Graph
A graph is a visual representation that illustrates mathematical information and relationships between two or more data sets. Utilizing symbols such as lines, dots, and bars, graphs allow for complex data to be presented in a clear and accessible manner. The history of graphing can be traced back to ancient civilizations, with early applications including genealogical family trees and recreational geometric games. The systematic use of graphs began in the 1600s, gaining traction in the 19th century through the work of figures like William Playfair, who pioneered modern graphing techniques, creating bar charts and pie charts to represent statistical information.
Graphs are essential tools in various fields, enabling users to convey relationships between measurable variables, such as speed, time, or money. Common types of graphs include line graphs, which illustrate changes over time; bar graphs, which compare values across categories; and pie charts, which depict parts of a whole. Each graph type serves unique purposes, and while their structures may vary, they typically include necessary components like titles, axes, scales, and symbols for clarity. Overall, graphs play a crucial role in data analysis and communication, facilitating understanding in diverse contexts.
Graph
A graph is a diagram that visually illustrates mathematical information. Graphs generally show relationships or other connections between two or more sets of data. This data is often represented on a graph using lines, dots, bars, segments of circles, or other visual symbols. The symbols will often form a pattern that shows how the sets of data relate mathematically. Mathematicians usually create graphs to quickly and easily present information that is too lengthy or complex to efficiently describe in words and create a striking and easily accessible picture of data relationships.
The basic idea of using graphics to represent mathematical concepts may be traced back to ancient times. It was not until the 1600s, however, that mathematicians began using graphing methods regularly. Graphs became common in many fields starting with the work of Scottish engineer William Playfair around 1800, and today they may be seen in countless contexts around the world. In modern times, people can select from a variety of graph types to best suit the data being analyzed.
Brief History
The idea of connecting mathematical concepts and drawings developed in the ancient world. At first, the main motivations were mostly recreational. People in ancient Egypt and Rome enjoyed games set on geometric game boards that required some mathematical skills and strategies.
An even more direct link to modern graphs was the "family tree." The concept of mapping lists of names and relationships on a visual "graph" likely originated in ancient Rome. There, many noble families used these representations to celebrate their genealogies. Although many early family trees were styled to resemble literal trees, later works most often featured plainer geometric forms similar to those of modern graphs.
Some mathematicians created simple graphs and charts in the coming centuries, but only in the seventeenth century did the practice become slightly more common. German philosopher and mathematician Gottfried Wilhelm Leibniz created theories based on the idea of representing mathematical concepts visually. In 1736, Swiss mathematician Leonhard Euler notably used a graphical approach to resolve a complex mathematical riddle called the Königsberg Bridge Problem.
Modern forms of graphs became widespread around the nineteenth century. The main pioneer of graphing during that time was Scottish engineer William Playfair. In his social, architectural, and geographic studies, he devised ways to represent complicated mathematical relationships using visual displays. For example, he created a diagram of divided circles to represent population and economic statistics, which established the prototype for modern pie charts.
Playfair also did much to develop and popularize the use of bar charts and graphs, in which the lengths of various bars represent mathematical quantities to be examined and compared. (Playfair was not likely the true inventor of the bar chart, though; during the fourteenth century, French philosopher Nicole Oresme used such graphing methods to explain his theories of velocity.)
In the coming generations, more mathematicians, scientists, and engineers began using various methods to adapt mathematical figures into visual displays. In the twentieth century, these methods are standard practice in countless occupations around the world.
Overview
Mathematicians, scientists, and other people who use graphs can choose from a wide variety of graph types. Each type differs somewhat and offers specific advantages for particular research and presentation goals, but all graphs have some similarities. The first is that they should show relationships between variables. These variables may include almost any measurable value, such as speed, time, money, or mass. If no relationship exists, the graph will likely be ineffective.
All graphs need special parts to signify and identify the necessary data. Although each graph type has a unique structure, most graphs need a title or a caption to explain their intended purpose. Many graphs need axes, which are vertical and horizontal boundaries for the graph, usually described as the x-axis and y-axis. The axes should have scales, which identify the system and range of measurement being used. For example, an axis measuring weight should have a scale in pounds, ounces, grams, or another similar system.
A data item on a graph should be represented with a simple symbol, such as a dot, a line, or a segment of a circle. The symbol should be identified so viewers can understand its meaning and significance. Symbols may be identified in words on the graph or in a legend, a box on the side of a graph that lists and identifies the symbols being used.
Many kinds of graphs are used for various purposes. One of the simplest and most common is the line graph, which uses an x-axis and y-axis to plot information about a mathematical change in a variable. For example, line graphs can be used to plot changes in temperature over several days or the amount of fuel left in a car over miles. A line graph produces a visual display in the form of one or more lines. The shape, angle, and direction of each line can be interpreted to determine how the variables being examined are related.
Another essential graph is the bar graph, which features two or more bars in horizontal or vertical columns. The length of each bar represents a particular value. The longest bar represents the greatest value, and the shortest bar represents the smallest value. These graphs are most useful when studying one variable in more than one context. An example would be a bar graph showing the number of students who have a birthday in each month.
Pie charts are graph-like diagrams that use circles to represent data. The full circle represents the total amount of data, while wedge-shaped divisions of the circle show segments of the data. Most pie charts use contrasting colors to make the different divisions clearer. Pie charts are useful for showing ratios of parts to a whole. For example, a pie chart may show the breakdown of a person's monthly expenses. The full circle represents all the money spent in a month, while different "slices" of the pie chart represent specific expenses, such as rent payments, car repairs, food bills, and so on.
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