How many pieces can you get?

[bigpooch]

I assume you mean straight lines. Then the maximum number
of pieces is just [n(n+1)/2] +1. After n lines divide the
circle into the maximum number of pieces, the next line can
cross through all n of these lines and then divide through
(n+1) regions, so there are (n+1) more regions; then, by
induction, the result follows.

Of course, this also applies not only to lines and a circle,
but also to planes and a sphere.

[jman3232]

if you have 3 lines you can make 8 pieces...

[Winenose]

[ QUOTE ]
if you have 3 lines you can make 8 pieces...

[/ QUOTE ]

Really?

[BouncinRound]

[ QUOTE ]
I assume you mean straight lines. Then the maximum number
of pieces is just [n(n+1)/2] +1. After n lines divide the
circle into the maximum number of pieces, the next line can
cross through all n of these lines and then divide through
(n+1) regions, so there are (n+1) more regions; then, by
induction, the result follows.

Of course, this also applies not only to lines and a circle,
but also to planes and a sphere.

[/ QUOTE ]

ya to the best of my knowledge 3 cuts = 7 pieces and this guy has the right generalization, well done chap

[Nicholasp27]

[ QUOTE ]
if you have 3 lines you can make 8 pieces...

[/ QUOTE ]

this is a circle, not a cake

[thylacine]

[ QUOTE ]
[ QUOTE ]
if you have 3 lines you can make 8 pieces...

[/ QUOTE ]

this is a circle, not a cake

[/ QUOTE ]

and even if it were, you would need an infinite number of lines to cut it into more than one piece. [img]/images/graemlins/grin.gif[/img]

[bigpooch]

Actually, about planes and the sphere: the maximum number
of pieces you can cut the sphere by n planes is
C(n+1,3)+n+1 for n>=0.

[jstnrgrs]

[ QUOTE ]
[ QUOTE ]
if you have 3 lines you can make 8 pieces...

[/ QUOTE ]

Really?

[/ QUOTE ]

A sphere can be cut into 8 pieces with 3 plains.

[BouncinRound]

ya perhaps a sphere can, but this post was about cutting a circle though (a 2d object). like a pizza without cutting off the cheese or something wacky. anyways, big pooch was on the money last time I checked