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The Story of Pi in Hypervideo

Visualization has always been an essential aid in the communication of mathematics. It is an important way to concretize concepts, to develop abstraction skills, and to motivate learning, for example in topology and geometry, and in the application of numerical methods to simulations of the real world.

Video has proven to be one of the most adequate ways to communicate visualization results, allowing to present in a rich cultural context a large quantity and diversity of information in a brief period of time. However, by itself, video has a limited capability to support learning. The structure and interaction introduced by hypervideo allow providing the user with greater control and autonomy, exploring links among the information conveyed by the video and complemented by other materials, augmenting its capabilities as a cognitive artifact.

The Story of Pi video discusses the early history of Pi and shows how it appears in a variety of formulas and applications, many of which have nothing to do with circles, namely in probability problems. It is part of a series of modules, developed under Project Mathematics! [20], to introduce basic mathematical concepts in high school or community college, using live action, music, special effects, and imaginative computer animation that bring mathematics to life.

Figure 1: Sequence of early attempts to estimate the value of Pi.

Figure 2: Animated derivations of the formula for the area of a circle.

The hypervideo developed for The Story of Pi structures and integrates the video with other materials, augmenting their individual affordances to support learning. Video can be navigated from different types of indexes that are presented in synchrony with the video. The textbook was converted into hypertext, respecting its underlying hierarchical structure, and further enriched with links involving text, images, video, and applications, allowing to capture relations among them and to illustrate or complement the information conveyed by each one. Some features of the hypervideo are presented in the following examples.

Figure 3: Navigation in the hypervideo: video indexes and integration of video and textbook.

 

By Tom M. Apostol, Teresa Chambel, Suzana NŠpoles,
Josť Francisco Rodrigues, and Lara Santos

The Story of Pi in hypervideo is described in this paper (pdf) and demo (pdf), and published as an interactive CD.

Other publications

 

Selection of Related Work:

Bentley, P., and D. Come. An Introduction to Creative Evolutionary Systems. In Bentley, P., and Corne, D (eds.) Creative Evolutionary Systems. Morgan Kaufmann, 2002.

Apostol, T., 1989. Project MATHEMATICS!- The Story of π – Program Guide and Workbook, CalTech, California Institute of Technology, Pasadena, CA 91125, USA.

Apostol, T., Blinn, J., 1993. Using Computer Animation to Teach Mathematics, CBMS Issues in Mathematics Education, V.3. 13-38.

Liestōl, G., 1994. Aesthetic and Rhetorical Aspects of Linking Video in Hypermedia. In Proceedings of ACM Hypertext’94. Edinburgh, UK, pp. 217-223.

Norman, D., 1993. Things That Make Us Smart. Addison Wesley Publishing Company.

 

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