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Some elements from our "math and science toolbox" are depicted here. They include scientific notation, unit conversion from one measurement system to another, a graph grid in polar coordinates, and vectors.
Original artwork created for Windows to the Universe by Randy Russell.

Tools for Math and Science

Some concepts are used in many different fields of science and serve as a general purpose "toolbox" that helps us understand and manipulate ideas across disciplines. These "tools for math and science" include systems of and units for measurement, lists of physical constants, mathematical tools and conventions, and visual and graphical tools.

In order to quantify our observations of nature, humans have developed systems of measurement, each of which includes an array of measurement units. Some units, like the meter and mile and pound, are familiar; others, like the ångström or farad or Röntgen, are generally unknown beyond the scientific fields that employ them. We need to know how to convert units from one system to another, as when we determine the metric temperature in degrees Celsius when supplied with the English Fahrenheit equivalent.

Some values and ratios seem to be inherent traits of the Universe in which we live. These basic traits, in the form of numerical values, are referred to as physical constants. Examples include the speed of light (c), the ratio of a circle's circumference to its diameter (pi), the gravitational constant (G), and the base of the natural logarithms (e).

The use of mathematical concepts and conventions is widespread throughout the sciences. Vectors help us comprehend and manipulate forces and motion. Scientific notation allows us to work with very large and very small numbers in ways that our minds can grasp.

We use graphs with Cartesian, polar, and logarithmic scales to help us "see" trends. We draw maps of Earth and the heavens, using Mercator or Albers Equal Area projections to most accurately depict certain features of terrain. We employ polar and spherical and Cartesian coordinate systems to specify the locations of objects in space or on the surfaces of planets.

Last modified September 12, 2008 by Randy Russell.

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Windows to the Universe, a project of the National Earth Science Teachers Association, is sponsored in part by the National Science Foundation and NASA, our Founding Partners (the American Geophysical Union and American Geosciences Institute) as well as through Institutional, Contributing, and Affiliate Partners, individual memberships and generous donors. Thank you for your support! NASA AGU AGI NSF