Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The maximum number of points in a plane such that the distance of any of these points from a given point in the plane is less than the distance of it from any other point is five.

share|improve this question
1  
What is your question? Do you want a proof, a reference, the name, a generalisation, an application? Please edit your post to make it clear exactly what it is you are looking for. –  Michael Albanese Jan 5 '13 at 3:32

1 Answer 1

Let $O$ be your given point.

Let the points $P_i$ satisfy your conditions, i.e. that $OP_i < P_i P_j \, \forall i, j$

Use Cosine rule to show that $\angle P_i O P_j > 60^\circ\, \forall i, j$.

Now order points $P_i$ in a clockwise manner around $O$. It follows that there are $< \frac {360}{60}$ such points. Hence, there are at most 5.

share|improve this answer

Your Answer

 
discard

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.