MIT Massachusetts Institute of Technology

How to Estimate the Value of Pi

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


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.



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.

This video, from the Numberphile YouTube Channel, presents a million digits of Pi on one piece of paper (1.05 miles).

This site, hosted by Science Friday, presents a simulator based on an experiment called Buffon’s needle, which estimates Pi by dropping sticks.

This site, sponsored by the National Council of Teachers of Mathematics, provides lesson and activity resources for International Pi Day.圆周率  (Chinese) (Chinese)

Watch optional video "Using a Computer to Estimate pi by Throwing Darts" (Chinese)

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This Lesson is in the following clusters: Geometry