MathDB

Consider all rational numbers of the form

\tfrac{p}{q}

where

p,q

are relatively prime positive integers less than or equal to

8

, and plot them on the

xy

-plane, where

\tfrac{p}{q}

corresponds to point

(p,q)

. Arrange the rationals in increasing order

\{P_1,P_2,\dots,P_n\}

and form a polygon by connecting points

P_i

and

P_{i+1}

for

1\le i<n

and connecting both

P_1

and

P_n

to the origin. What is the area of the polygon?

Problem Statement