- In mathematics, the von Neumann paradox, named after John von Neumann, is the idea that one can break a planar figure such as the unit square into sets of points and subject each set to an area-preserving affine transformation such that the result is two planar figures of the same size as the original. This was proved in 1929 by John von Neumann, assuming the axiom of choice. It is based on the earlier Banach–Tarski paradox, which is in turn based on the Hausdorff paradox.
- The Puzzle of the Metallic Line Stars
In the puzzle of the metallic line (Am) stars, there still seem to be missing pieces. While the “normal” A stars have elemental abundances close to solar, the classical Am stars show stronger absorption lines for most heavy elements in their spectra. Elements with ionization potentials that nearly agree with those of hydrogen or helium have reduced abundances. The Ca ii and Sc ii lines are especially weak. The Am stars have no ultraviolet emission lines. They are binaries that, with very few exceptions, have rotational velocities vsin i lower than 100 km s−1. Of the main‐sequence A stars, 20% to 30% are Am stars. Here we rediscuss previous suggestions that tried to explain the peculiar line strengths in the Am star spectra. In particular, we compare the well‐studied properties of Hyades A and Am stars in order to identify reasons that can or cannot explain the differences. We find that accretion of interstellar material by A stars with distorted magnetic fields, which are weaker than those in peculiar A (Ap) stars, has the best chance of explaining the main characteristics of the peculiar heavy‐element abundances in Am star photospheres. Charge‐exchange reactions also seem to be important.