







Two circles 
20170813 

Ladines pose la question : Find the equation of the circle passing through points of intersections of circles x²+y²=4y and x²+y²=2x and the center is on line y=2 Penny Nom lui répond. 





The intersection of planes 
20040907 

Joshua pose la question : I was wondering about the intersection of planes. Can planes intersect? Penny Nom lui répond. 





The intersection of two graphs 
20040728 

JJ pose la question : Is there a way to find the intersections of these graphs algebraically?
x^2 + y = 4 & 2x  y = 1
I got (1.45, 1.9) and (3.45, 7.9) with a graphing calculator.
AND THESE...
y = 3.29x & y = 5.5(x^0.5)+ 10000
I got x at 3133 with a graphing calculator.
Penny Nom lui répond. 





Squares in a rectangle 
20031021 

Raj pose la question :
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? Chris Fisher lui répond. 





Diagonals in a polygon 
20020410 

Murray pose la question : If you have a regular polygon with n sides and you draw all (n3)n/2 diagonals how many intersection will they form with each other and how many sections will they devide the polygon into. Caude Tardif and Chris Fisher lui répond. 





If you conect all the vertices of a regular ngon... 
20020401 

Murray pose la question : If you conect all the vertices of a regular ngon with lines you will have (n3)(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. Claude Tardif lui répond. 





Dividing a Circle 
19990412 

Mike Kenedy pose la question : 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.
 4 into11
 5 into 16
 6 into 22
 7 into 29
 8 into 37
 etc...
I am stumped and cannot figure out the equation, though I'm sure it involves squares. Can you help? Penny Nom lui répond. 





How many intersections? 
19971008 

James pose la question : (a) A collection of eight points, no three collinear. If lines are drawn between each pair of these points, how many points of intersection would there be? (b) what would your answer have been in part (a) if there had been n points to start with? Chris Fisher lui répond. 

