If you want to view a hypercube, it's actually pretty easy. First of all, consider the corners of the unit hypercube: (0,0,0,0), (0,0,0,1), (0,0,1,0), (0,0,1,1), (0,1,0,0), (0,1,0,1), (0,1,1,0), (0,1,1,1), (1,0,0,0), (1,0,0,1), (1,0,1,0), (1,0,1,1), (1,1,0,0), (1,1,0,1), (1,1,1,0), and (1,1,1,1). Then in order to see all the possible projections, just rotate it around the w axis, project into three-space, then put the resulting 3d figure into OpenGL and rotate around the x, y, and z axes on screen.
Rotations are done in 4d much like in 3d -- A rotation can be expressed as a linear transformation, and rotations and reflections are uniquely represented as matrices for which transpose(A) = inverse(A), whether A is 2x2 or 7x7. If there's enough demand, I suppose I could write such a program, but I'd have to learn OpenGL first.
First of all, if you have 30 lines of code the same, perhaps it is because they are the *best* 30 lines of code for the problem. For example, there are many ways of finding all the primes between 1 and n, but the sieve of erathosthenes method is better than every other method that could possibly exist. Would the university complain if two people handed in this code:
(I apologize for any typos resulting from my typing this on the fly; you get my point, though.)
If so, they're stupid beyond belief. The point is, no conclusion can be reached unless we can read both peoples' source code, and everybody with something to lose prefers to cover up and pretend nothing has happened rather than to be open and admit they've done something wrong, so I don't think that will happen soon.
Secondly, how large is this program? If this is a 35 line program with 30 lines in common, that's one thing. If this is a parser/compiler/linker for a full-featured OO language (which is a project in many good CS classes), that's nothing and could occur completely by accident.
Slashdot Mirror
As I recall, the "discrete units" for Boltzman were atoms, which nobody believed in at the time. Quanta are units of energy.
If you want to view a hypercube, it's actually pretty easy. First of all, consider the corners of the unit hypercube: (0,0,0,0), (0,0,0,1), (0,0,1,0), (0,0,1,1), (0,1,0,0), (0,1,0,1), (0,1,1,0), (0,1,1,1), (1,0,0,0), (1,0,0,1), (1,0,1,0), (1,0,1,1), (1,1,0,0), (1,1,0,1), (1,1,1,0), and (1,1,1,1). Then in order to see all the possible projections, just rotate it around the w axis, project into three-space, then put the resulting 3d figure into OpenGL and rotate around the x, y, and z axes on screen.
Rotations are done in 4d much like in 3d -- A rotation can be expressed as a linear transformation, and rotations and reflections are uniquely represented as matrices for which transpose(A) = inverse(A), whether A is 2x2 or 7x7.
If there's enough demand, I suppose I could write such a program, but I'd have to learn OpenGL first.
First of all, if you have 30 lines of code the same, perhaps it is because they are the *best* 30 lines of code for the problem. For example, there are many ways of finding all the primes between 1 and n, but the sieve of erathosthenes method is better than every other method that could possibly exist. Would the university complain if two people handed in this code:
main() {
int table[N], i,j,s;
s = sqrt(N);
for(i = 2; i N; i++) table[i] = i;
for(i = 2; i N; i++) {
if(table[i]) {
printf("%d\n", i);
for(j = i*(i+1); j s; j += i) table[j]=0;
}
}
}
(I apologize for any typos resulting from my typing this on the fly; you get my point, though.)
If so, they're stupid beyond belief. The point is, no conclusion can be reached unless we can read both peoples' source code, and everybody with something to lose prefers to cover up and pretend nothing has happened rather than to be open and admit they've done something wrong, so I don't think that will happen soon.
Secondly, how large is this program? If this is a 35 line program with 30 lines in common, that's one thing. If this is a parser/compiler/linker for a full-featured OO language (which is a project in many good CS classes), that's nothing and could occur completely by accident.
Put a touch sensor with a big bumper pad, so if the cat jumps up, it hits the button, and then the lego thing hits something.