论文标题
几何证明$ \ sqrt {3} $，$ \ sqrt {5} $和$ \ sqrt {7} $是不合理的
A geometric proof that $\sqrt{3}$, $\sqrt{5}$ and $\sqrt{7}$ are irrational
论文作者
论文摘要
我们通过对Tennenbaum的几何形状证明$ \ sqrt 2 $是不合理的，几何表明$ \ sqrt n $对于$ n = 3,5,7 $是不合理的。我们还表明，这种方法不能用于证明$ n $的$ \ sqrt n $的非理性性。
We show geometrically that $\sqrt n$ is irrational for $n=3,5,7$ by adapting Tennenbaum's geometric proof that $\sqrt 2$ is irrational. We also show that this method cannot be used to prove the irrationality of $\sqrt n$ for a bigger $n$.
