Compass — Definition, Formula & Examples
A compass is a hinged drawing tool with a pointed end and a pencil end, used to draw circles, arcs, and transfer distances in geometric constructions.
In Euclidean geometry, a compass is a construction instrument that, given a center point and a radius length, produces the locus of all points equidistant from that center — that is, a circle or arc of specified radius.
How It Works
Place the pointed end of the compass on the paper at the point you want as the center. Spread the arms so the pencil end is the desired radius away. Rotate the compass around the center point to draw a circle or arc. To transfer a distance, set the compass width to match a given segment, then move it to a new location and mark off that same length. Together with a straightedge, a compass can bisect angles, construct perpendicular lines, and create regular polygons.
Worked Example
Problem: Using a compass, construct an equilateral triangle with side length 5 cm.
Step 1: Use a straightedge to draw a base segment AB that is 5 cm long.
Step 2: Set your compass to a width of 5 cm. Place the point on A and draw an arc above the segment.
Step 3: Without changing the compass width, place the point on B and draw another arc that intersects the first arc. Label the intersection point C.
Answer: Triangle ABC is equilateral with all three sides measuring 5 cm.
Why It Matters
Compass-and-straightedge constructions form the foundation of Euclidean geometry, the system studied throughout middle and high school. Architects, engineers, and designers still rely on the principles behind compass constructions when creating precise technical drawings.
Common Mistakes
Mistake: The compass width slips while drawing, producing an arc with an inconsistent radius.
Correction: Tighten the hinge on your compass before drawing. Hold the compass at the top and rotate it steadily with one hand, keeping downward pressure light and even.