Little integer problem

1. Aug 28, 2005

sitedesigner

ok,

a/b c/d

a,b,c,d are all integers
b and d are > 0

find a number inbetween a/b and b/d using a,b,c,d that is an irrational number.

thanks :!!)

2. Aug 28, 2005

CarlB

The difference between the two rational numbers is

$$\frac{ad-bc}{bd}$$

If you can find an irrational number that is smaller than this, you can add it to the lesser of {a/d, b/c}.

Carl

3. Aug 28, 2005

StatusX

You could pick a strictly increasing curve (like y=x^2, for x>0), find the x values that generate these two fractions as y values, and find the y value for the number halfway (or anywhere) between these two x values. It's a safe bet this will be an irrational number.

4. Aug 28, 2005

sitedesigner

so that will work for sure carl?