MIT Massachusetts Institute of Technology

How to Estimate the Value of Pi

Renyong Feng
Teacher of Mathematics
Verakin High School of Chongqing
Chongqing, China

冯仁勇
数学老师
中国重庆第二外国语学校

This lesson is about the estimation of the value of Pi. Based on previous knowledge, the students try to estimate Pi value using different methods, such as: direct physical measurements; a geometric probability model; and computer technology. This lesson is designed to stimulate the learning interests of students, to enrich their experience of solving practical problems, and to develop their critical thinking ability. To understand this lesson, students should have some mathematic knowledge about circles, coordinate systems, and geometric probability. They may also need to know something about Excel. To estimate Pi value by direct physical measurements, the students can use any round or cylindrical shaped objects around them, such as round cups or water bottles. When estimating Pi value by a geometric probability model, a dartboard and darts should be prepared before the class. You can also use other games to substitute the dart throwing game. For example, you can throw marbles to the target drawn on the floor. This lesson is about 45-50 minutes. If the students know little about Excel, the teacher may need one more lesson to explain and demonstrate how to use the computer to estimate Pi value. Downloadable from the website is a video demonstration about how to use Excel for estimating Pi.

这是一节关于值估算的实践课。学生们运用所学的物理测量方法、几何概型知识和电脑信息技术等估算值。通过这节课,希望激发学生的学习兴趣,体验科学的实践过程,培养他们的发散思维能力。学生在学习这节课之前,需要具备一些有关圆形面积计算,坐标概念以及几何概型等基本知识,还需要了解电子表格的一般应用和操作。学生通过直接测量的方法来估算值时,可以运用身边随手可得的材料比如水杯水瓶等圆柱形的物体以及细线量尺来测量。在用几何概型法来估算时,需要准备一套投掷飞镖的工具,当然也可以用其它实验来代替。例如,可以在地上画那个把子,然后老师可以选择普通的小石子进行设定距离投掷就可以的。这节课大概需要45分钟到50分钟,一节课就可以了。如果学生电脑方面不太熟悉,也可以单独再用一节课专门介绍最后用电脑模拟掷飞镖的那个实验。

 

Renyong Feng liked physics very much when he was in high school. However for some reason he majored in math in college. He has taught high school math for about 25 years and greatly enjoys teaching. He feels that he has had a rich experience in teaching and education during those years. 

我中学时代特别喜欢物理,上大学学的是数学,从事高中数学教学25年,非常热爱自己的 教育教学工作。在培养优秀中学生方面很有经验和优势

This site, sponsored by “wikiHow to Do Anything”, presents four ways to discover Pi  using circles.
http://www.wikihow.com/Discover-Pi-for-Yourself-Using-Circles

This video, from the Numberphile YouTube Channel, presents a million digits of Pi on one piece of paper (1.05 miles).
https://www.youtube.com/watch?v=0r3cEKZiLmg

This site, hosted by Science Friday, presents a simulator based on an experiment called Buffon’s needle, which estimates Pi by dropping sticks.
http://www.sciencefriday.com/blogs/03/12/2014/estimate-pi-by-dropping-sticks.html

This site, sponsored by the National Council of Teachers of Mathematics, provides lesson and activity resources for International Pi Day.
http://www.nctm.org/resources/content.aspx?id=28520

http://zh.wikipedia.org/wiki/圆周率  (Chinese)

http://baike.so.com/doc/3397799.html (Chinese)

Watch optional video "Using a Computer to Estimate pi by Throwing Darts" (Chinese)
http://blossoms.mit.edu/videos/files/chinese/using_computer_estimate_pi_throwing_darts_chinese_flash

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This Lesson is in the following clusters: Geometry