How did the Germans define who was Jewish?

My hypothesis is that the Germans did science or observations on people, which they believed looked like they were Jewish. Germans can measure peoples head, nose, eye width etc. to figure out what ethnicity they were. Since Jews are known to have larger noses, it would be easy to figure out what man or woman was a Jew. According to history books, I was correct with my hypothesis because some Germans, did in fact measure a mans nose who they believe was Jewish. They used this method for a while, and that was simply how they determined who was Jewish. Nazis had the authority to stop a man or woman and observe him or her and could say whether they were Jewish or not and execute them or apply a Star of David into the back and front of their clothing. In some cases, some Jewish people, had the Star of David tattooed into some part of their body to be easily recognized by the nazis. Later on in 1935, the nazis had the official definition of a Jew because of the Numerang Laws, which were anti Jewish statuses. "According to this German law, anyone with three Jewish grandparents was a Jew, as was anyone with two Jewish grandparents" (The Holocaust FAQ). Anyone who is married to a Jewish person or who has a Jewish parent was also considered Jewish(The Holocaust FAQ). 

"The Holocaust FAQ", auschuwitz.dk