The parliamentary arithmetic suggests Merkel would actually be in quite a stable position if she goes it alone, without calling fresh elections.
Generations of Germans have worked to create a positive national identity based on difficult self-reckoning with the Nazi era. The recent election attacks that progress.
Angela Merkel must continue to resist the temptation to cede political ground to the populists.
After taking more than 13% of the vote, this young party is entering parliament for the first time. And a lot of people are upset about it.
The chancellor wins again, but the rise of the populists will probably force the next administration to the right.
German elections are typically tame. Jockeying for power takes place later, in negotiations for a coalition government. Could the xenophobic Alternative for Germany form the opposition?