Question

Has any one thought of finding the mid point of any two points ONLY with the help of compass ?

Answer 1

@Callisto @jim_thompson5910 @Hero @.Sam. @ghazi @campbell_st @kropot72 @Luigi0210 @Preetha @rajathsbhat

Answer 2

Check out here friends :
http://gogeometry.com/circle/mascheroni_compass_1.htm

Great !!!

Answer 3

I just posted so that more & more people can know about this

Answer 4

i never thought about that before, that is an awesome link im gonna check that out!

Answer 5

That's why I posted that here . :)

Answer 6

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?

Answer 7

Callisto you can not draw even a line

Answer 8

thats what i thought too @Callisto but you only have a compass in this example, not a straightedge

Answer 9

Oh... *facepalm*

Answer 10

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

Answer 11

That's the main trick here

Answer 12

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..

Answer 13

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 ..........

Answer 14

@Callisto is it o.k.

Answer 15

@mathslover

Answer 16

@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

Answer 17

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

Answer 18

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)

Answer 19

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

Answer 20

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........

Answer 21

Hey its simple....
checkout..
http://easycalculation.com/analytical/learn-midpoint.php

Answer 22

I learnt this two years back, I think.

Answer 23

Wait, I learnt something else.