丟番圖估計在解決有理數、無理數、代數數甚至非代數數被有理數或代數數用適當的估計方法逼近他們最接近的值，使得差距在最大與最小值之間，本研究目在於極值分母次方最小化。

Diophantine approximation solves the problems of a rational, irrational, algebraic, or transcendental number which be approximated by a rational or algebraic number. The main goal of the theory is to compare the distance between a given real number α and a rational number p/q is quiet closed to 0. This kind of problem is replaced by finding perfect enough upper and lower bounds of the above difference. The purpose of this research is aimed to minimize the denominator power of the extreme value.

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