Can You Find an Irrational Number Between Two Rational Fractions?

[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 :!)

 

[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

 

[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.

 

[sitedesigner]

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

so that will work for sure carl?