Question

It is possible to draw $n$ circles so that each circle intersects each other circle exactly twice (but impossible for any two circles to intersect three times.) For example, here are sets of two, three, and four circles where each circle intersects each other circle exactly twice: Write a recurrence relation describing the maximum number of intersection points on $n$ circles. (Hint: if you have 7 circles, you can add an eighth and it will add two points of intersection with each of the 7 existing circles.) Write a closed-form formula for the number of intersection points on $n$ circles, and write a proof that it is correct. (Hint: the closed-form formula will be quadratic.)

          It is possible to draw $n$ circles so that each circle intersects each other circle exactly twice (but impossible for any two circles to intersect three times.) For example, here are sets of two, three, and four circles where each circle intersects each other circle exactly twice:

Write a recurrence relation describing the maximum number of intersection points on $n$ circles.
(Hint: if you have 7 circles, you can add an eighth and it will add two points of intersection with each of the 7 existing circles.)

Write a closed-form formula for the number of intersection points on $n$ circles, and write a proof that it is correct. (Hint: the closed-form formula will be quadratic.)

It is possible to draw n circles so that each circle intersects each other circle exactly twice (but impossible for any two circles to intersect three times.) For example, here are sets of two, three, and four circles where each circle intersects each other circle exactly twice:

Write a recurrence relation describing the maximum number of intersection points on n circles.
(Hint: if you have 7 circles, you can add an eighth and it will add two points of intersection with each of the 7 existing circles.)

Write a closed-form formula for the number of intersection points on n circles, and write a proof that it is correct. (Hint: the closed-form formula will be quadratic.)

Added by Max P.

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