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Topic: [math-learn] Stem & Leaf Plots with Decimals
Replies: 21   Last Post: May 5, 2008 5:31 PM

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 Ladnor Geissinger Posts: 313 From: University of North Carolina at Chapel Hill Registered: 12/4/04
[math-learn] Re: length and area; sidewalks and roads
Posted: May 5, 2008 4:42 PM
 att1.html (13.7 K)

Yes of course the actual curves on roads are not sections of circular
rings, but could be thought of as the limit of a succession of narrow
sections of such rings with gradually increasing and then decreasing
curvature. The technical point is that such a region can be swept out
by a line segment of length w with its center on the centerline of the
road and always perpendicular to the centerline, because the radius of
curvature of the centerline is always larger than w/2.

Note that the above method of sweeping out the road area does not work
for the straight-edged "sidewalks" described before, and even the
notion of centerline is a bit tricky as you get near a sharp corner.
But such details won't bother those just beginning to study geometry.

--- In math-learn@yahoogroups.com, "Ralph A. Raimi" <rarm@...> wrote:
>
> Ladnor Geissinger speaks of the areas of road surfaces, when they
> have a turning somewhere, as if the curved portion has circular
> boundaries. I believe that road-builders avoid circles here, since

this
> would imply a sudden transition from zero to a non-zero acceleration in
> the normal direction, requiring a sudden jerk of the steering wheel.
> Instead they make the curvature change more gradually from zero to the
> maximum they intend, holding that max (circular motion) for a rather

short
> distance until they are ready for a gradual decline of curvature to
> straight-on motion. I have no idea what formulas they use, if any. It
> might be a seat-of-the-pants drawing-board solution, for all I know,

for I
> have noticed no uniformity in road-building practice here, some
turnings
> being less comfortable than others in my rough experience.
>
> Ralph A. Raimi Tel. 585 275 4429 or (home) 585 244 9368
> Dept. of Mathematics, Univ.of Rochester, Rochester, NY 14627
> <http://www.math.rochester.edu/people/faculty/rarm/>
>
> "Algebra is conducive to symbolic reasoning." (PSSM, p.345)
>

Date Subject Author
4/9/08 Jon Wilson
4/10/08 Jon Wilson
4/10/08 Prof Martin Weissman
4/10/08 Ron Ferguson
4/10/08 Prof Martin Weissman
5/4/08 lolly45101961
5/4/08 Ed Wall
5/4/08 Marie Bahlert
5/4/08 Rex Boggs
5/4/08 Ed Wall
5/5/08 GS Chandy
5/5/08 Rex Boggs
5/5/08 Ralph A. Raimi