For our distant ancestors, recognizing whether they were about to step on grass, off a cliff, on slippery mud, or into a pond probably was critical information. Perhaps as a result, the human brain has evolved an ability to recognize visual patterns. Since we have this ability, it provides us a valuable tool for analyzing other kinds of information.
Recall that Pythagoras proposed that mathematics and numbers revealed the essence of the universe. Plato taught that mathematics could be used to explain the universe. Their followers were increasingly successful in measuring and understanding aspects of the physical world then learning to use that understanding to control the world to their benefit.
As their society emerged from the Midevil period, some Europeans such as Thomas Bradwardine (c. 1295-1349) tried to clarify the causes of change such as motion. He and other fellows at Merton College searched for geometric methods of visualizing mathematical patterns for speed and other properties that change. They began to draw bars and histograms of lengths proportional to successive measurements. Nicole Oresme of Paris used what today would be called graphs to quantify physical qualities such as speed, displacement, temperature, whiteness, and heaviness, but also nonphysical qualities such as love, charity and grace. For example, he used the geometry of a graph to prove a uniformly accelerated object travels the same distance as it would, had it travelled steadily at the average (Sav) of its initial (Si) and final (Sf) speeds. (The area of the distance rectangle is equal to the area of the trapezoid because moving the pink triangle doesn't change its area.)
That search for patterns in the phenomena of our world continues with efforts such as Stephen Wolfram's A New Kind of Science in which he uses computers and a program called Mathematica to seek patterns in the apparent chaos of vast collections of related numbers.
While histograms, pie charts, and other bar graphs are helpful in visualizing patterns in one aspect of nature, we are often more interested in how one aspect of nature relates to another aspect. For example, a fireman needs to know how the height water can be delivered from a fire hose depends on the water pressure. Such information can be visually presented by a line graph. Traditionally such a graph is made manually with pencil and graph paper. But computer programs using spreadsheets such as Excel can also generate such graphs. Learning to manually draw good graphs with all the necessary parts is a valuable precursor to manipulating Excel to make similar graphs. Incidentally, making a pretty graph using a computer program such as Excel often requires more time than to make a good graph manually!
At this point, many people believe they have previously learned how to make graphs, skip further instruction, then construct FLAWED graphs! A word of advice: Don't assume you already know everything; at least read the links below about making graphs and search for construction details that make a pretty but useless graph into effective communication.
connect the dots.Recall that all measurements contain experimental error, so as a result, most dots are not exactly where they should ideally be located. To compensate for this experimentally error, try to draw a straight line that compromises, coming closest to nearly all the dots. Sometimes a straight line does not fit well. In that case, consider
Construct a line graph for data such as provided in Table #1 below.
|Time (minutes)||Distance (miles)||Time (minutes)||Distance (miles)|
Nearly all computers have applications for constructing spreadsheets. Such applications usually are capable of constructing graphs from series of data entered into the spreadsheet. If you are working on a computer that uses an operating system from Microsoft, you probably have a spreadsheet program called Excel. Jim Askew at Howe High School in Howe, Oklahoma has created instructions for making graphs using Excel. To learn more about making effective line graphs using Excel, use this link to Jim Askew's instructions.
Using a computer spreadsheet such as Excel, construct a line graph for the data in Table #1 above.
to Physical Science experiment 3-2