Napoleon's Theorem and Beyond

The use of Microsoft Excel to explore old, well-known geometrical theorems is set in the context of Napoleon's Theorem. A number of results emanate from the investigation, and spreadsheet examples are given to show how Excel can effectively model such results. The article concludes with a generalisation with respect to lines drawn from the vertices of a triangle. The generalisation links a number of known results in a novel way, and provides a new understanding of triangle properties. The article is not written solely from the geometrical point of view, and emphasis is placed on the role that spreadsheets can play in developing an environment in which ideas can be explored and discovered. The benefits of using Excel in the context of a geometric investigation are outlined in terms of student control and ease of learning of the environment together with the spreadsheet's ability to cope with exceptions without halting.