4 Jul 2013

Nine Points in a Square: Middle Secondary Mathematics Competition Question


Show that given any 9 points inside a square of side 1 we can always find 3 which form a triangle with area less than 1/8.

Junior Balkan Mathematical Olympiad 1997



You may also wish to try different numbers of points within a unit square. Start with just 3 and go all the way up to 9. As in the question above, if you are allowed to pick any 3 points from those given, such that they form a triangle with area less than x, find the minimum value of x in each case.


HARD Question for the Level (Black)
Feel free to comment, ask questions and even check your answer in the comments box below powered by Disqus Google+.

If you enjoy using this website then please consider making a donation - every little helps :-)

You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.

Don’t forget to follow Gifted Mathematics on Google+Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.
Related Posts Plugin for WordPress, Blogger...