TWT2011-Archimedes+rediscovered+through+Technology

**Presenters: Nicholas Wasserman & Itir Arkan ** **School: Marymount School **
 * Session: 26. Archimedes rediscovered through Technology**

**Description: ** Archimedes found powerful ways to use estimation in mathematics. His approaches to finding Circumference, Surface Area, and Volume involve a significant amount of mathematical reasoning and calculation. Part history, part technology, participants will  recreate Archimedes’ estimates through modern technology. They will use GSP5 to generate Archimedes’ upper and lower bounds  to trap pi by using inscribed and circumscribed regular polygons; data from this investigation will be analyzed statistically using  Fathom. Google Sketchup allows 3-D visualization of his approaches to estimate the Surface Area and Volume of a sphere - both having a ratio of 2/3 when compared to the cylinder circumscribing it. The 3-D navigation ability in Sketchup allows participants  to visualize Archimedean calculations.

Participants will learn useful features of GSP5, Google Sketchup, and Fathom while calculating Archimedes’ upper and lower bound estimates for pi, SA and Volume of a sphere, and more.

Instructions for attendees: If available, bring a laptop with the three software programs (Geometers Sketchpad (GSP5), Fathom, and Google Sketchup (a free download online)). There's a possibility the presenters may be able to bring a few computers that have all the software on them for those not able to bring laptops of their own.

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