On Mon, 7 Nov 2005, Chuckk Hubbard wrote:
Not that I don't appreciate the snide commentary, but this is why I'm asking. You can't forget the sin*sin part. i stands for "imaginary". (slowly: i is "imaginary"). Turning the product of sines into the negative product of sines is imaginary. There is no number that, squared, equals -1. There is no number that, squared, equals -1. It's not really there.
depends on how people define "number". In math, it's usual to use an extended definition which isn't so limited as to forbid sqrt(-1) from existing.
also, to understand the word "imaginary" in math, you have to first understand that its meaning is completely distinct from any meaning of "imaginary" outside of math.
likewise for Real... "Real" is just a name. Small integers have a relatively high tangible quality to them, but it gets mostly downhill from there. "Real" numbers are arguably much less tangible than integer numbers, rational numbers, algebraic numbers, and then some. The numbers PI and E are a lot more tangible than almost all (100%) of the Real numbers.
Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju Freelance Digital Arts Engineer, Montréal QC Canada