| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
If you've seen Donald Duck in Mathemagic Land, you probably remember the part
with the Golden Rectangle. They then constructed a spiral curving from
a-b-g-h-i (in my rendition below). I'd like a formula for the spiral.
As an approximation, I was going to deal with it in 90� pieces. For the first
piece, I was going to start with an arc starting at a, centered at c. As I
swing the arc toward b, however, I would decrease the radius and slide the
center to d. For the next segment, the centerpoint would move from d to e as
the arc swung to g.
Would someone provide me with a better algorithm.? It seems to me that this
method would only be continuous for the zeroth and first derivative.
-- Chuck Newman
c h
a---------------------
| | | |
| i|--| |
| d|-------|g
| | e |
| | |
| | |
| | |
---------------------
b
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1768.1 | AUSSIE::GARSON | nouveau pauvre | Wed Jun 16 1993 01:14 | 17 | |
re .0
I'm not familiar with Donald Duck etc. but from the looks of it, with
suitable choice of axes, in polar coordinates, you want to fit an
equation of the form:
�
r = Ak
where 0 < k < 1
Having done this it should be easy to come up with parametric equations
for x and y in terms of � if you want Cartesian coordinates.
I recall that the above is called a "logarithmic spiral".
HTH
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