Definitely don't need a picture from space. Why don't airliners fly in a straight line? Because the shortest distance between two points on a sphere is not a straight line but an arc.
Why is the shadow of earth on the moon always curved? Because there is only one shape that will always produce a curved shadow no matter what angle the light source comes from. That shape is a sphere. If the earth were flat like a dinner plate, then at some point we would see a shadow on the moon like a straight line or a band of shadow.
I recently heard a discussion between a group of young people on the train on this subject. It was pretty scary.
