在家里，我就像一只被困在鸽笼里的火烈鸟。

In my family, I am flamingo in the flock of pigeons.

你可以简要地说其实证明就是初等矩阵理论，三角不等式和鸽笼原理的运用。

You can say that the proof USES nothing beyond elementary matrix theory, repeated use of the triangle inequality, and the pigeonhole principle.

鸽笼式分类架，信件架，文件格小隔间或凹室，如桌子里，用来放文件；格架。

A small compartment or recess , as in a desk, for holding papers a cubbyhole .