# Classroom Problem - Graphing

## Coordinate Systems 6.3

### Basic Terms and Concepts

• Coordinate systems define points or other elements in space
• Each numeric value (coordinate) associated with a dimension
• Each linear dimension is represented by an axis
• Relationship of dimensions define coordinate system
• Each dimension may have its own unit of measure
• A set of coordinates with values of zero is the origin
• Visual representations of coordinate systems are called graphs

### Types Of Coordinate Systems

• Cartesian
• Mutually perpendicular axes
• Typically two or three dimensions
• Axes define dimensions
• Quadrants are area between axes
• Polar
• Defined by a linear axis and one angular dimension
• Distance from the origin defines measure on linear axis
• Angular dimension must be defined by a reference angle and cw or ccw rotation

### Application/Conventions

• Labeling and orientation
• Horizontal axis usually labeled X
• Vertical axis usually labeled Y
• Third axis (if any) usually labeled Z
• Numbering
• Positive numbers are usually up, to the right, or ccw
• Negative numbers are usually down, to the left, or cw
• Cartesian coordinates are stated in the order (X, Y, Z)
• Polar coordinates are stated in the order (Distance, Angle)
• Absolute coordinates
• Defined relative to the coordinate system origin
• Relative coordinates
• Defined relative to another location

### Representing time 20.3.2

• Points in time
• A representation (picture/snapshot) of current state
• A position along a graph axis
• Discrete changes in time
• A series of pictures/images
• Arrows or step numbers on a diagram
• Multiple positions along a graph axis
• Continuous changes in time
• Animation
• Continuous element on a graph or diagram
• lines
• arrows
• ribbons

## Background

The recent Mars Pathfinder Mission is a source of lots of great scientific data. Both the latest mission and the Viking missions in the last decade gathered temperature data from the surface of Mars. The U. of Washington, has set up a special site for how this and other weather data can be used in the classroom. In addition to weather data, there is also a wealth of images of the surface of Mars and close-ups of rocks using various types of probes.

## Data Gathering

Data from these and other pages was saved through Netscape (or Explorer) as a text file and opened within Excel. The Import Wizard in Excel steps you through the process of setting the proper delimiters (spaces and tabs in most cases) along with other parameters so that the different dimensions of data are put in their own rows or columns.

The Pathfinder temperature consists of temperature values taken from three probes at different heights from the surface of the planet: 0.25, 0.5, and 1.0 meters. The Viking 1 lander had a single temperature probe at 1.6 meters. The time measurement (the independent variable is measured in Mars solar days (sols), approximately 24.6 hours. Day (sol) 95 for the Viking 1 mission is approximately equivalent to day 1 of the Pathfinder mission.

Once the data is in Excel, it will probably need to be cleaned up so that the Chart Wizard can make better sense of it. Among other things, you may want to:

• Change the precision to two decimal places
• Have the top row be the labels you want on your graph
• Remove rows containing spurious or unwanted data values

One way to give yourself more flexibility is to keep your raw data on the first page of the Excel workbook and create new pages with various modified versions of the data.

A cleaned up version of the data might look like this:

## Graphing

In order to decide how the data can be appropriately visualized, the variables which make up the data need to be evaluated and an appropriate type(s) of visualization chosen. The notes on visualization principles will help you review this method.

Once the data is in Excel, charts can be created with the Chart Wizard.

One type of graph you might make would be a line graph:

You will need to do a number of modifications on the graph to get it looking like you want it to

Another possible visualization would be to create a polar (radar) graph:

You will need to transpose the data so that all the data values for each temperature probe is in a row rather than a column. To do this you need to create a new Excel page, copy the data for one solar day (this will make one revolution around the polar graph), and Paste Special/Transpose into the new page.

## Further Work

The data of the rocks on Mars is derived from probes using both visual light energy and other wavelengths. Exercises can be put together how probe data from different energy sources can be used both alone and together to test hypotheses about the rock composition and history.