115 solving $f(f(x))=g(x)$ 94 Is the sphere the only surface all of whose projections are circles? Or: Can we deduce a spherical Earth by observing that its shadows on the Moon are always circular? 61 Is there a dense subset of the real plane with all pairwise distances rational? 59 How to solve $f(f(x)) = \cos(x)$? 57 Smoothness of distance function in Riemannian Manifolds

### Reputation (30,308)

 +20 Smoothness of distance function in Riemannian Manifolds +30 Mathematics of doodling and the winding number +10 Smoothness of $f(\sqrt x)$ +10 Is there a dense subset of the real plane with all pairwise distances rational?

### Questions (24)

 55 How do they verify a verifier of formalized proofs? 32 Is every smooth function Lebesgue-Lebesgue measurable? 27 An unfair marriage lemma 26 Easy proof of the fact that isotropic spaces are Euclidean 24 A set that can be covered by arbitrarily small intervals

### Tags (137)

 694 mg.metric-geometry × 66 190 real-analysis × 5 502 dg.differential-geometry × 65 174 fractional-iteration × 2 346 gn.general-topology × 21 173 linear-algebra × 21 210 geometry × 18 172 gt.geometric-topology × 19 205 ca.classical-analysis-and-odes × 18 152 set-theory × 6

### Bookmarks (45)

 202 What elementary problems can you solve with schemes? 67 Can analysis detect torsion in cohomology? 52 Atiyah-Singer index theorem 51 Open map D⁴ → S² 49 vector balancing problem