PLANE SHAPES

A plane shape is a portion of a plane bounded by straight or curved lines or a combination of the two.

The number of different types of plane shapes is infinite, but we are concerned with those which are of importance to you as a sheet metal craftsman. We will cover the circle, triangle, quadrilateral, other polygons, and ellipses.

CIRCLES

Definitions:

A CIRCLE is a closed curved line in which any point on the curved line is equidistant from a point called the center. (Circle 0).

A RADIUS is a line drawn from the center of a circle to a point on a circle. (As OA, OB, OX, and OY.)

A DIAMETER is a line drawn through the center of a circle with its ends lying on the circle.

A DIAMETER is twice the length of a radius. (AB is a diameter of circle 0.)

A CHORD is a line joining any two points lying on a circle. (CD is a chord of circle 0.)

An ARC is a portion of the closed curved lines which forms the circle. It is designated by CD. An arc is said to be subtended by a chord. Chord CD subtends arc CD.

A TANGENT is a straight line which touches the circle at one and only one point. (Line MZ is a tangent to circle 0.)

A CENTRAL ANGLE is an angle whose vertex is the center of a circle and whose side are radii of the circle. (As XOY, YOA, and XOB.)

CONCENTRIC CIRCLES are circles having the same center and having different radii.

The CIRCUMFERENCE of a circle is the distance around the circle. It is the distance on the curve from C to A to X to Y to B to D and back to C.

Some examples of problems involving circles applicable to sheet metal work are as follows:

1. Construct a tangent to circle 0 by use of a square.

Solution:

Step 1. Place the square in a position so that one side touches the center and the other side touches the circle.

Conclusion:

A line drawn along the second side will be tangent to the circle.

2. Divide a circle into 6 equal parts.

Solution:

Step 1. Using a radius of the circle, begin at any point, and step off chords equal to the radius. If done accurately, this will make 6 divisions of the circle.

3. Divide a semicircle into 6 equal parts.

Solution:

Step 1. At 0 erect a perpendicular to AB.

Step 2. With point A as the center and radius equal to A0, swing an arc cutting the circle at E.

Step 3. With point B as the center and the same radius as in step 2, swing an arc cutting the circle at F.

Step 4. With the same radius, and point C as the center, swing arcs cutting the circle at points G and H,

Conclusion:

4. Divide a circle into 8 equal parts.

Problem:

To divide circle 0 into 8 equal parts.

Solution:

Step 1. Draw diameter AB. Draw CD perpendicular to AB, thus dividing the circle into 4 equal parts.

Step 2. Bisect the central angle COB. Mark the point of the intersection of the bisector and circle 0.

Step 3. From B swing an are equal to BP and from this intersection with the circle, draw the diameter, thus dividing circle 0 into 8 equal

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