Re: Golly, that was easy...
- From: John C. Polasek <jpolasek@xxxxxxxxxx>
- Date: Sun, 14 Jan 2007 22:47:57 -0500
On 14 Jan 2007 08:58:54 -0800, "Edward Green"
<spamspamspam3@xxxxxxxxxxx> wrote:
I recall straining my mind over diagrams full of angles and
perpendiculars, deriving (once) or trying to recover (many times) the
addition formulas for cosine and sine. I'm not sure when I first
discovered they were both contained, without any effort at all, in the
statement exp[i(a+b)] = exp[ia]exp[ib].
What makes the exponential function so unreasonably useful?
The efficiency of exp(ia) must be that it empowers the single scalar
'a' to keep track of both the sine and cosine of the angle. Any
scalar b can be added to a, thus forming the addition of a second
angle. Now expia * expib points to simple multiplication of the
cartesian components e.g. sin(a) to get the result of adding two
angles. Does that help?
John Polasek
.
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- Golly, that was easy...
- From: Edward Green
- Golly, that was easy...
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