rate

=Rate= toc Rate is a comparison of two quantities. It is significant to the study of scale, since the transformation that one implements to generate a series of scales often has a rate, or an aspect of transformation unit per time unit. =Rate as Source of the Natural Logarithm= Rate, for example, is the key to the emergence of the natural logarithm e; e is the ratio of scale B to scale A when the ratio of B to A is identical to the additive rate of growth between the two scales.

=Rate as Source of a Distortion in Zoomed Superscale Surveys= Rate is also a problem as rate does not always scale in the same was as the physical quantity under consideration. For example, in the Eames's film Powers of Ten the rate of transition in the sequence from one meter to ten meters is one meter per second, a velocity that is permitted; but the transition from 10^20 to 10^21 occurs at a velocity that is physically impossible according to the standard model of physics and its Einsteinian constraints. This does not mean the zoom at this rate should not occur: it just means that this distortion needs to made overt and clear to the viewer of the superscale survey.

=Examples of Rates= The following examples are from "Scaling the Natural World Using Dimensional Analysis Curriculum" by Kass.

Rate Examples
A rate is a comparison of two different quantities. A rate tells us the quantity of one thing per quantity of a second thing. For example, 55 miles per hour, 25 students per teacher, $5 for 3 gallons of gas, 96 cents for 3 candy bars are all rates. These rates can each be written as fractions:.
 * 55 miles 25 students $5 96 cents
 * 1 hour 1 teacher 3 gallons 3 candy bars

Reciprocal rate examples
The reciprocal rate is a rate that is reversed or turned around. For example, the reciprocal rate of
 * 96 cents is 3 candy bars
 * 3 candy bars 96 cents

Conversion Rate Examples
A conversion rate is a special rate where the quantities are equal, but the units of measurement are different. In other words, the two quantities are equal and each quantity can be changed into the other quantity in the rate. Examples are
 * 12 inches 1 yard 5 fingers
 * 1 foot 3 feet I hand

=Links= Zoomed surveys: include component="pageList" hideInternal="true" tag="zoom" limit="100"