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Exploring Infinite Series through Baravelle Spirals

 Activity Description Activity Guide Resources

This activity is an introduction to the concept of convergent infinite series using a recursive geometric construction. This activity has been adapted from the following article: Choppin, J. M. (1994). Spiral through recursion. Mathematics Teacher, 87(7), 504-508.

Mathematics Topics: The students will explore the concept of a convergent infinite series using partial sums. This activity connects a number of algebra and geometry topics, as well as to involve students in formal calculations, visualizations, pattern discovery and recursion.

Mathematical Thinking: Students will be asked to investigate numerically and visually the sums of infinite series. Students will further conjecture and prove their ideas behind the sums of specific infinite series.

Technology: This activity uses several Sketchpad commands such as: New Sketch, playing back Scripts, Loop, Midpoint, Segment, Polygon Interior and Area.

The following sketches illustrate geometric representations of three different convergent infinite series summing to 1/3, 1, and 1/4 respectively.

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