What is the maximum number of times that six circles of the same size could intersect? For example, draw two circles that are the same size. What's the greatest number of times they could intersect? Now what if you add another circle, and another, etc.? (Circles that lie on top of each other do not intersect - they're simply the same circle, so "infinity" isn't a valid answer.)
What if you've got 10 circles, what if you have any number of circles?
Make sure your explanation is thorough and would explain to another student how to solve the problem. You may use a picture to support your solution - however a picture without an explaination about how it supports your solution will not be awarded any points.
N.H.
ReplyDeleteI found that the maximum number of times that 6 circles can intersect is 10. This can be found by using the equation 2x-2 to find the number of times that a circle can intersect, the number of circles being x.
SD
ReplyDeleteI found a relationship between circles of the same size after finding how many intersections per circle to circles. This means that for 6 circles there will be 10 inter sections per circle, shown in the picture and the chart. The equation is y=2x-2, meaning that ten circles will give you 18 intersections per circle.
The total number of intersections that 6 circles that are the same size can make is 20 pionts. I found it by using paint to place all six circles together and counting the number of intersections. The equation for the number of circles and intersections is x2-x=y. x=# of circles.y= # of intersections.
ReplyDeleteMikey Giambra
POW
Oct. 15
A.A.M.
ReplyDeleteX^2-x
If you were to have 10 circles you would plug that in for x. So your equation would be 10(10)-10
100-10=90
JHS
ReplyDeleteSIMPLY CIRCLES POW
The equation Joseph and I came up with to get the most number of intersections between a number of circles is X to the power of 2-X= # of intersections.
We tested it on a few numbers X could be to see if it was accurate.
X=2:
2 times two is four. Four subtract two is two. The number of intersections between two circles is also two.
X=4
4 times 4 is 16. 16 subtract 4 is 12. There are 12 intersections between 4 circles.
For the problem there are six circles. Therefore, X=6
6 times 6 is 36. 36 subtract 6 is 30.
The answer to the problem is 30 intersections.
S.S.
ReplyDeleteWhen thinking about this problem, I decided to start of easy and look at the small factors. Two circles of equal size can only intersect each other twice. Ring one intersects rings 2, 3, 4, 5, and 6 two times each so that’s ten. That means for each of the circles there will be 10 intersections. The equation that you could use, is x2-x=y. X would represent the number of circles and the Y would represent the number of intersections.
First I looked at the intersection of two or three circles to figure out the effects of adding another circle. Then I found an equation that worked:(x*x)-x
ReplyDelete6 Circles=30 Intersections
10=90 Intersections
GW
ReplyDeleteSix Circles
The maximum number of intersections 6 circles can have is 30.
To get this answer I first started with your suggestion of first finding the intersections of 2 circles. The number of intersections 2 circles can have is 2. I continue with this method then came up with the equation I = x(x-1). To see if my equation worked I used it with 3.
I= 3(3-1)
I=9-3
I= 6
To double check me answers I used circles and counted 6 intersections. I also tried it with 4 to make sure the equation didn’t just work with 3.
I=4(4-1)
I=16-4
I=12
To double check I again used circles. Then I used my equation with 6 and got 30.
Then I used it with 10 and got 90.