Just a simple demo. The goal was to minimize the upper bound of needed checks along the tic-tac-toe gameboard.

Brief Explanation

The result was achieved by assuming that the elements of the 3x3 matrix could be mapped to the [1,9] interval in N by the bijective application (from [1,3]x[1,3] to [1,9]):

f(i,j)=i+3(j-1);

Now let n=f(i,j), for each i,j in [1,3].

• If n is 5, there are 4 checks needed (the middle row, the middle column, both diagonals);
• If n is any other odd number (1,3,7,9), it stays in the corner, so ther are only 3 checks needed (a row, a column, a diagonal);
• For even numbers the upper bound decreases to 2 (a row and a column only).

So the number of needed controls stays between 2 and 4, in a maximum range of 8 (3 rows, 3 columns, 2 diagonals) - it would be nice if tic-tac-toe was not a complete game in which neither player can win...:P

Here it goes the code and the link to the main article.

Su suggerimento di Andrea, ho scritto due righe che permettessero di disegnare curve piane parametriche, e questi sono i risultati =P

Appena ho un momento preparo un'applet in modo che tutti possiate vedere come dispongo inutilmente del mio tempo ^____^

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After a brief talk with Andrea, I've written a couple of code lines able to draw plain parametric curves, and these are the results.

As soon as I get a minute, I will export an applet so you can all see how well do I waste my time :P

Here there are some stuff I made as a contest for students of our java course: