Western concert flute cases C). Modern flutes may have a longer foot joint, a "B-foot", with an extra key to reach B. From high to low, the members of the concert flute family include: Each of the above instruments has its own range. The piccolo reads music in C (like the standard flute), but sounds one octave higher. The alto flute is in the key of G, and the low register extends to the G below middle C; its highest note is a high G (4 ledger lines above the treble staff). The bass flute is an octave lower than the concert flute,
Smallest-circle problem Smallest-circle problem The smallest-circle problem or minimum covering circle problem is a mathematical problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane. The corresponding problem in "n"-dimensional space, the smallest bounding-sphere problem, is to compute the smallest "n"-sphere that contains all of a given set of points. The smallest-circle problem was initially proposed by the English mathematician James Joseph Sylvester in 1857. The smallest-circle problem in the plane is an example of a facility location problem (the 1-center problem) in which the location of a new facility must be chosen