老师详细解释了这个数学公式。

The teacher explained the ___mathematical formula in detail.

此外，他研究了人体并发明了数学公式来描述他的发现。

Furthermore, he studied the human body and invented ___mathematical formulas to describe his findings.

她的数学能力帮助她解决了复杂问题。

Her ___mathematical abilities helped her solve complex problems.