Please help with this paragraph of the article, i dont understand

[wmac]

Hello,

- I am a CS student and I am trying to simulate movements of people using a theory described in Helbing's paper.

I have put the paragraph in below address:

www.host111.com/question/helbing.jpg

- The problem is that I have passed college physics and math about 10 years ago ! :) and now need to understand above paragraph to be able to find a numerical solutions for it. (unfortunately I have been a software developer since then and shame that I have forgotten most of the things)

1- Would someone please help me understand this paragraph of the article?

2- What that Gradian mathematically and physically mean?

3- Would you please introduce me some quick references for a) physical side of it i.e potential functions b) mathematical side ie gradian etc?


Thank you very much in advance.

Mac

[HallsofIvy]

1- Would someone please help me understand this paragraph of the article?

Cute article! It is basically saying that we all feel uncomfortable if we get too close to another person (especially a stranger) and so will slow down if we are moving toward another person. While we are standing still there will be circle around us marking the distance we prefer to keep between ourselves and others- but when we are moving we take how fast we are approaching others into account and that circle becomes an ellipse- the "radius" is longer in front of us than to the side.

(I remember reading about a reception involving British and Italian diplomats. Since the "comfort distance" when talking to other people was smaller for the Italians than the British, the Italians kept trying to move closer, the British kept moving back. Everyone in the room was in constant motion!)

2- What that Gradian mathematically and physically mean?
According to MathWorld, a gradian is an angular measure in which an entire circle is 400 gradians (so that 90 degrees corresponds to 100 grads). It's used most often in surveying roads and laying out slopes. I used to have a calculator that allowed you to set it to take input for sine and cosine as "degrees", "radians", or "gradians" but haven't seen that in a long time.

Or did you mean gradient? That's more in keeping with your other questions. It's essentially the derivative (or rate of change) of a function of several variables. It is a vector pointing in the direction of greatest change and its length is the rate of change in that direction. If you were standing on the side of a hill with altitude given by z= f(x,y), the gradient of f would point directly up the hill. (That's in the U.S.A. In England, apparently, the term "gradient" is often used to mean the one-dimensional derivative.)

3- Would you please introduce me some quick references for a) physical side of it i.e potential functions b) mathematical side ie gradian etc?
That's a very broad question. Here are a couple of links:

hyperphysics.phy-astr.gsu.edu/hbase/gradi.html
en.wikipedia.org/wiki/Gradient