THE DEFINATION:
SCALE.
The scale of a map is the ratio of a single unit of distance on the map to the equivalent distance on the ground. The scale can be expressed in four ways: as a ratio, a fraction, in words and as a graphical (bar) scale.
A scale expressed as a ratio of say 1:25,000 means that one unit on the map represents 25,000 units on the ground, ie 1 millimetre represents 25,000 mm, expressed better as 25 metres.
The statement 'one millimetre represents 25 metres' is an expression of scale in words.
Scale expressed as a fraction, 1/25,000, means that any distance on the map is 1/25,000 th the distance on the ground. It expresses the amount of reduction of distances used to represent detail on the map. The 25,000 value is called the scale denominator.
Due to showing the curved surface of the earth on a flat map surface, the scale varies from place to place. Thus a representative fraction is stated for scale which is correct at the centre of the map and which varies elsewhere. While called representative fraction, it really is the representative ratio.
A scale expressed as a ratio of say 1:25,000 means that one unit on the map represents 25,000 units on the ground, ie 1 millimetre represents 25,000 mm, expressed better as 25 metres.
The statement 'one millimetre represents 25 metres' is an expression of scale in words.
Scale expressed as a fraction, 1/25,000, means that any distance on the map is 1/25,000 th the distance on the ground. It expresses the amount of reduction of distances used to represent detail on the map. The 25,000 value is called the scale denominator.
Due to showing the curved surface of the earth on a flat map surface, the scale varies from place to place. Thus a representative fraction is stated for scale which is correct at the centre of the map and which varies elsewhere. While called representative fraction, it really is the representative ratio.
SCALE (RATIO)
The concept of scale is applicable if a system is represented proportionally by another system. For example, for a scale model of an object, the ratio of corresponding lengths is a dimensionless scale, e.g. 1:25; this scale is larger than 1:50.
In the general case of a differentiable bijection, the concept of scale can, to some extent, still be used, but it may depend on location and direction. It can be described by the Jacobian matrix. The modulus of the matrix times a unit vector is the scale in that direction. The non-linear case applies for example if a curved surface like part of the Earth's surface is mapped to a plane, see map projection.
In the case of an affine transformation the scale does not depend on location but it depends in general on direction. If the affine transformation can be decomposed into isometries and a transformation given by a diagonal matrix, we have directionally differential scaling and the diagonal elements (the eigenvalues) are the scale factors in two or three perpendicular directions. For example, on some profile maps horizontal and vertical scale are different; in particular elevation may be shown in a larger scale than horizontal distance.
In the case of directional scaling (in one direction only) there is just one scale factor for one direction.
The case of uniform scaling corresponds to a geometric similarity. There is just one scale throughout.
In the case of an isometry the scale is 1:1.
In the general case of a differentiable bijection, the concept of scale can, to some extent, still be used, but it may depend on location and direction. It can be described by the Jacobian matrix. The modulus of the matrix times a unit vector is the scale in that direction. The non-linear case applies for example if a curved surface like part of the Earth's surface is mapped to a plane, see map projection.
In the case of an affine transformation the scale does not depend on location but it depends in general on direction. If the affine transformation can be decomposed into isometries and a transformation given by a diagonal matrix, we have directionally differential scaling and the diagonal elements (the eigenvalues) are the scale factors in two or three perpendicular directions. For example, on some profile maps horizontal and vertical scale are different; in particular elevation may be shown in a larger scale than horizontal distance.
In the case of directional scaling (in one direction only) there is just one scale factor for one direction.
The case of uniform scaling corresponds to a geometric similarity. There is just one scale throughout.
In the case of an isometry the scale is 1:1.
NANOSCALE
Although a metre is defined by the International Standards Organization as `the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second' and a nanometre is by definition 10- 9 of a metre, this does not help scientists to communicate the nanoscale to non-scientists. It is in human nature to relate sizes by reference to everyday objects, and the commonest definition of nanotechnology is in relation to the width of a human hair.
Unfortunately, human hairs are highly variable, ranging from tens to hundreds of microns in diameter (10-6 of a metre), depending on the colour, type and the part of the body from which they are taken, so what is needed is a standard to which we can relate the nanoscale. Rather than asking anyone to imagine a millionth or a billionth of something, which few sane people can accomplish with ease, relating nanotechnology to atoms often makes the nanometre easier to imagine. While few non-scientists have a clear idea of how large an atom is, defining a nanometre as the size of 10 hydrogen, or 5 silicon atoms in a line is within the power of the human mind to grasp. The exact size of the atoms is less important than communicating the fact that nanotechnology is dealing with the smallest parts of matter that we can manipulate.
Unfortunately, human hairs are highly variable, ranging from tens to hundreds of microns in diameter (10-6 of a metre), depending on the colour, type and the part of the body from which they are taken, so what is needed is a standard to which we can relate the nanoscale. Rather than asking anyone to imagine a millionth or a billionth of something, which few sane people can accomplish with ease, relating nanotechnology to atoms often makes the nanometre easier to imagine. While few non-scientists have a clear idea of how large an atom is, defining a nanometre as the size of 10 hydrogen, or 5 silicon atoms in a line is within the power of the human mind to grasp. The exact size of the atoms is less important than communicating the fact that nanotechnology is dealing with the smallest parts of matter that we can manipulate.
CELEST SCALE
The defination of celest scale is it not related with nanoscale.
The mean this scale is getting bigger.
EXTREME SCALE
Getting bigger then ever. The saize is more bigger the celest meter.
This scale give more detailing on an object.
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