What fractions can you find between the square roots of 56 and 58?
Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.
The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?
The scale on a piano does something clever : the ratio
(interval) between any adjacent points on the scale is equal. The
keyboard is a repeating pattern of seven white keys with a black
key in between two whites in five places. If you play any note,
twelve points higher will be exactly an octave on.
The piano is made this way to allow a key change in the music
without re-tuning the instrument.
C to G is the two to three ratio, explored in the
earlier problems. It's called a "fifth", because it's the fifth
note along the white keys starting from C .
Is C to G an exact two to three ratio, or just off and, if so,
by how much?