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.
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