I have been reading about different map projections and kind of understand where the problem lies. And also, most of the problem was that the old cartographers did not have any other tool other than their pencil and paper.

Is it possible to just draw out every kilometer, every curve on an actual scale on a very big piece of paper with a scale of say, 1 cm ~ 1 Km? I know we will need a very big paper, but then if we use a computer instead of a paper, then scaling down and up would be simpler right?

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    You question is not entirely clear. No matter how big the piece of paper, you are still projecting from 3D to 2D with all the distortion this entails, if that is what you are asking. – John Powell Aug 8 '15 at 4:16
  • It is possible - its usually called a globe. Even at 1:100000, you need to deal with curvature. – BradHards Aug 8 '15 at 4:32
  • The recent thread at gis.stackexchange.com/questions/151909 addresses this question directly: it discusses how much error is forced on us in making a planar map of the earth's surface, whether we are using pencil and paper, an abacus, or an electronic computer to do calculations. – whuber Aug 8 '15 at 16:23

I don't think you get what the problem is at all.

The problem is that the earth is curved; It isn't an sphere; It's not an oblate spheroid, it an even more complex shape, called the Geoid.

And whenever you try to go from this Curved shape to a flat plane (like the paper you are talking about) you will have some or the other distortions.

That is why surveyors usually will go with a two dimensional coordinate system, and then plot or map everything in that coordinate system.

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    Although this is all perfectly correct, the situation may be a little subtler than you suggest. For instance, if part of the earth's surface were a cylinder or even a cone, then it would be manifestly "curved"--but what aksappy asks for would be possible to do in that case. – whuber Aug 8 '15 at 16:21

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