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In the sport of orienteering, you navigate a course of landmarks or control points as safely and in as little time as possible.

Equipped with a compass and a map setting out the topography and the landmarks, you are asked to determine distances and directions that lead you to the particular destinations and ultimately the finish line.

This activity tests your physical and mental stamina. You must exhibit patience, prudence and knowledge of geometric principles.

One of these involves quadrants.

During the course run or hike, you can use quadrants to help guide you to the control points you must reach to finish the course.

Your map might not tell you a particular quadrant for the control point you seek.

In that case, you will have to figure it out as you navigate the course.

The concept of a quadrant

The answer to what are the four quadrants on a map starts with the concept of a plane.

In geometric terms, a plane refers to a two-dimensional (flat) surface that in theory extends infinitely.

When you look at a map, you are viewing something on a plane.

However, the map of your course has boundaries.

From the geometric definition of a plane comes the Cartesian coordinate system, developed by French mathematician and philosopher Rene Descartes.

In this system, a vertical line and horizontal line divide the plane into four sections, called quadrants.

You get a point, called the origin, where the vertical line and horizontal line intersect at a 90-degree angle.

From your days in high school or college, you probably used the coordinate system in graphing and solving algebraic equations.

The Cartesian system consists generally of these elements:

  • X-Axis: The horizontal line
  • Y-Axis: The vertical line
  • Coordinates: A pair of numbers representing a point on the plane

Coordinates on a graph appear as (x,y), with x representing the number of units to the right or left of the y-axis and y representing the number of units above or below the x-axis.

Specifically:

  • (0,0) is the coordinate for the origin
  • “x” is to the right of the y-axis
  • “-x” is to the left of the y-axis
  • “y” is above the x-axis
  • “-y” is below the x-axis

Quadrants and the coordinate system

The intersection of the x-axis and y-axis create four quadrants, which are identified by Roman numerals.

These quadrants go counterclockwise:

  • Quadrant I: Right of y-axis, above x-axis (x,y)
  • Quadrant II: Left of y-axis, above x-axis (-x,y)
  • Quadrant III: Left of y-axis below x-axis (-x-y)
  • Quadrant IV: Right of y-axis, below x-axis (x,-y)

Quadrants and directions

You can relate what are the four quadrants on a map to the direction in which you might travel, at least from a point of origin.

Points above the x-axis are north, while those below it are south. “X” points located to the right of the y-axis are east of the y-axis, and those to the left lie to the west.

As such, quadrants have the following directions or bearings from the origin:

  • Quadrant I: Northeast
  • Quadrant II: Northwest
  • Quadrant III: Southwest
  • Quadrant IV: Southeast

To help illustrate quadrants, consider the references you sometimes hear to the northeastern quadrant of a hurricane as typically having the strongest winds and heavy rains.

Meteorologists are talking about those communities or areas located to the northeast of the center of the hurricane circulation — i.e., the eye.

Think of the center of the hurricane as an origin from which the quadrants are determined.

The Bearings

Your map might not label the quadrants as such. However, the control points you encounter serve as separate origin points on that plane known as your map.

From these points, you find the quadrants of your next landmark on the course.

A successful outing of orienteering requires that you know your bearings to identify the quadrant of your target.

This helps you in knowing whether you’re heading in the right direction and to the right place.

Orient your map

You cannot identify the quadrant of your control point or target location until you have first oriented your map.

This allows you to match the map to the course and its objects or features.

Critically, orientation of the map involves pointing your map and yourself toward “true north” so that you correctly identify the quadrant for the control points on your course.

The process involves not only having the arrow on the compass pointing north.

You must also compensate in your direction of movement for the earth’s magnetic pull, which creates a “magnetic north.”

Relating the bearings to quadrant

Bearings introduce another concept of geometry — the circle. It measures 360 degrees.

This basic principle underlines how you understand and use bearings on a compass to help identify the quadrant for the control point.

When you use a compass, you will see a series of numbers ranging from 0 to 360 degrees.

This is the azimuth method of indicating direction:

  • 0/360 degrees is due north
  • 90 degrees is due east
  • 180 degrees is due south
  • 270 degrees is due west

The quadrant bearing method more readily helps you identify quadrants. The reading begins with either “(N)” (north) or “S” (south) and then a number of degrees either east or west.

For instance, if your bearing calls for you to move “north 35 degrees east,” then you are in Quadrant I.

A bearing of “south 12 degrees west” puts your control point in Quadrant III.

If your compass provides only azimuth numbers, you can convert the azimuth to a quadrant bearing as follows:

  • 1 to 89 (Northeast/Quadrant I): No adjustment is necessary. You simply use the azimuth bearing as the quadrant bearing
  • 91 to 179 (Southeast/Quadrant II): 180 degrees minus the measure of the azimuth angle
  • 181 to 269 (Southwest/Quadrant III): The measure of the azimuth angle minus 180 degrees
  • 271 to 359 degrees (Northwest/Quadrant IV): 360 degrees minus the measure of the azimuth angle

Orienteering affords exercise, fun and lessons in patience and perseverance.

During your time on the course, you may have to perform math calculations and apply your knowledge of geometry.

These skills help you identify quadrants to less than the chances of confusion and otherwise getting lost.

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