不可公度比与古希腊数学的转向

西帕索斯最早证明了不可公度线段的存在，其长度就是一个无理数．古希腊几何学家却拒绝承认无理数是数，导致了希腊数学由算术向几何学的转向，并由此推动了公理化思想的发展，使数学的严密性达到了更高的境界．因为放弃了对无理数的研究，致使算术和代数的发展受到限制，几何学畸形发展的局面在欧洲持续了两千多年．

On the Transition of Incommensurable Ratio and Ancient Greek Mathematics

Hippasus initially proved the existence of incommensurable line segments whose length is thought to be an irrational number. However ancient Greek geometricians refused to acknowledge irrational number is also a number and as a result,Greek arithmetic began to shift their focus to geometry. This shift promoted the development of Axiom and the preciseness of mathematics alsoreached its peak. But due to the neglect of the irrational number study,the advancement of arithmetic and algebra was greatly restricted and the unbalanced development of geometry persisted in Europe for more than 2000 years