Examples Of A Line Graph example essay topic

Mathematics and Science Essay Mathematics is the language of science that provides tools necessary for deeper analysis of scientific concepts and applications. In many cases, students often discover that it is one or more math skills that initially block their ability to understand new science concepts. In science classes students learn how to recognize when particular mathematics procedures are applicable so that they can select the correct methods needed to solve new problems. These new problems often require not only an ultimate solution but also an understanding of how to interpret what is given, relate cause-and-effect, and set up any initial equations.

Many connections can be found between math and science. Elements such as graphing, geometry, and basic algebra are a few concepts used to explain scientific ideas. In fact, several scientific discoveries and theories are based on mathematical equations alone. Many scientists have used mathematics as the basis of their discoveries. People like Louis Past uer, Johannes Kepler, and Neil's Bohr have titles of Biologists, Physicists, and Astronomers.

In all actuality their work has proven them to be mathematicians as well. Many aspects of science are based on geometrical concepts that are used to express the forms and structures of such phenomena (Tracy, 200). Astronomy encompasses elements such as symmetrical formations and elliptical orbits that can only be expressed through a geometrical framework (Tracy, 195). Past Astronomers based much of their findings on geometry alone. Johannes Kepler was one of the first great developers in the history of astronomy. A German sent to Prague, Bohemia (now the Czech Republic), became the assistant to a man by the name of Tycho Brahe (Gingerich, 116).

The two did not get along well. It has been said that Brahe actually did not trust Kepler and was afraid that his bright, young assistant might overshadow him (Gingerich, 116). To keep Kepler busy Brahe gave him the task of understanding the orbit of the planet Mars, which was particularly troublesome. It is believed that part of the reason Brahe gave the Mars problem to Kepler was because he hoped it would occupy Kepler while Brahe worked on his theory of the Solar System (Gingerich, 118).

Ironically, the Mars data allowed Kepler to formulate the correct laws of planetary motion. Kepler firmly believed in the Copernican system, which includes seven axioms that Copernicus used to formulate his conclusions. The most prevalent of the seven axioms was the fact that he believed the sun was at the center of the universe (Gingerich, 120). This idea confused Kepler thus leading him to research further.

While doing research on Mars, Kepler concluded that the orbit of the planet was not circular, rather it was elliptical (web). For an ellipse there are two points called foci (focus for singular) such that the sum of the distances to the foci from any point on the ellipse is a constant (Gingerich, 121). The diagram below shows the foci marked with an "x". This gives the equation of a + b = constant. This defines the ellipse in terms of distances a and b. (web). From Kepler's discovery of elliptical orbits he was able to formulate his Three Laws of Planetary Motion.

The First Law uses geometrical concepts to explain why the orbits of the planets are ellipses, with the sun at one focus of the ellipse (Gingerich, 121). Kepler's Second Law demonstrates several aspects of geometry. First, he used elliptical shapes to represent the orbit of the planets. Next, Kepler gives an example of measuring the effect of a shadow by stating that the Sun sweeps out equal areas in equal times as the planet travels around the ellipse (Gingerich, 121). Below are Johannes Kepler's First and Second Laws of Planetary Motion (web). Kepler's Third Law of Planetary Motion was developed using algebraic equations, rather than geometrical shapes and patterns.

This law shows how the ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semi-major axes (Gingerich, 122). In this equation, P represents the period and R represents the length of its semi-major axes. The subscripts "1" and "2" distinguish quantities for planet 1 and 2 respectively. Thus, Kepler's Third Law of Planetary Motion is (web): Astronomy and the work of Johannes Kepler makes clear that mathematical concepts are integral to science. In his work, we saw that geometry and algebra are used to explain scientific concepts. Other aspects of mathematics, for example, graphing are also used in science.

Understanding graphs is essential for scientists because graphs are a visual way of representing information obtained through study and observation. Graphs can often reveal trends, tendencies or patterns in data that are not evident by examining a long list of hand written data (Charlesworth, 88). Many areas within the sciences use graphs for these reasons. In Physics, scientists and students use graphs to plot data such as mass versus volume and time versus temperature. Astronomers often plot data such as the period of time the sun casts a shadow on a given object.

Graphs are simply another form of supplying data and results. The developer of Cartesian Geometry was a French philosopher, scientist and mathematician named Ren'e Descartes (Gauknoger, 16). Descartes was educated at the Jesuit College of La Fl " echo in Anjou. He entered the college at the age of eight years (Gauknoger, 17). He studied there until 1612, studying classics, mathematics, logic and traditional Aristotelian philosophy (Gauknoger, 18). School made Descartes understand how little he knew.

The only subject which was satisfactory in his eyes was mathematics. This idea became the foundation for his way of thinking, and was to form the basis for all his works. Descartes wrote many famous books on his philosophical speculations, ideas on geometry, and explanations of physical phenomena. However, perhaps today's society is most familiar with his development of the Cartesian coordinate system.

It is said that, .".. as he lay in bed sick, he saw a fly buzzing around on the ceiling, which was made of square tiles. As he watched he realized that he could describe the position of the fly by the ceiling tile he was on", (Gauknoger, 31). After this experience, he developed the coordinate plane to make it easier to describe the position of objects (Gauknoger, 31). In order to use graphing in science, it is consequential for students to understand the various components of a graph.

Two-dimensional graphs have an x-axis that is horizontal and a y-axis that is vertical. The Cartesian coordinate system is ideal for representing the relationship between quantities and variables or x and y (Appling, 67). The x-axis is the independent quantity or variable. This is the trigger, the cause or the action on the subject (Appling, 68). The y-axis is the dependent variable or the effect, result or reaction from the subject (Appling, 68). A relationship in which the two quantities or variables are directly proportional will create a graph in which the data points are increasing in both the x and y directions.

In other words, the two quantities move in the same direction. A relationship in which the two quantities are inversely proportional will create a graph in which one quantity increases while the other decreases. Below are examples of both types of graphs (web). There are many different styles of graphs and graphic techniques that can be used both science and geometry. First, there are line graphs.

Line graphs look like those above and usually show the changes in a variable in relation to the second variable. A line graph is simply a way to look at how something changes usually over time or sometimes over space (Charlesworth, 95). A second style is called a bar graph. Bar graphs run either horizontal or vertical. The information on this type of graph is plotted as thick bars rather than points.

Bar graphs usually show the differences between the variables given. Bar graphs are often used for giving a comparison of absolute numbers (Charlesworth, 96). There also exists a type of graph called a pie chart. This type of graphing system is usually used to show percentages.

It is in the shape of a circle and is often distinguished by using different colors to represent portions of the total part. A pie graph allows us to compare parts of the whole with each other, or a fraction of the whole that each part takes up (Charlesworth, 96). The following three graphs are examples of a line graph, a bar graph and a pie graph (web). The connections that can be made between mathematics and science are endless.

Many scientists, mathematicians, teachers, and students have proven this true. These two subjects go hand in hand. It would be impossible to find the displacement of a liquid or the velocity of a spinning object if one had no mathematical background. The concepts and applications learned in mathematics are essential for accomplishing scientific problems.

Bibliography

Appling, Jeffrey R. Math Survival Guide: Tips for Science Students. New York: Wiley Press, 1994.
Charlesworth, Rosalind. Math and Science for Young Children. New York: Delmar Learning Company, 2003.
Gauknoger, Stephen. Descartes: An Intellectual Biography. New York: Oxford University Press, 1995.
Gingerich, Owen. The Eye of Heaven: Ptolemy, Copernicus, Kepler. New York: American Institute of Physics, 1998.
Tracy, Dianne M. "Linking Math, Science and Inquiry Based Learning", School Science & Math. Vol. 103, Issue 4 (April 2003).
web October 2003.