SELECT StudentName, RoomNumber
FROM StudentClassroom
JOIN Students ON Students.StudentID = StudentClassroom.StudentID
JOIN Classrooms ON Classrooms.ClassroomID = StudentClassroom.ClassroomID

doesn’t seem to be correct isn’t it ?

The haversine fomula is more accurate over short distances than some slightly simpler formulas, e.g. based on the law of spherical cosines. So, while it mathematically true:

sin(dLat/2)*sin(dLat/2) = (1 – cos(dLat))/2

the left-hand side avoids any loss of precision by cancellation that could occur on the right-hand side when the difference in latitudes dLat is small.

Brad asks about:

“The Haversine formula on Wikipedia doesn’t have Math.Min(1, Math.Sqrt(a)) in it, just Math.Sqrt(a).

“Do you know whether Min is important here? I’ve decided not to use it.”

A comment by the ubiquitous SQL expert Joe Celko cleared this up for me. It is useful at the other extreme of distances when two points are nearly at opposite sides of the sphere (antipodal). Then it guards against round-off errors leading to a > 1, which would make an arcsine calculation blow-up.

Finally, with regard to including altitude (and presumably, a difference in altitudes) in the distance calculation, it seems to me one has now entered a context in which “great circle” distances (produced by the haversine formula) may be less the question than Euclidean (straightline) distances. Someone might want to give the context in which they consider altitude important, e.g. orbital calculations? The haversine formula assumes a spherical model, and as Brad also pointed out, the variation in radius from north/south latitude variation can exceed the variation in altitude.

Adrian’s suggestion, to add the altitude to the Earth’s radius, is correct if one is asking about the distance between two points of equal altitude. However this would be a correction of less than 0.2% even at Mount Everest’s elevation.

When a difference in altitude is smallish relative to the great circle distance, a quick approximation is to add the two. This is essentially the approximation of a right triangle’s hypotenuse by adding the lengths of the two legs, reliable when one leg is much longer than the other. If the two distances were similar in magnitude, the Pythagorean formula would be more accurate, i.e. the square root of the square of altitude difference plus the square of the great circle distance.

regards, mt

Good explanation on the junction table!! You are a star disaster!!

Jim

Good Knuth, Bad Knuth

Although that your code is valid for most practical purpose, I’m afraid that the algorithm is not a correct Fisher-Yates shuffle implementation. There should be N! possible permutation (instead of N^N produced by your code) from which one of permutation will be chosen.

Consider using this code :

for (int i = ary.Length – 1; i >= 0; i++)
{
int r = rnd.Next(0, i + 1);

int tmp = ary[i];
ary[i] = ary[r];
ary[r] = tmp;
}