Z - Math terms glossary

z-axis The line in a three-dimensional coordinate system containing those points whose first and second coordinates are 0.

zero angle An angle whose measure is zero.

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Y - Math terms glossary

y-axis The vertical number line in a coordinate graph. The line in the coordinate plane, usually vertical, or in space, containing those points whose first coordinates (and third, in space) are 0.

y-coordinate   The second coordinate of an ordered pair or ordered triple.

Ex: in the coordinate pair (3,-2), the negative two is the y-coordinate.

yard (yd)  A unit of length in the U.S system of measurement equal to 3 feet or 36 inches.
y-intercept The y-coordinate of a point where a graph crosses the y-axis.

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X - Math terms glossary

x-axis  The horizontal number line in a coordinate graph. The line in the coordinate plane or in space, usually horizontal, containing those points whose second coordinates (and third, in space) are 0.

x-coordinate  The first coordinate of an ordered pair or an ordered triple.

Ex: in the coordinate pair (3,-8), the three is the x-coordinate.

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W - Math terms glossary

walk The composite of a reflection and a translation parallel to the reflecting line, also known as a glide reflection.

whole number Any of the numbers 0, 1, 2, 3, ... .
width (of a rectangle) A dimensional of a rectangle or rectangular solid taken at right angles to the length.
window That part of the plane that shows on the screen of an automatic grapher or automatic drawer.

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V - Math terms glossary

value of a numerical expression  The number that is the result of evaluating a numerical expression.

Ex: the value of 2+3X4 is 14. Remember, the order of operations says that multiplication must be done first when evaluating this.

value of an algebraic expression The number that is the result of evaluating an algebraic expression.

Ex: the value of 3y +8 = 11 is 1.

value of a variable  A number that is substituted for a variable.

variable  A symbol that can stand for any one of a set of numbers or other objects.

vector A quantity that has both magnitude and direction.

velocity the rate of change of distance with respect to time.

vertex (plural vertices) The point two sides of a polygon have in common. The point of intersection of the sides of an angle.

vertex angle The angle included by equal sides of an isosceles triangle.
Here the vertex angle is at the top.

vertex of a polyhedron Any of the vertices of the faces of the polyhedron.

vertical angles Two nonstraight and nonzero angles formed by two intersecting lines, but which are not a linear pair. Vertical angles will always be congruent.

vertical component of a vector The second component in the ordered pair description of a vector, indicating its magnitude along the y-axis of the coordinate plane.

Ex: Here we see a vector with an ordered pair description of (7,3). Three is the vertical component of this vector.

 

vertical line A line with an equation x = h on the coordinate plane.

Ex: The line x = -2 has every x value locked at -2 for every value of y, and it looks like this:

volume Measurement of the space inside a three-dimensional, or solid figure. The number of unit cubes or parts of unit cubes that can be fit into a solid. Also called capacity.

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U - Math terms glossary

undefined terms A term used without a specific mathematical definition.

uniform scale   A scale in which numbers that are equally spaced differ by the same amount. When creating a number line or coordinate grid system, you use a uniform scale.

Ex:

union of two sets The set of elements which are in at least one of the sets.

Ex: Let's say you are given the sets A={3,4,5} and B={4,5,6}, the union of the sets A and B, written A U B, would be {3,4,5,6}. Notice that there is no need to list the 4 and 5 twice.

unit cost  The cost per one unit of an object.

unit fraction A fraction with 1 in its numerator and a natural number in its denominator.

Ex: 1/3, 1/7 etc.
Remember ZERO is not a natural number nor is 1/2 or .5 or -7, so no such numbers will be found in the denominator of a unit fraction.

uniquely determined A situation in which there is exactly one element satisfying given conditions.

Ex: In the equation 3x+4=13, x is uniquely determined because only one number satisfies this situation, 3.

unit cube A cube in which every edge has length one unit.

unit square A square in which each side has length one unit.

unknown A variable which can be assigned different values.

unlike terms Terms that involve different variables or the same variable with different exponents.

EX: 3, 3x, and are all unlike terms.

U.S system of measurement A measurement system in common use in the United States today, based on inches and pounds. Also called the customary system of measurement.

12 inches = 1 foot	8 ounces = 1 cup	16 ounces = 1 pound
36 inches = 1 yard	2 cups = 1 pint	2,000 pounds = 1 ton
5,280 feet = 1 mile	2pints = 1 quart
1 square mile = 640 acres	4 quarts = 1 gallon

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T - Math terms glossary

table  An arrangement of data in rows and columns.

Take-away Model for Subtraction If a quantity y is taken away from an original quantity x with the same units, the quantity left is x - y.

tangent A line, ray, segment, or plane which intersects a curve or curved surface in exactly one point.

tangent of an angle The ratio (length of leg opposite to the angle/length of leg adjacent to the angle) in a right triangle. Abbreviated tan.

tangent circles Two circles that have exactly one point in common.

EX: Here we see a design made of lots of tangent circles.

tenth  A word name for

terminal point The endpoint of a vector.

terminating decimal  A decimal that ends. Also called finite decimal.

terms  Numbers or products of numbers and variables that are added.

Ex: 3x +-8xy + 9 is an expression with three terms.
Ex: also has three terms, remember the last subtraction here can be written as + .

tessellation  A filling up of a two-dimensional space by congruent copies of a figure that do not overlap. The figure which is copied is commonly called the "fundamental region"

tetrahedron A polyhedron with four faces.

theorem A statement deduced from postulates, definitions, or other previously deduced theorems.

30-60-90 triangle A triangle in which the three angles measure 30, 60, and 90.

3-dimensional coordinate system A system of coordinates used to locate points in space by their distances and directions from three mutually perpendicular lines.

three-dimensional figure A figure whose points do not all lie in a single plane.

transformation  The movement of a figure in a plane from its original position, the preimage, to a new position, the image. Also called a map. Transformations can occur when there is a reflection, a rotation, a translation, or a glide reflection of the original image.

translation A transformation in which every point of the preimage moves in the same direction by the same amount to form the image. A translation is also referred to as a "slide".

translation image The result of adding the same numbers to the coordinates of the points in a figure. In the drawing above, triangle A'B'C' is the translation image of triangle ABC. Also called slide image.

transversal A line that intersects two or more lines.

trapezoid A quadrilateral that has (at least) one pair of parallel sides.

*NOTE some definitions omit the words at least.

traversable network A network in which all the arcs may be traced exactly once without picking up the tracing instrument.

*NOTE: a network is only traversable if it has less than three odd nodes (an odd node has an odd number of arcs entering it).

trial and error  A problem-solving strategy in which various solutions are tried until the correct solution is found.

triangle A polygon with three sides.

Triangle-Sum Property  In any triangle, the sum of the measures of the angles is 180°.

triangular region  A triangle and the space inside it.

triangulate To split a polygon into nonoverlapping triangles. Triangulation is usually used to help find the areas of polygons.

trigonometric ratio A ratio of the lengths of the sides in a right triangle.

trillion  A word name for 1,000,000,000,000 .

trillionth A word name for , or .00000 00000 01.

trisect To divide into three congruent parts.

truncate  To cut off a number at a particular decimal place. Truncation does not mean that the decimal is rounded up, a part of it is simply cut off.

Ex: 0.666666666666666 truncated to the hundredths place is 0.66.
*NOTE some calculators are programmed to truncate and others to round up. A rounding calculator with a ten digit display would show 0.666666667 for the decimal above.

truth value The condition of a statement in logic; either true or false.

turn A transformation in which every point of the preimage is rotated by a given angle about a point (in two dimensions) or a line (in three dimensions).They are also called rotations.

A turn in the clockwise direction is considered negative and one in the counterclockwise direction is considered positive.

two-column proof A form of written proof in which the conclusions are written in one column and the justifications are written beside them in a second column.

EX:

Given: Figure ABCDEF as drawn below
Prove: Figure ABCDEF is not a polygon.
1.) Figure ABCDEF is a union of segments in the plane:	1.) Given
2.) , , , , and are the only segments in the figure.	2.) Given
3.) intersects with only at point B, and point A intersects no other segment.	3.) Given
4.) Therefore, Figure ABCDEF is not a polygon.	4.) It violates the definition of polygon.

two-dimensional Pertaining to figures that lie in a single plane, or to their geometry. This is "flat land" so to speak.

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S - Math terms glossary

scale factor of size transformation In similar figures, the ratio of a distance or length in an image to the corresponding distance or length in a preimage. Also called ratio of similitude.

Ex: When comparing the following small right triangle to its similar large right triangle, we see a scale factor of 1/2 or 0.5.

scalene triangle A triangle with no two sides of the same length.

scientific calculator  A calculator which writes very large or small numbers in scientific notation and uses the powering, factorial, square root, negative, and reciprocal keys. This type of calculator has the proper arithmetical, "order of operations" installed in its brain. So it knows that parentheses must be calculated first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right.

*Remember a cheap, non scientific calculator will perform the operations in the order that you enter them, so if you type 3+2x4 on a non scientific calculator, you get 20, which is the WRONG answer. The multiplication needs to be done FIRST so the correct answer is 11. A scientific calculator will give you the correct answer, because it knows it must multiply FIRST.

scientific notation for large numbers A way of writing a large number in terms of a positive integer power of 10 multiplied by a number greater than or equal to 1 and less than 10.

Ex:

scientific notation for small numbers A way of writing a small number in terms of a negative integer power of 10 multiplied by a number greater than or equal to one and less than 10.

Ex:

secant to a circle A line that intersects a circle in two distinct points.

sector of a circle The figure bounded by two radii and the included arc of the circle.

segment On a line, the set consisting of the distinct points A and B (its endpoints) and all points between A and B. Also called line segment.

semicircle  Half a circle. The arc of a circle whose endpoints are the endpoints of a diameter of the circle.

Ex: is a semicircle of circle C.

short ton  A unit of weight in the U.S. system of measurement equal to 2,000 pounds.

side  One of the segments which makes up a polygon. One of the rays of an angle. One of the faces of a solid.

side of an angle An angle is the union of two rays with the same endpoint.

The rays are the sides and the common endpoint is called the vertex. There are many types of angles. See the definitions for zero angle, right angle, straight angle, acute angle, obtuse angle and reflex angle.

side of a polygon One of the segments whose union is a polygon; also, the length of that segment.

similar figures Two figures that have the same shape, but not necessarily the same size.

simple closed curve A figure that is closed and does not intersect itself.

simple fraction  A fraction with an integer in the numerator and a nonzero integer in the denominator.

sine of an angle The ratio (leg opposite the angle / hypotenuse) in a right triangle. Abbreviated sin.

size change factor  A number which multiplies other numbers to a change their size.

Ex:

Here we see a size change factor of 1/2 going from the large triangle to the small. Or a size change factor of 2 if going from the small to the large triangle.

size change of magnitude k A transformation in which the coordinates of the original figure have all been multiplied by k. Also called size change factor, and ratio of similitude.

skew lines Lines that do not lie in the same plane and do not intersect.

slant height of a regular pyramid The altitude from the vertex on any one of the triangular, lateral faces of the pyramid. It is important to remember that the slant height is not the acutal height of the pyramid itself; it is just the height of one of the triangles that form a face of the pyramid.

slant height of a right cone The length of a lateral edge of the cone. It is important to note that the slant height of a right cone is not the height of the cone itself; it is just the distance a bug would walk if he walked in a straight line from a point on the base directly up to the vertex of the cone.

slide A translation of a given preimage. This occurs when given numbers are added to every "x" coordinate and or "y" coordinate of the preimage. The result is that the image appears to "slide" away from the preimage.

slide image The result of adding the same number to the coordinates of the point in a figure. Also called translation image.

slope The name for the constant rate of change between two points on a line. The amount of change in the height of the line as you go one unit to the right. The slope of the line through (x1,y1) and (x2,y2) is
................SLOPE IS ALSO DESCRIBED AS:

.

A line with a positive slope will rise uphill from left to right.

A line with a negative slope will fall downhill from left to right.

A line with zero slope is horizontal because it has no rise between any two points.

A vertical line has undefined slope because between any two points there is no run.

slope-intercept form An equation of a line in the form y=mx+b, where m is the slope and b is the y-intercept.

small circle of a sphere The intersection of the sphere and a plane that does not contain the center of the sphere.

solid The union of a surface and the region of space enclosed by the surface.

solid geometry The study of figures in three-dimensional space.

solution  A value of a variable that makes an open sentence true.

Ex: Given 3x+4=10, ............x=2 is the solution.

solving an open sentence  Finding value(s) of the unknown(s) in an open sentence that make it true.

solving a proportion  Finding the value of a variable that makes a proportion true.

space The set of all points in a geometry.

space figure A figure whose points do not all lie in a single plane. Also called a three-dimensional figure.

special case  An instance of a pattern used for some definite purpose.

Ex: Given the inequality , x=0 is a special case. In fact this special case proves that the given statement is false, because
would be 0, and 0 is not greater than zero. Thus this special case is a counterexample to the given statement.

sphere  The set of points in space at a fixed distance (its radius) from a point (its center).

*Note this definition implies that all of the points on the iterior, or at a distance less than the radius, are not part of the sphere. If you want all those points too, you need something called a spherical solid.

square  A four-sided figure with four right angles and four sides of equal length. A rectangle with the same length and width.

square root  If A = s^{^2} , then s is called a square root of A.

Ex: since both 3 and -3 are 9 when squared. Remember there are always two possible square roots, one positive, called the "principal" square root, and one negative.

square units  Units for measuring area.

Ex: square inches, square meters, square miles, etc..

standard form of an equation for a line A equation for a line in the form Ax+By=C, where A and B are not both zero.

straight angle An angle whose measure is 180°.

straightedge An instrument for drawing the line through two points which has no marks for determining length.

Substitution Principle  If two numbers are equal, then one may be substituted for the other in any computation without changing the results of the computation.

subtrahend  b in the subtraction a - b.

sufficient condition p is a sufficient condition for q if and only if p implies q.

sum The result of an addition.

supplementary angles  Two angles whose measures add to 180°.

surface The boundary of a three-dimensional figure.

surface area  The sum of the areas of the faces of a solid.

symmetry diagonal (of a kite) The diagonal that connects the ends of the kite.

symmetric figure  A figure that coincides with its reflection image over a line.

symmetry line For a figure, a line m such that the figure coincides with its reflection image over m. See above the heart figure with the symmetry line down its center.

symmetry plane For a figure, a plane M such that the figure coincides with its reflection image over M.

synthetic geometry A geometry studied without the use of coordinates.

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