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.

## Traveling Nitrogen Classroom Activity Kit

Check out our online store - minerals, fossils, books, activities, jewelry, and household items!...more

## Fundamental Forces

The interactions in the Universe are governed by four forces (strong, weak, electromagnetic and gravitational). Physicists are trying to derive a unified theory that would describe all the forces in nature...more

## 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"...more

## Starting Points for Science

Some basic concepts find applications in many, many places throughout science, especially physical science. We have grouped these "starting points for science" into three clusters: space, time, and matter....more

## What is a Supercomputer?

Some scientific problems and processes are so complex that you need SUPERCOMPUTING power to tackle them! Just what is a supercomputer? A supercomputer is a computer that is among the largest, fastest or...more

## Using Computers for Science

In the last decades, computers have become a normal part of life. They are used to send e-mail, write a school report or look up recipes. They are used to keep track of the balance in your bank account....more

## Universal Time

When it is noon where you live, it is midnight on the opposite side of the world. Usually when we think of time, we mean "the time of day where I live". If we say something happened at 9 AM, we mean it...more

## The Magnetic Field

The force of magnetism causes material to point along the direction the magnetic force points. This property implies that the force of magnetism has a direction. As shown in the diagram to the left, the...more

Windows to the Universe, a project of the National Earth Science Teachers Association, is sponsored in part is sponsored in part through grants from federal agencies (NASA and NOAA), and partnerships with affiliated organizations, including the American Geophysical Union, the Howard Hughes Medical Institute, the Earth System Information Partnership, the American Meteorological Society, the National Center for Science Education, and TERC. The American Geophysical Union and the American Geosciences Institute are Windows to the Universe Founding Partners. NESTA welcomes new Institutional Affiliates in support of our ongoing programs, as well as collaborations on new projects. Contact NESTA for more information.