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Swinging an arch is the solution to many layout and construction problems.
IIf you think a compass is only for drawing circles, think again. This simple and inexpensive device can divide almost anything into precise and equal sections, build complex polygons and find the precise settings to make miter cuts at any angle. Most carpenters own or have access to this incredibly powerful layout, design, and troubleshooting tool, but don’t realize its capabilities.
Take the compass out of your toolbox and play together. If you need to, borrow one from the nearest elementary school student or buy a cheap one. By the time you get to the end of this article, you’ll probably want to have a nice one. At the very least, you’ll have a newfound respect for this simple device.
Divide by two, show square
People often turn to numbers when they don’t need them, and this can slow them down or lead to frustration. Where a compass really shines is to divide things in half. Many geometric constructions are based on two points at equal distances from something else. The important part is that of equality, not the actual measurement.
Despite what you may have thought in high school, geometry is useful, relevant, and empowering. Let’s start with a straight line of any length. Attach the tip of the compass to one end of the line and place the other end anywhere beyond the halfway point. It doesn’t matter how far. Do not worry; just set the distance by eye and swing an arc above and below the original line. Without changing the settings, attach the tip of the compass to the other end of the line and swing the arcs up and down from there.
The intersections of the arcs are at equal distances from each end of the line, and when you use a ruler to draw from one intersection to the other, the new line intersects the original line exactly at the midpoint. Even better, it’s at right angles to the original.
Attach the tip of the compass to the intersection of the two lines and zero the distance to put the lead at the end of the original line. Now swing an arc along the perpendicular line. Connect that intersection with the end of the first line and you’ve just drawn a perfect 45 ° angle.
Without changing the compass setting, swing the arcs from the ends of the line at 45 ° so that they intersect. Take the ruler and connect the intersection with the ends of the angled line. One line is parallel to the first line and the other is parallel to the perpendicular line. The result is a perfect square.
Polygons with Compass
IIf you need to create an equilateral triangle, set the distance between the cardinal points to the length of one side. Draw a line of that length and from each end swing the intersecting arcs above the line. Connect the points to create the triangle.
To create a hexagon, first draw a circle and, without changing the compass setting, set the compass point anywhere on the perimeter. Work your way down the perimeter and connect the intersections with the lines to create a hexagon. If you move away from the perimeter points of the hexagon in the center of the circle, you will create six equilateral triangles along with a visual explanation of how (and why) this method works.
You can easily cut out the corners of a square and turn it into a perfect octagon. Find the center by drawing diagonal lines from corner to corner. The point where these lines cross is the exact center of the square. Attach the tip of the compass in one corner and place the plumb on the center point. Swing two arcs from each corner to intersect with each horizontal and vertical line. Connect those dots and you have an octagon.
If you want to create an oblique frame in one of these shapes, you can determine the cutting angles using the method described in the article, but an even simpler method is to draw lines parallel to the shape. This method also works if you want to cut two pieces of different widths. Draw from corner to corner and set the bevel gauge on the drawing. Use it to set the cut and don’t worry about how many degrees there are in each corner.
Two ways to a perfect angle
In addition to dividing the lines exactly in half, you can also use the compass to divide the corners in two. This will be a lifesaver when you need to cut a whimsical corner.
For practice, draw two lines from a single point at any angle. Set the compass at a reasonable distance and swing the arcs from the intersection of the two lines to cross each line. Move the cardinal point to each intersection and swing the arcs in the opening between the lines. Draw a line from the point where the arcs meet at the intersection of the two lines.
This divides the angle into two equal parts and the drawn angle can be used to set the tilt meter. Your chamfer gauge, in turn, sets your saw to make the cuts and to check the cuts after they are made. A simple solution, no numbers were used and no brain cells were harmed in the process.
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