Mouhefanggai: A page in ancient Chinese mathematics

Volume of a sphere is introduced in secondary 3 of the Hong Kong mathematics syllabus. Many textbooks simply state the formula. Much emphasis is laid on formula application. We have much reservation on this approach. Mathematics teachers know well that the formula derivation takes only a few lines by using integral calculus which is not yet learned by students. Nevertheless the sphere is such a common and important solid that its volume determination is highly demanding in many practical situations. Actually its computational formula V=(4/3)πr³ is known long before the development of calculus. Nations of different culture tackle the problem in various ways. In China the result was drawn from the study of a solid called mouhefanggi (牟合方蓋) by the joined effort of a number of mathematicians. This idea was first introduced by Liu Hui (劉徽) in the Nine Chapters on the Mathematical Art (九章算經). We are not only amazed by these mathematicians’ brilliant thoughts but are also deeply impressed by their persistent efforts over centuries in search of the solution. The study of this page in our ancient mathematics history may enhance the learners’ spatial sense and adjoin human touch to our highly cognitive subject – mathematics. In this paper we share with readers our classroom experiences – the method we present mouhefanggi to our students and the way we use manipulative and modern technology (virtual manipulative) in guiding our students to visualize and understand the underlying geometrical concepts. Copyright © 2010 Tung-Ping Cheung & Shi-Pui Kwan.