Introduction to dimensioning

[jehovajah]

http://m.youtube.com/watch?v=gB9n2gHsHN4

Trying to motivate a measure of dimension through exponents. Why exponents?

When we dimension a real object we measure in one orientation, rotate orthogonally and measur and finally measure mutually orthogonally. Exponents typically count this kind of rotating measurement practice.

So if I measure a line without any rotation dimension is exponentially 1
 If I rotate and measure that line orthogonal to the first  the exponent is 2 . Why ? Because we want to count the product factorisation . Finally factoring a solid cube counts3 orthogonal factors.

So what if the rotation is not orthogonal?  This is where we shift to the logarithmic measure as a generalisation of rotating measures. If I rotated the line by 45° the area of the parallelogram is half the area of the square. What logarithm gives that value? That is used to express the dimension process.

It indicates that the measurement process is not orthogonal , it is how roughly the process is done!

The box counting method counts this variation in area /exponent 2 and so how rough the process is. For higher dimensions balls or spheres are used . These measure variation from the 3 exponent. Higher exponents may be considered but a better grasp of the measuring process is needed for it to make sense.