MIT Massachusetts Institute of Technology

Fun on the Sphere

Jiang Muyan “Jimmy”
Senior Year student
The Verakin School
Chongqing, China

Assistance provided by: 
MIT Professor Richard Larson
Verakin teacher, Huang Rongxiu
BLOSSOMS China liaison, Ling Wang
 Verakin students - Li Siyi, Li Hang, Yu Bing, Zhao Chongbo

姓名和单位
蒋牧颜(Jimmy)
中国重庆第二外国语学校高中生

其他支持和帮助者:
MIT 教授, 理查德·拉尔森
重庆二外教师,黄荣秀
BLOSSOMS 中国区联络人, 王玲
重庆二外学生, 李思佚,黎杭,余冰,赵崇博

This lesson focuses on sphere geometry. It aims to encourage students to solve real science problems in our daily life and explore the unknowns on the sphere. Although some of the ideas in the video are slightly challenging, the overall difficulty of the lesson is suitable for all students above junior level. To follow the lesson, students need to have some basic knowledge about circles, planar geometry and so on. It will take approximately 50 minutes to complete the whole class. During the class, the materials listed here are needed: small globes, pens, paper, scissors, calculators, soft rulers, rubber band, balls with different size, some strings, etc. It is important to present a globe throughout the class to help students visualize the problems. For example, in the Muslim Prayer problem, it is really important to make students understand the geographical location of Mecca and Boston on both the map and the globe.

这堂课是关于球面几何的。它旨在激发学生在解决生活实际问题和探索球面上的未知的兴趣。虽然有一部分知识和问题具有一定的挑战性,但总体而言课程难度适合所有初中生以上的学生。学生需要有一些关于平面几何的圆的基础知识等。整堂课大约需要50分钟来完成。课堂里需要以下材料:小型地球仪,笔,草稿纸,剪刀,计算器,软尺,橡皮筋,不同大小的球,短绳等。地球仪需要一直展示在学生前贯穿整堂课,这样学生更方便直观的理解问题。例如,在穆斯林礼拜问题中,让学生清楚的看到波士顿和麦加在地球仪和地图上分别的地理位置是非常重要的

Jiang Muyan, “Jimmy”, is a student from Chongqing, China. He is a fan of math and soccer. It has been his great honor to participate in the BLOSSOMS project and work closely with his partners in that project. In the past year, his team carefully designed and videotaped this lesson, and they sincerely hope all of you would find it useful and interesting.

蒋牧颜(Jimmy)是一名来自中国重庆的高中生。他是数学和足球的铁粉。在去年一年里,他和他的团队精心设计并拍摄了这堂课,他们真诚的希望观众能在这堂课里体验到有趣的有用的东西。

This resource, sponsored by Wolfram MathWorld, presents the algorithm of the Traveling Salesman Problem that is referred to in this lesson.
http://mathworld.wolfram.com/TravelingSalesmanProblem.html

This Wikipedia site provides a comprehensive overview of Spherical Geometry.
https://en.wikipedia.org/wiki/Spherical_geometry

This site, hosted by Math Fun Facts, provides an interesting discussion of Spherical geometry.
https://www.math.hmc.edu/funfacts/ffiles/20001.2.shtml

This resource by Math Is Fun presents a short and fascinating discussion about Spherical Geometry.
https://www.mathsisfun.com/geometry/sphere.html

以下资料由Wolfram MathWorld提供,里面包含了视频里提到的旅行商人问题。
http://mathworld.wolfram.com/TravelingSalesmanProblem.html

这个维基百科网页提供了完整的球面几何的概述介绍。
https://en.wikipedia.org/wiki/Spherical_geometry

这个Math Fun Facts的网页展示了一些关于球面几何有趣的讨论。
https://www.math.hmc.edu/funfacts/ffiles/20001.2.shtml

Math Is Fun的这个网页有一些简短但吸引人的关于球面几何的讨论。
https://www.mathsisfun.com/geometry/sphere.html

Title Language Format  
Fun on the Sphere (English, mp4) English MPEG 4 Download
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