Introduction
Dolbear's Law states the relationship between the air temperature and the rate at which Snowy Tree Crickets chirp.Â
CricketÂ Â |
A.E.Dolbear |
For many years people have recognized a relationship between the temperature and the rate at which crickets are chirping. The method of determining the temperature in degrees Fahrenheit is to count the number of chirps in a minute and divide by 4, and then add 40. In 1898, A. E. Dolbear noted that "crickets in a field [chirp] synchronously, keeping time as if led by the wand of a conductor. He appears to be the first person to write down a formula in a scientific publication, giving a linear relationship for the temperature based on the chirp rate of crickets. The mathematical formula that he gave is:
Equation of a line is given by the equation as
is known as slope intercept form of the line. The variable is the independent variable and is the dependent variable. is the slope and is the interceptThe cricket equation given above can be written
As written above, the independent variable is which is number of chirps per minute. The temperature,, is the dependent variable. The slope is
, and the intercept is 40.Equations are used in many areas to model the world around us. A biologist will use them to get an idea of how a population of animals might change over time. An economist or financial adviser will use them to predict the economy or the future profits of a company. An engineer will use them to work out the exact proportions of a building, like a bridge or a sky scraper, and how much and what kind of materials to use.
In short, equations are a fact of life for many people, and to be able to work with them you need to start with the simplest ones â€“ the linear equations.
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant time the first power of a variable. Such an equation is equivalent to equating a first-degree polynomial to zero. These equations are called "linear" because they represent straight lines in Cartesian coordinates.