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Algebra

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15 Mar 2008 13:24:43 IST

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7 lines are drawn in a plane, such that no two of them are parallel. Prove that, the angle between any two of them is atleast 26 degrees

edit: there is atleast one pair of lines such that the angle between them is more than 26 deg

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pardesi .svk

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15 Mar 2008 13:37:54 IST

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i think the question needs some rephrasing it shud actually be
7 lines are drawn in a plane, such that no two of them are parallel. Prove that, the angle between some two of them is atleast 26 degrees

because consider this situation two lines which intersect at 10 degrees(say) and now from a point P draw 5 lines concurrent at P whic intersect those two lines at various points

sandeep ramesh

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15 Mar 2008 13:38:11 IST

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maybe the method is pigeon hole but why is this system wrong?

radon

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15 Mar 2008 13:44:26 IST

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But sir i have drawn a figure in which angle between any two lines is coming less than 26 but then also no law of geometry is being violated ......in the figure assume that angle between any two lines is suppose 10 degrees than where is the fault??

Hari Shankar

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15 Mar 2008 13:45:53 IST

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sorry, i made 2 mistakes:

1. I should have phrased it as there is atleast one pair of lines such that the angle between them is more than 26 deg

2. I should have said, pros keep out!

Pigeonhole principle it is.

Hari Shankar

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15 Mar 2008 13:47:55 IST

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btw, now that i have your attention kvs and rohit, how about solving that upperbound problem.

Looks like I have to use a ventilator to keep it alive

pardesi .svk

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15 Mar 2008 13:52:41 IST

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yes i will try that ....

sandeep ramesh

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15 Mar 2008 13:56:00 IST

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pardesi same thoughts

sandeep ramesh

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15 Mar 2008 13:57:35 IST

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pigeon hole eh? Why in algebra? Ask to create a forum for combinatorics

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