Professor Galperin discussed the problem of dissecting a pentagon using the diagonals as shown.
The first question is whether the areas a1,a2,...,a10 taking rational values implies that the area a11 is a rational number. The answer is that it does. But more surprisingly, we need only a1,a2,...,a9 to take rational values in order to imply that the areas a10 and a11 take rational values.
Professor Galperin was able to show that it is only necessary that 5 consecutive triangles have rational areas in order to show that all of the dissected areas are rational for the pentagon. In addition, he indicated how the result generalizes.
No comments:
Post a Comment