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mathslover

  • one year ago

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

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  1. mathslover
    • one year ago
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    @Callisto @jim_thompson5910 @Hero @.Sam. @ghazi @campbell_st @kropot72 @Luigi0210 @Preetha @rajathsbhat

  2. mathslover
    • one year ago
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    Check out here friends : http://gogeometry.com/circle/mascheroni_compass_1.htm Great !!!

  3. mathslover
    • one year ago
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    I just posted so that more & more people can know about this

  4. funinabox
    • one year ago
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    i never thought about that before, that is an awesome link im gonna check that out!

  5. mathslover
    • one year ago
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    That's why I posted that here . :)

  6. Callisto
    • one year ago
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    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?

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  7. mathslover
    • one year ago
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    Callisto you can not draw even a line

  8. funinabox
    • one year ago
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    thats what i thought too @Callisto but you only have a compass in this example, not a straightedge

  9. Callisto
    • one year ago
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    Oh... *facepalm*

  10. mathslover
    • one year ago
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    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|

  11. mathslover
    • one year ago
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    That's the main trick here

  12. mathslover
    • one year ago
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    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..

  13. geerky42
    • one year ago
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  14. harsh314
    • one year ago
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    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 ..........

  15. harsh314
    • one year ago
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    @Callisto is it o.k.

  16. harsh314
    • one year ago
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    @mathslover

  17. funinabox
    • one year ago
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    @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

  18. harsh314
    • one year ago
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    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

  19. funinabox
    • one year ago
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    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)

  20. funinabox
    • one year ago
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    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

  21. harsh314
    • one year ago
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    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........

  22. Koikkara
    • one year ago
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    Hey its simple.... checkout.. http://easycalculation.com/analytical/learn-midpoint.php

  23. ParthKohli
    • one year ago
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    I learnt this two years back, I think.

  24. ParthKohli
    • one year ago
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    Wait, I learnt something else.|dw:1361686704868:dw|

  25. shubhamsrg
    • one year ago
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    WAOW ! :O (Y)

  26. ghazii
    • one year ago
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    |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 :)

  27. thinkpot
    • one year ago
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    i think @ghazii approach is correct

  28. shubhamsrg
    • one year ago
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    you are not allowed to use a scale, i.e. draw lines! That is what the ques is all about!

  29. mathslover
    • one year ago
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    yep @shubhamsrg , @ghazii you are not allowed to join any two points either by free hand or by using ruler or any other accessory.

  30. ghazii
    • one year ago
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    interesting then :) let me think for a while

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