aufgehen
to open
To open; to no longer be closed.
Plötzlich ging die Tür von alleine auf.
Suddenly the door opened by itself.

to open / rise / work out
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to open
To open; to no longer be closed.
Plötzlich ging die Tür von alleine auf.
Suddenly the door opened by itself.

'Aufgehen' (to open / rise / work out) is a separable verb. The prefix 'auf-' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Jeden Morgen geht die Sonne um sechs Uhr auf.
Every morning the sun rises at six o'clock.
The prefix 'auf-' often indicates an opening or an upward movement. You can see this in meanings such as a door that opens, the sun that rises, or dough that rises.
Der Hefeteig muss an einem warmen Ort eine Stunde lang aufgehen.
The yeast dough needs to rise in a warm place for an hour.
The expression 'in etwas aufgehen' means to devote oneself fully and completely to something. The thing one devotes oneself to is in the dative after the preposition 'in'.
Er ist ein leidenschaftlicher Gärtner und geht total in seiner Gartenarbeit auf.
He is a passionate gardener and is totally absorbed in his gardening.
The mathematical meaning is often used figuratively. When a plan or idea 'nicht aufgeht' (doesn't work out), it means that it does not work or is not successful.
Sein Plan, ohne Ticket ins Konzert zu kommen, ist nicht aufgegangen.
His plan to get into the concert without a ticket did not work out.
When 'aufgehen' (to rise) describes a movement in the sky, the subjects are almost always celestial bodies. Typical subjects are 'die Sonne' (the sun), 'der Mond' (the moon), or 'ein Stern' (a star).
In dieser klaren Nacht kann man viele Sterne aufgehen sehen.
On this clear night, you can see many stars rise.
In the kitchen, especially when baking, 'aufgehen' (to rise) means that something increases in volume. Typical subjects are 'der Teig' (the dough), 'der Kuchen' (the cake), or 'das Soufflé' (the soufflé).
Damit der Kuchen schön aufgeht, darfst du die Ofentür nicht zu früh öffnen.
So that the cake rises nicely, you must not open the oven door too early.
When something that was fastened comes loose by itself, you use 'aufgehen' (to come undone). Typical subjects are 'ein Knoten' (a knot), 'eine Schleife' (a bow), 'eine Naht' (a seam), or 'ein Reißverschluss' (a zipper).
Pass auf, dein Schnürsenkel ist aufgegangen!
Watch out, your shoelace has come undone!
to go
'gehen' and 'aufgehen' can both mean, with dough, that it gets bigger. 'Der Teig geht' and 'Der Teig geht auf' are very similar in this context. 'aufgehen' often makes the change a little clearer: you can see that the dough is getting higher and lighter. 'gehen' is also used in the fixed expression 'den Teig gehen lassen' (to let the dough rise), when the dough is supposed to rest for a while. Learners may confuse the words because here they mean almost the same thing. The important point is: this similarity applies only to dough or baked goods, not to the other meanings of 'gehen'.

Im Ofen geht das Brot schön auf.
The bread rises nicely in the oven.
Der Hefeteig muss eine Stunde an einem warmen Ort gehen.
The yeast dough has to rise in a warm place for an hour.