Scale is an important concept to understand for many reasons. Using scale makes it easy to work with measurements and lengths. For example, a cartographer uses a scale of one inch to a foot when making maps.
In music, a scale is an ordered group of musical notes that has a consistent interval pattern across its octave. A particular scale is usually identified by its tonic and adopted interval pattern.
Definition
A regular gradation in steps or degrees; a graduated series. For example, the scale of a mountain; the musical scale (do-re-mi-fa-so-la-ti); or a map scale (1:50).
Mapping involves flattening the curved Earth into a two-dimensional visual representation called a map. This creates noticeable distortions that vary across the map, and the scale at which the distortion is measured depends on the type of map projection.
Conformal mapping systems preserve angles and have isotropic scale factors. Other map projections, like the Mercator projection, have scale factors that change with latitude. This causes distorted geometry in regions at high latitudes and true geometry in low latitudes. A map scale can be determined for each location by dividing the total map distance by the distance on the ground at that latitude.
Meaning
The term scale is used in many ways when talking about geographic phenomena and the way they are represented on maps. It is also a verb, meaning to “scale” something up or down. It is important to understand the different meanings of the word so you can use it correctly and avoid confusion.
For example, the equator is at a scale of 1:k (where k is the inverse of the radius of curvature of the Earth), so if you transfer a separation on the equator to a bar scale it will show the correct distance between points. However, if you use a Gall-Peters projection on a meridian it will be at a scale of 1:k while the parallel is much higher, and you will have a distortion.
This is because the projection has changed the point scale as well as the parallel and meridian scales. Scale is a property of both the point scale and the map projection, and the variation of these properties over the surface of the sphere is what gives rise to the distortions seen on maps.
Examples
For example, a questionnaire might ask respondents to rank their responses to questions such as “How important is it for you to have a scale that measures in ounces?” or “How important is it for you to be able to use the scale without having to turn on a light?”
These are ordinal scale variables, where you can group values together into groups and name those groups. For these types of variables, it doesn’t make sense to average the different possibilities because they aren’t ranked in a meaningful way. The classic example of this is eye color, where it doesn’t make sense to say that one person’s eyes are blue or green or brown and then compare those with someone else’s.
On the other hand, interval scales have both identity and magnitude. They have a standardized order (such as 1 yard in a blueprint equals 190 yards) and the difference between each value is the same amount, so adding or subtracting is meaningful.
Applications
Scalable applications are crucial for businesses that need to adapt quickly to user demand. When an application can handle growth, users have a smooth experience and are more likely to return to the business. This can improve sales and increase customer retention.
Successful app scaling requires technical expertise and strategic planning. It involves many elements including database scalability, modern architecture, loading speed, and servers. It is also important to use caches and reduce database queries to keep up with traffic demands.
Scale is a mathematical concept used by architects, engineers, and students to draw maps and objects that are too large or small for accurate measurements. Students also use scale when solving problems like Similar Triangles and Ratio and Proportion questions. Learn more about scale by practicing with Vedantu’s free math practice.