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

Using smartphone photographs of the Moon to acquaint students with non-Euclidean geometry