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mathslover
Has any one thought of finding the mid point of any two points ONLY with the help of compass ?
@Callisto @jim_thompson5910 @Hero @.Sam. @ghazi @campbell_st @kropot72 @Luigi0210 @Preetha @rajathsbhat
Check out here friends : http://gogeometry.com/circle/mascheroni_compass_1.htm Great !!!
I just posted so that more & more people can know about this
i never thought about that before, that is an awesome link im gonna check that out!
That's why I posted that here . :)
What about this? 1. Draw a circle with radius r centred at point A. 2. Draw a circle with the same radius r centred at point B. 3. Draw a horizontal line between A and B 4. Draw a line joining the intersection points of the two circles. 5. Is the intersection point of the horizontal and vertical line the mid-point of A and B?
Callisto you can not draw even a line
thats what i thought too @Callisto but you only have a compass in this example, not a straightedge
You are not allowed to draw a segment either by free hand or by a ruler or any thing.. You even can't join the the two points|dw:1361682511189:dw|
That's the main trick here
I asked my juniors and they came up with the same soln and some of them drew circles and circles and got some point which looks like a mid pt. but they were not able to *prove* that..
it is easy take the point A as the pivot and then draw circle take the point b and draw a circle the length of the radius should be adjusted so that the two circles intersect at just one point and that would be the midpoin.....but both radiuses should be equal ..........
@harsh314 that line of reasoning is right, although you are unable to do that with just 1 compass. you wont know the radii are equal unless their starting point and ending point are equal, which you don't intrinsically know
yes i do agree that i would not be able to know the exact point at first but by demarcation of points in the subsequent tries i would be able to get such a point..........the second thing i don't emphasize on the use of 2 compasses......it can be done with the help drawing with just single compass and shifting the pivot .............draw to circles intersecting a just 1 point and also having the equal radius and the centre of the 2 circles must be the 2 points given
the point im trying to make is it is impossible to know if the radii are equal. basically what you are suggesting is taking the limit as the radii approach an equal value however, you will never be able to know what this limit is, because you have no direct way of measuring it (with just a compass, that is)
i mean, sure, you might get really really really really really close to having them equal (and thus creating a midpoint) but the point of proofs isn't to get really really really really close but rather find equalities
see when you set you have drawn the 2 circles taking the given points as the origin and intersecting at just 1point you can measure the radii of one of the circle with the help of your compass by expanding one of its arm and keeping the other fix as pivot on the centre now fit it onto the second one .......its simple yaar........
Hey its simple.... checkout.. http://easycalculation.com/analytical/learn-midpoint.php
I learnt this two years back, I think.
Wait, I learnt something else.|dw:1361686704868:dw|
|dw:1361789886736:dw| place point of compass at one end, measure more than half of the distance and form an arc on above and below the line segment and similarly with the same width place needle of compass over another end and cut the two arcs that you have already formed , now join the intersection of arcs and you will get the mid point of the line or the perpendicular bisector , learned it in 6th grade :)
i think @ghazii approach is correct
you are not allowed to use a scale, i.e. draw lines! That is what the ques is all about!
yep @shubhamsrg , @ghazii you are not allowed to join any two points either by free hand or by using ruler or any other accessory.
interesting then :) let me think for a while