In commutative diagram we define the term 'flat module', but what is actually the meaning of the adjective 'flat'? I guess that the 'flat' here maybe a geometric description of 'torsion free', which is an equivalent expression in the context of PID. And torsion free has good geometric image. But I cannot persuade myself to accept this description. I would appreciate it if anyone who is familiar with the original usage of this terminology can come to my aid.