Friday, 4 November 2011

An Interesting Rectangle Partitioning

Recently reminded of this pretty idea...


Came across a geometry problem with an interesting result which I did not suspect... thought I would share...
In the figure, rectangle ABCD is inscribed with a triangle by selecting points E and F on the segments AB and BC respectively, so that triangles AED, BEF, and CFD all have equal area. Find the ratios of AE:EB and BF:FC. I was surprised, and pleased, hope you are as well.
at

4 comments:

  1. Tito Eliatron4 November 2011 at 20:53

    I guess GoldenRatio is a serious candidate

    ReplyDelete
  2. Joshua Zucker5 November 2011 at 06:27

    It's not immediately obvious that such points even exist, so this is a nice treat on many levels.

    ReplyDelete
  3. Vid5 November 2011 at 14:48

    That hardly even looks like a rectangle.. I guess the triangle inside it is playing tricks on my eyes.

    ReplyDelete
  4. Maria Miller23 January 2012 at 16:14

    Hi! I posted this on my blog. Pat, I copied the picture off your blog, let me know if you don't want that.

    ReplyDelete