Glossary

A

• Acute angle - Any angle between 0° and 90° .

• Adjacent side - The side of a right triangle that is next to the reference angle. (Not hypotenuse)

• Angle - 1. The shape made by two straight lines meeting in a point. 2. The space between those lines. 3. The measurement of that space in degrees or radians.

• Angle of turn - The angle created when a line of work is turned. The angle of turn is formed between where the original line would have gone (if it had not turned) and the line going in the new direction.

• Arc function (also called inverse function) - The function used to find the degrees of an angle when the ratio of the sides of the angle is known. The six arc functions are: arc sine, arc cosine, arc tangent, arc cosecant, arc secant, and arc cotangent.

• Arc - A curved line whose points are equal distances from a single point.

• Arc length - The length of a curved line.

• Area - The measurement of a surface, expressed in square units.

B

C

• Central angle - An angle whose vertex is located at the center of a circle.

• Center length - The distance of the straight line or piece of material between the arcs of an offset.

• Center Mark Back - The distance used in marking and cutting a miter from the center line.

• Chord - A straight line from one point on a circle to another point on the circle. The longest chord of a circle is the diameter.

• Circle - A curved line in a plane that encloses a space. Every point on the curved line is exactly the same distance from the center point.

• Circumference - The distance around a circle.

• Common side of two triangles - A line that is shared by two triangles. It can be the hypotenuse of one triangle and the leg of the other.

• Compass - A tool used to draw circles and curved lines.

• Complementary angles - Two angles whose sum equals 90° . The two lesser angles of a right triangle are always complementary.

• Conversion - For fractions : The process of changing the numerator and the denominator of a fraction to make a new fraction of equal value. Example: 1/2 to 2/4. For units of measurement : The Process of changing a unit of measurement to a different unit of measurement while keeping the value the same. Example: 2 feet to inches, 2 feet = 24 inches.

• Cosecant - One of the functions of an angle. It is found by dividing the length of the hypotenuse of a right triangle by the length of the opposite side of a reference angle.

• Cosine - One of the functions of an angle. It is found by dividing the length of the adjacent side of a reference angle by the length of the hypotenuse.

• Cotangent - One of the functions of an angle. It is found by dividing the length of the adjacent side of a reference angle by the length of the opposite side of a reference angle.

D

• Decimal - Shortened version of decimal fraction.

• Decimal fraction - A fraction in which the denominator is 10 or a power of 10 (such as 100, 1000, 10,000, etc.). The denominator is seldom used. Instead, a dot called a decimal point is placed in front of the numerator. The denominator can be inferred by the number of decimal places behind the decimal point. If there is one number to the right of the decimal point, the denominator is 10. If there are two numbers to the right of the decimal point, the denominator is 100. There will be the same number of zeroes in the denominator as there are decimal places.

• Degree - A unit of measurement for angles. (Also see Radians.)

• Denominator - The bottom number in a fraction. It identifies the number of portions into which the whole has been divided. In the fraction 9/16", the whole inch has been divided into 16 parts, and the measurement is equal to 9 of those parts.

• Diameter - A straight line from one side of a circle to the other side that passes through the center. Also the measurement of that line.

• Division bar of a fraction - The line between the numerator and the denominator of a fraction.

E - F - G

• Equilateral triangle - A triangle with equal sides and equal angles.

• Formula - An equation that follows a rule. Formulas contain variables that when replaced by numbers, allow unknown quantities to be found. An example of a formula is the Pythagorean Theorem, a squared + b squared = c squared.

• Fraction - A number that expressed a portion of a whole. The denominator of a fraction represents the number of the portions the whole has been divided into, and the numerator expresses the number of the portions measured. The fraction 1/4 could be stated as 1 our of 4 parts of the whole.

• Fractions, ruler - The portions into which the English units of measurement such as inches can be divided -- for example, halves, fourths, eighths, sixteenths, and thirty-seconds.

• Functions of an angle - The name of a particular ratio of the sides of a right triangle. The name of the function will depend on which side is divided into which side. There are six possible ways to divide the sides of a right triangle into each other. There are six functions for each angle. The names are: sine, cosine, tangent, cosecant, secant, and cotangent.

• Functions table - A table of the functions of angles. This table allows one to find either the function of an angle or the degree of an angle.

H - I - J

• Hypotenuse - The longest side of a right triangle. It is always located directly across from the right angle.

• Improper fraction - A fraction which is equal to one or more than one.

• Inside arc - The shortest arc of a turn.

• Inverse - A term which means turned upside down. For example the ratio top/bottom is expressed inversely as bottom/top.

• Isosceles right triangle - A 45° right triangle. There is only one right triangle that has two equal legs - the 45° right triangle.

• Isosceles triangle - A triangle that has two equal legs and two equal angles.

K - L

• Legs of a right triangle - The sides of a right triangle other than the hypotenuse.

• Level - Even, flat, not having any part higher or lower than another part.

• Lowest term fraction - A fraction which can not be reduced to a lower term.

M - N

• Measuring fractions - The fractions used with English units of measurement when measuring distance. See Fractions, ruler.

• Metric measurement - Measurements which use metric units of measurement.

• Minute - A division of a degree. There are 60 minutes in each degree.

• Miter - To cut material at an angle.

• Mixed number - A whole number and a fraction.

• Needs - The unknowns of a formula, or the measurements needed to do a calculation.

• Numerator - The top number of a fraction. It indicates the number of portions of a whole.

O

• Obtuse angle - An angle between 90° and 180° .

• Offset - To change the direction of a line by making a turn and correcting back to the original direction by making another turn. Also, offset is the term used to identify such a turn.

• Offset box - An imaginary box which is used when drawing thumbnail sketches to calculate offsets.

• Opposite side - The side of a right triangle that is opposite the reference angle.

• Outside arc - The longest arc of a turn.

P - Q

• Parallel lines - Lines that are in the same plane and always the same distance apart.

• Perpendicular - a 90° angle between two lines. It is also called a right angle.

• Pi (¼ ) - The ratio of the circumference of a circle to its diameter. It is the whole number 3 and a decimal fraction that has endless decimal places. We usually round it off to four decimal places (3.1416) for our work.

• Plane - A flat, level or even surface.

• Plumb - Exactly Vertical. A line that is perpendicular to ground level is plumb.

• Point of tangency - The point where a circle and a tangent line touch.

• Pythagorean theorem - The formula a squared + b squared = c squared, which signifies that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the length of the other two sides.

R

• Radians - A measurement of an angle or an arc length based on the length of the radius. One radian is an arc equal in length to the radius. One radian = 180° / π = 57.295° .

• Radii - More than one radius.

• Radius - A straight line from the center of a circle to a point on the circle. Also the measurement of that line.

• Radius of an arc (or elbow/bend) - The distance from the vertex of an arc to the center line of the elbow or bend.

• Ratio - A comparison of one value to another value by division.

• Ratios of the sides - The division of one side of a right triangle by another side. The ratios of the sides are directly related to the number of degrees in the reference angle.

• Rectangle - Any four-sided plane with four right angles.

  Reference angle - The angle being referred to in any given problem.

• Regular polygon - A polygon which has equal angles and equal sides and can be inscribed in a circle.

• Right angle - A 90° angle.

• Right triangle - A triangle with one angle equal to 90° and two angles whose sum is 90° .

• Rolling offset - A simple offset that is rolled to one side.

• Rounding off a number - Simplifying a number by slightly raising or lowering its value. Accuracy in work is restricted by the tools used in that work. Calculations can not be any closer than what the tools allow, so numbers are rounded off to a point useful for that tool. Needed accuracy will vary among trades or jobs.

S

• Secant - One of the functions of an angle. It is found by dividing the length of the hypotenuse of a right triangle by the length of the adjacent side of a reference angle.

• Sector - A part of a circle which includes two radii connected by the arc.

• Second - A division of the minutes of a degree. There are 60 seconds in each minute of a degree.

• Simple offset - A procedure by which a center line is moved up, down, or over to reach a new path going in the same direction. A simple offset uses two same angle turns.

• Sine - One of the functions of an angle. It is found by dividing the length of the opposite side of a reference angle by the length of the hypotenuse of the right triangle.

• Square root - A factor of a number which when squared produces that number. A square root multiplied by itself equals the number under the square root symbol.

• Square - The product of a number multiplied by itself.

• Straight angle - An angle of 180° (in other words, a straight line).

T

• Take out - The distance that a fitting extends over the center line of a hypotenuse of an offset triangle.

• Take out formula - A formula for finding the take out of an elbow. The take out formula is: Take out = Tan 0/2 x radius of the elbow.

• Tangent - One of the functions of an angle. It is found by dividing the length of the opposite side of a reference angle by the length of the adjacent side of a reference angle.

• Tangent line - A straight line which touches just one point on a circle.

• Theta ( ) - A letter of the Greek alphabet that is used as a variable for unknown angles or when referring to any angle.

• Triangle - An enclosed geometric form with three straight sides. The angles of a triangle always equal 180° .

• Triangle of roll - A triangle in a rolling offset box that contains the angle of roll. It is usually the first triangle calculated.

• Turn - To change direction.

U - V - W

• Unit circle - A circle with a radius of 1 unit.

• Units of measurement - Terms which describe fixed standard measurements.

• Variables - Letters of the alphabet used as symbols to represent numbers that can change or are to be determined.

• Vertex - The point at which two straight lines come together to form the angle.

• Volume - The amount of space occupied in three dimensions, expressed in cubic units.

• Whole numbers - Numbers which contain no fractions.

X - Y - Z

• Zero degree angle - An angle with no space between the two lines. In other words, the two lines are occupying the same space. The difference between a straight angle and a zero degree angle is that the vertex is in the middle of the line for a straight angle but at the end of the line for a zero degree angle.