1. Joined
    30 Sep '12
    Moves
    731
    03 Oct '14 23:25
    I am polishing off a book by mathematician Ian Stewart by reading the end notes. For brevity I'll leave out the last paragraph of the note. I use ^ for taking a power and sqt[ ] for square root.

    "Introduce the norm
    N(a + b sqt[15]) = a^2 - 15 b^2

    which has the lovely property

    N(xy) = N(x) N(y)

    Then

    N(2) = 4 N(5) = 25 N(5+sqt[15]) = 10 N(5-sqt[15]) = 10"

    It seems to me that N(2) = 2^2 - 15 0^2 = 4, which is not 10. What am I doing wrong?
  2. SubscriberAThousandYoung
    All My Soldiers...
    tinyurl.com/y9ls7wbl
    Joined
    23 Aug '04
    Moves
    24791
    04 Oct '14 01:22
    Originally posted by Paul Dirac II
    I am polishing off a book by mathematician Ian Stewart by reading the end notes. For brevity I'll leave out the last paragraph of the note. I use ^ for taking a power and sqt[ ] for square root.

    "Introduce the norm
    N(a + b sqt[15]) = a^2 - 15 b^2

    which has the lovely property

    N(xy) = N(x) N(y)

    Then

    N(2) = 4 N(5) = 25 N(5+sqt[15]) = 10 N ...[text shortened]... ]) = 10"

    It seems to me that N(2) = 2^2 - 15 0^2 = 4, which is not 10. What am I doing wrong?
    After the "Then" there are four separate lines. It is not one line.

    N(2) = 4

    N(5) = 25

    N(5+sqt[15]) = 10 because 5^2-1^2*15 = 10

    N(5-sqt[15]) = 10 because 5^2-(-1)^2*15 = 10
  3. Joined
    30 Sep '12
    Moves
    731
    04 Oct '14 05:23
    Hey thanks!

    That's got to be it. The typesetting was poor in the way it jammed things together, and I wasn't smart enough to figure out that was what was going on.