DouKaku?

import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class Sample176 {

    public static List<Rational> rationalizes(final double d) {
        final Map<Rational, Double> map = new HashMap<Rational, Double>();
        for (int index = 1; index < 10; index++) {
            int nume = (int) (d * index);
            Rational r1 = new Rational(nume, index);
            Rational r2 = new Rational(nume + 1, index);
            if ((r2.doubleValue() - d) - (d - r1.doubleValue()) > 0) {
                map.put(r1, Math.abs(r1.doubleValue() - d));
            } else {
                map.put(r2, Math.abs(r2.doubleValue() - d));
            }
        }
        List<Rational> result = new ArrayList<Rational>(map.keySet());
        Collections.sort(result, new Comparator<Rational>() {
            public int compare(Rational o1, Rational o2) {
                return Double.compare(map.get(o1), map.get(o2));
            }
        });
        return result;
    }

    public static void main(String[] args) {
        System.out.println(rationalizes(1.732051));
        System.out.println(rationalizes(3.141593));
        System.out.println(rationalizes((double) 1920 / 1080));
    }

}

class Rational extends Number {
    public final int numerator;
    public final int denominator;

    public Rational(int p, int q) {
        int nume = p;
        int deno = q;
        if (deno == 0) {
            throw new IllegalArgumentException("#N/A");
        } else if (nume == 0) {
            deno = 1;
        } else if (deno < 0) {
            nume *= -1;
            deno *= -1;
        }
        int r = gcd(nume, deno);
        numerator = nume / r;
        denominator = deno / r;
    }

    private int gcd(int n, int m) {
        int p = n;
        int q = m;
        int r = p % q;
        while (r > 0) {
            p = q;
            q = r;
            r = p % q;
        }
        return q;
    }


    @Override
    public int intValue() {
        return numerator / denominator;
    }
    @Override
    public long longValue() {
        return this.intValue();
    }
    @Override
    public float floatValue() {
        return (float) this.doubleValue();
    }
    @Override
    public double doubleValue() {
        return (double) numerator / denominator;
    }


    @Override
    public int hashCode() {
        return numerator + denominator * 7;
    }
    @Override
    public boolean equals(Object obj) {
        if (this == obj) return true;
        if (!(obj instanceof Rational)) return false;
        Rational other = (Rational) obj;
        return this.denominator == other.denominator
            && this.numerator == other.numerator;
    }

    @Override
    public String toString() {
        return String.format("%d/%d", numerator, denominator);
    }
}