IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Areas of triangles and other polygons with vertices from various sequences

  • Nov. 11, 2016
  • 2:30 p.m.
  • LeConte 312

Abstract

A triangle with vertices given by Fibonacci numbers as follows:

$(F _ n, F _ {n+k})$, $(F _ {n+2k}, F _ {n+3k})$, and $(F _ {n+4k}, F _ {n+5k})$ has area $\frac{5}{2}F^4 _ kL _ k$ for $k$ even and $\frac{F^2 _ kL^3 _ k}{2}$ for $k$ odd.

We have extended this result calculate the area of triangles with vertices using other sequences and from there to calculate the area of any n-gon with such vertices.

This is joint work with Charles Cook of USC Sumter.

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