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## #1 2006-02-25 13:43:58

razor
Member
Registered: 2006-02-24
Posts: 6

### Pentagram

we have a pentagram.How we can with two lines create nine not covertly triangles?

Last edited by razor (2006-02-25 13:47:57)

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## #2 2006-02-25 17:52:53

MathsIsFun
Registered: 2005-01-21
Posts: 7,660

### Re: Pentagram

I am not sure what "not covertly" means, but my biggest problem is: how is it possible to get nine triangles with only two lines? Best I can do is 5. I can get 9 with three lines!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #3 2006-03-01 03:49:49

ashwil
Member
Registered: 2006-02-27
Posts: 121

### Re: Pentagram

Trick question!

A pentagram already has 5 triangles within it. Joining any two pairs of alternate nodes on the inner pentagon will create 3 new triangles within the central pentagon and one more with one of the extarnal points. Total 9.

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## #4 2006-03-01 03:53:24

ashwil
Member
Registered: 2006-02-27
Posts: 121

### Re: Pentagram

Scrub that last post! That method actually creates 12 triangles!!

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## #5 2006-03-01 04:24:37

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Pentagram

Here's what I get:

Last edited by krassi_holmz (2006-03-01 04:25:35)

IPBLE:  Increasing Performance By Lowering Expectations.

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## #6 2006-03-01 08:38:17

MathsIsFun
Registered: 2005-01-21
Posts: 7,660

### Re: Pentagram

Pentagram ... I should read more careully!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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## #7 2006-03-01 10:05:42

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Pentagram

I agree with what krazzi has.

Why did the vector cross the road?
It wanted to be normal.

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## #8 2006-03-01 17:34:04

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

### Re: Pentagram

Now the other main question: are there another combinations?
For which numbers it is possible to cut the pentagram(or we may start with circle) with k lines?
Hm... Interesting.

IPBLE:  Increasing Performance By Lowering Expectations.

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