Cutting a Circle

Algebra Level 3

What is the minimum number of straight cuts required to divide a circle into 2017 pieces?


The answer is 63.

Miles Koumouris by Miles Koumouris , 20, Australia

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1 solution

Tom Engelsman
Sep 28, 2017

For any circle, the number of straight cuts needed to divide it into x x pieces is computed per:

N = 1 2 ⋅ ( x 2 + x + 2 ) N = \frac{1}{2} \cdot (x^2 + x + 2) .

Since we desire N = 2017 N = 2017 pieces, we have:

2017 = 1 2 ⋅ ( x 2 + x + 2 ) ⇒ x 2 + x + 2 = 4034 ⇒ x 2 + x − 4032 = 0 ⇒ ( x + 64 ) ( x − 63 ) = 0 2017 = \frac{1}{2} \cdot ( x^2 + x + 2) \Rightarrow x^2 + x+ 2 = 4034 \Rightarrow x^2 + x - 4032 = 0 \Rightarrow (x+64)(x-63) = 0

We only require the positive root, hence x = 63 \boxed{x = 63} cuts.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

I think you have the variables in the first equation mixed up. Avoid letting your notation do double duty, even with capital and lowe case.

Calvin Lin Staff - 3 years, 8 months ago

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