I don't know, I passed the "rounding to the next order of magnitude because it's good enough and nobody will notice" class with flying colours

I got 1000%, or something close

π = 1 is fine in a Fermi approximation

I don't even have a car in Germany, i can do everything using public transportation. you can subscribe to a monthly fee of 49 euros, this enables you to use the train in Germany, no matter where. If it's for commuting or traveling around Germany. The downside, it's only for regional trains, the slow ones. If you travel around Germany, it would take a long time, which is no downside for me, on the contrary.

But yeah, the one thing they are famous for, is being late.

north americans: Wait, you guys get trains?

The trains are fine it's the network that's the problem, and it's only going to get worse as they're finally catching up with decades of infrastructure under-investment.

Some corridors are simply over capacity, meaning delays and cancellations are unavoidable. If you don't happen to be driving through one of those corridors everything is mostly fine, if you are it's constant chaos, chaos that constantly radiates outwards. If you think that 15 minutes buffer are plenty to catch the next train -- nah. Forget it: Your train indeed might be delayed by that much, and the next one might not be able to wait because having the delay spread out would be even worse for the network. If you actually want to plan a route with multiple stopovers you need to make sure that every single leg has regular trains so you can get the next one. Silver lining? If you miss a connection like that you're allowed to get on any train you want to get to your destination.

Then look to the Japanese for train structure.