# What is the minimum number of co-ordinates used to perfectly describe the shape,orientation and position of an n-dimensional object?

What is the minimum number of co-ordinates used to perfectly describe the shape,orientation and position of a n-dimensional object? How do I make an approach to this problem? I am confused with the shape and orientation. How many dimensions do we need to measure even common 3-d objects?

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if the shape is (piecewise) smooth, then countable infinity, I believe. – Yrogirg Aug 20 '12 at 13:36
Is this question intended as stated? Leaving out the description of the shape would render an answerable question: "What is the minimum number of parameters required to perfectly describe the position and orientation of an arbitrary object in n-dimensional space?" – Johannes Aug 20 '12 at 14:56
Notice that every object which is indeed describable will be describable on a one dimensional string. You can e.g. tape a video where you explain exactly how the object looks like and where the points are etc. and then take an Edding marker and paint that files data on a long thread, e.g. in Morse code. – NikolajK Aug 20 '12 at 15:22
If you remove shape, this has an answer--- it's N position variables plus N(N-1)/2 orientation variables. Why are you asking about shape? – Ron Maimon Aug 21 '12 at 3:36