Draw a rectangle with sides of 3 and 4. Divide the sides into 3 and 4 equal parts respectively. Draw squares joining the points on the sides of the rectangle. You will have 12 small squares inside the 3 x 4 rectangle.
If you draw a diagonal of the rectangle, it will intersect 6 of the the 12 smaller squares.
Similarly, if you have a 4 x 10 rectangle, the diagonal would intersect 12 of the 40 squares inside the rectangle.
Is there an algebric equation that determines the number of squares that will be intersected by the diagonal of a rectangle?
From Murray: If you have a regular polygon with n sides and you draw all (n-3)n/2 diagonals how many intersection will they form with each other and how many sections will they devide the polygon into. Answered by Caude Tardif and Chris Fisher.
From Murray: If you conect all the vertices of a regular n-gon with lines you will have (n-3)(n/2) lines inside the polygon. I want to find out how many sections these lines divide the polygon into and how many intersections they have with each other. Answered by Claude Tardif.
From Mike Kenedy: I am having trouble with a homework question for bonus marks. A Circle is continually divided by lines that do not intersect the center so that they produce the most pieces of circle. For example
1 line divides the circle into 2.
2 into 4.
3, however into 7.
5 into 16
6 into 22
7 into 29
8 into 37
I am stumped and cannot figure out the equation, though I'm sure it involves squares. Can you help? Answered by Penny Nom.