  Although they are sometimes considered problematic to grasp by students, the
concepts behind non-Euclidean geometry can be taught using astronomical images.
By using photographs of the Moon taken with a smartphone through a simple
telescope, we were able to introduce these concepts to high-school students and
college newcomers. By recognizing different Moon geological structures within
the photograph, we teach students how to calculate distances of mountain ranges
or areas of craters on the Moon's surface, introducing the notions of geodesics
and spherical triangles. Furthermore, students can empirically see that the
correct estimations for the actual values cannot be obtained using flat
geometry. Instead, by using three--dimensional curved geometry, precise
estimates of lengths and areas of geological elements in the Moon can be
computed with less than 4\% error. These procedures help students understand,
concretely, non-Euclidean geometry concepts.
