# enlighten me on the book's end note

Paul Dirac II
Posers and Puzzles 03 Oct '14 23:25
1. 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. AThousandYoung
All My Soldiers...
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. 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.