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In atmospheric, earth, and planetary sciences, a scale height, usually denoted by the capital letter H, is a distance (vertical or radial) over which a physical quantity decreases by a factor of e (the base of natural logarithms, approximately 2.718).
A base-10 log scale is used for the Y-axis of the bottom left graph, and the Y-axis ranges from 0.1 to 1000. The top right graph uses a log-10 scale for just the X-axis, and the bottom right graph uses a log-10 scale for both the X axis and the Y-axis. Presentation of data on a logarithmic scale can be helpful when the data:
A height function is a function that quantifies the complexity of mathematical objects. In Diophantine geometry , height functions quantify the size of solutions to Diophantine equations and are typically functions from a set of points on algebraic varieties (or a set of algebraic varieties) to the real numbers .
Order of magnitude is a concept used to discuss the scale of numbers in relation to one another. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are within about a factor of 10 of each other. [1] For example, 1 and 1.02 are within an order of magnitude.
A graphical or bar scale. A map would also usually give its scale numerically ("1:50,000", for instance, means that one cm on the map represents 50,000cm of real space, which is 500 meters) A bar scale with the nominal scale expressed as "1:600 000", meaning 1 cm on the map corresponds to 600,000 cm=6 km on the ground.
Here two scales represent known values and the third is the scale where the result is read off. The simplest such equation is u 1 + u 2 + u 3 = 0 for the three variables u 1 , u 2 and u 3 . An example of this type of nomogram is shown on the right, annotated with terms used to describe the parts of a nomogram.
For example, aligning the rightmost 1 on the C scale with 2 on the LL2 scale, 3 on the C scale lines up with 8 on the LL3 scale. To extract a cube root using a slide rule with only C/D and A/B scales, align 1 on the B cursor with the base number on the A scale (taking care as always to distinguish between the lower and upper halves of the A scale).
The atomic length scale is ℓ a ~ 10 −10 m and is given by the size of hydrogen atom (i.e., the Bohr radius, approximately 53 pm).; The length scale for the strong interactions (or the one derived from QCD through dimensional transmutation) is around ℓ s ~ 10 −15 m, and the "radii" of strongly interacting particles (such as the proton) are roughly comparable.