Modelling in Mathematics
A model is basically a representation of something that is considered to be real.
Around us in everyday life there are always many examples of models. Some of these will include small versions of cars, buses, planes, boats and so forth and these are referred to as "model cars", "model buses", ...
There are other examples of models such as depictions of buildings, house plans, town and city design and many more instances of similar types of models.
When a person attempts to look like another person or when an item of clothing is worn by a person to show a particular style, a person may be called a 'model' or they may be said to be modelling.
In all cases, a model is simply a representation of an 'object'. In Mathematics the concept of modelling is extremely important because it will allow in most cases some form of diagram to be drawn so that a particular strategy can be more readily identified in order for a solution to be found to a particular problem.
Samples of Mathematical Models
With increased knowledge and understanding will come greater ability to use available resources to solve problems. Let us look at two very simple problems that can be solved in different ways. The method utilised will in general depend on the degree of knowledge and understanding. There is no right or wrong way but if appropriate skills are known then the resultant outcome can be found more easily.
The first model involves the use of Mathematics in the building and construction industry. Irrepesctive of what country or culture, the majority of people on the planet will have a structure or building in which they work or live. Beside the builders, it will happen regularly that maintenance or construction around a building will need to happen and this is best achieved if relevant skills are known. Of course, it is not essential to have the skills or knowledge but will make the processes needed much simpler.
The second model represents the speed of an aeroplane (airplane) during flight. This would seem to be quite difficult to determine the air speed of a plane while it is flying, especially if a person were not onboard the plane and if they didn't have any access to the instrumentation. Vehicles that travel on the Earth, such as cars, motorcycles, trucks and so forth can easily have their speed determined by the driver or by methods such as speed radar detection.
Obstacles with flight include such things as height, speed, accessibility and so on. It is possible to determine the speed of an airplane given that a person will have access to a small amount of basic measuring equipment for time and angles. It is necessary to have access to a reasonably clear and relatively flat area of land as well as knowing that the person can position themselves along the flight path.
The procedure for measuring the speed of any land based object such as speed of motor vehicles, speed of balls in sports such as golf, tennis, cricket, speed of athletes in running events and so forth are usually much easier because distances are more easily determined as is the timing which makes for easier calculations.
The third model uses circle geometry and the Earth to determine how quickly we are moving. Many people would assume that they are not moving or may indeed be stopped. This seems a logical assumption until we recognise that time of day (including night and day) require the Earth to be rotating relative to the Sun and Moon. When a person sleeps, they are stationary relative to the Earth's surface, but compared to their position on the planet they are actually moving quite quickly. The following model shows the speed that an object on the Earth's surface will be moving. Two positions are considered ... One is at the Equator and the other is at a latitude of 30 degrees North in New Orleans (USA). It will also be noted that the speed of rotation on the Earth's surface is influenced by the position on the planet.
Regardless of whether or not a Mathematical question relates to a real world situation, the use of a mathematical model or sketch will generally make the solution of problems easier to understand. It can be seen that Mathematics relies upon many different topics and concepts and the ability to be able to solve problems relies upon knowledge of each to make the process as simple and easy as possible.