Steiner’s proof of what is now called theSteiner-Lehmus theoremwas published in 1844, the same year as the bookThe three musketeers, written by the French author Alexandre Dumas. The mottoOne for all, all for one (Einer für alle, alle für einen; Un pour tous, tous pour un; Uno per tutti, tutti per uno)of the three musketeers came into widespread use in Europe in the 19th century, and its essence is that the three musketeers are inseparable; each member pledges to support the group, and the group supports each member. Now there are three classical geometries of constant curvature, namely Euclidean, spherical and hyperbolic geometries, and one can argue that, like the three musketeers, these geometries should be considered as being inseparable; that is, an idea, theorem or proof in any one of them should automatically be considered in the other two. The issue here should be not only to decide whether a particular result is true, or false, in a given geometry, butto understand which particular properties of the geometries make it so.
Variation in faecal corticosterone metabolites in an Arctic seabird, the Little Auk (Alle alle) during the nesting period
