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If 8 points in a plane are chosen to lie on or inside a circle of diameter 2cm then show
that the distance between some two points will be less than 1cm.
how should i proceed for this?
 one year ago
 one year ago
If 8 points in a plane are chosen to lie on or inside a circle of diameter 2cm then show that the distance between some two points will be less than 1cm. how should i proceed for this?
 one year ago
 one year ago

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shubhamsrgBest ResponseYou've already chosen the best response.0
will this help ? suppose a pointP at random is chosen at a distance <1 from O taking P as center and constructing a circle of radius 1, shaded reigon is the common region ,,as P gets closer to O,,space in which any other point can lie becomes lesser.. but how do i prove whole cirlce gets shaded after max 7 points ?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
dw:1344942451700:dw
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.1
hmm is there a definition for the points? what if all the eight points are on the circle and spaced closely.
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
well we have to prove there'll be min 2 of those 8 points which will have separation less than 1 cm..
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.1
oh i read the question wrong, sorry. i will try it again.
 one year ago

Ishaan94Best ResponseYou've already chosen the best response.1
Area of the circle must be \(\pi\). Each point could be imagined as a circle of area \(\pi/4\), maybe?
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
i dont get it?? come again..
 one year ago

mykoBest ResponseYou've already chosen the best response.2
dw:1344946376091:dw like you see there are maximum 7 points with distance >=1. If I put one more point it's distance with some point will be less than 1
 one year ago

shubhamsrgBest ResponseYou've already chosen the best response.0
cool.. maybe this is satisfactory enough!! thanks..
 one year ago
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