 我们为什么要学数学?——神奇的斐波那契数列


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?



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.



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.



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



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.



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?