Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

the following question beat me. How from given any 9 points inside a square of side 1 we can always find 3 which form a triangle with area less than $1/8$ .

share|cite|improve this question
I guess you allow flat triangles. – 1015 Jan 14 '13 at 0:50
up vote 6 down vote accepted

Draw a horizontal line to split the square into two rectangles of area $\frac{1}{2}$. One of the rectangles must contain at least 5 of the points.

Now draw a vertical line to split that rectangle into two squares of area $\frac{1}{4}$. One must contain at least 3 points.

Now you need to show that any triangle inside a square of area $\frac{1}{4}$ has area at most $1/8$, which is discussed here: Maximum area of a triangle in a square

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.