2020 Singapore Mathematics Project Festival Viviani’s Theorem and its Related Problems
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availability of previous work, applicability, etc. We narrowed our choices down to theorems related to
triangles, because triangles are the most basic polygons (3-sided polygons), which promises further
extension by altering conditions, such as increasing the number of sides or introducing new lines.
Finally, we decided that Viviani’s Theorem would be the topic of our project on the grounds that it features
basic constructions that are easy to follow, that its algebraic components can be recorded and observed
using basic programming on software like Microsoft Excel, and that it inspires us with different ways to
extend.
During our project, we used the online application, GeoGebra to confirm the conditions and requirements
needed for our extension and proof of the Viviani’s Theorem, as well as to create shapes used in our report
and presentation. We constructed the figure based on the original conditions of the theorem, then tried
dragging points around and adding/eliminating points and lines. To examine the CVS property of each
polygon, we wrote a sum function of all the distances and linked it to an Excel sheet, which automatically
recorded the sums as we changed the position of the arbitrary interior point. This helps us a lot in testing
our hypothesis and spotting the exceptions.
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