Glossary
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Mathematical Terminology & Other Obscure Words
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


A

  • adjacent angles:  a pair of angles which share a common side
  • altitude:  the line segment which extends from the top of an figure/object to its bottom in such a way that the length of this segment corresponds to the "height" of the entity; in the context...
    ...of a triangle, extends from one of the vertices to a point on the line which contains the side (a.k.a., base) opposite of that angle such that it forms a perpendicular intersection with the line
    ...of a trapezoid, extends from one of the parallel sides to the line segment containing the other (opposite) side such that it forms a perpendicular intersection with the parallel side; both the parallelogram and rhombus figures are applicable entities
  • analogous:  similar or equivalent in some respect(s) but otherwise different; corresponding in some aspect(s); similar in function but not in structure or origin
  • a priori: (Latin) literally, "before the fact;" pertaining to or characterized by something which does not depend on observation or prior experience
  • arbitrarily:  randomly or without a specific bias, cause or reason
  • arithmetic mean:  a type of average (measure of central tendency), which is defined as the sum of all the values in a set of numerical data divided by n (where n = # of values in the data set); this value is usually the most common usage of the word "average," and typically it is labeled as either (lowercase Greek letter "mu") to denote a population mean or x (referred to a "x bar") to denote a sample mean

  • B

  • Bell curve:  a.k.a. the normal curve, is an idealized statistical graph of a frequency (or relative frequency) distribution for a random variable quantity whose mean, median and mode are identical; the distribution is symmetrical about this (center-line) value.
  • bimodal:  pertaining to a set of data values in which there are two modes (trimodal refers to three modes, etc.); see mode

  • C

  • circle:  two-dimensional, closed curve consisting of all points which are equidistant from a center point
  • Circumference:  the distance around a circle, often denoted by the (uppercase letter) C; it is found by either of the quantities 2πr (where r is the length of the radius) or πd (where d is the length of the diameter)
  • coefficient:  a quantity (usually a numerical constant) which is multiplied by another quantity following it in an expression; e.g., in the algebraic expression 4x2 - 6 x, the coefficient of (the first term) x2 is 4 and the coefficient of (the second term) x is -6.
  • complementary angles:  two (adjacent) angles which form a right angle; i.e., the sum of their angle measures is 90
  • composite figure:  any 2-dimensional figure whose composition consists of simpler figures (e.g., triangles, squares, rectangles, circles, etc.) or portions thereof
  • composite object:  any 3-dimensional object whose composition consists of simpler objects (e.g., cubes, polygonal prisms, spheres, cones, etc.) or portions thereof
  • congruent figures:  any two-dimensional figures (usually with reference to polygons), which are identical in shape and size (contrast with similar figures)
  • congruent objects:  any three-dimensional objects (usually with reference to polyhedra), which are identical in shape and size (contrast with similar objects)
  • cube root:  the cube root of any quantity x, denoted as either3  xor x1/3, is defined as the value of y where y 3 =  x

  • D

  • diagonal:  line segment extending from one of the vertices of a polygon to a non-adjacent, vertex
  • diameter:  a line segment whose two endpoints lie on a circle and which pass through the center of the circle

  • E

  • equilateral: all sides being of equal length, usually in reference to a triangle whose three sides are all the same (length) and whose three interior angles are all congruent (each one measuring 60)
  • Erathosthenes:  the Greek-born scholar and director of the Library of Alexandria (ca. 300 B.C.E.) who is historically credited with deducing an estimate for the Circumference of the Earth
  • extrapolate:  to find an estimate of a value beyond a set of given values (in a sequence), based on the prevailing pattern or tendency (often a proportion) of the original values

  • F

  • factor: [n] any of the quantities involved in a multiplication; [v] to express a given quantity as a product of two or more (typically simpler or prime) quantities
  • frequency:  the number of times an element of data occurs (in the raw data), or the collective number of data elements that occur in a specific category (of the group data)
  • frequency distribution:  a statistical inventory (usually in table format) which indicates the frequency with which each data element occurs (in the raw data) or the collective frequency of data elements occuring in a specific category (of the group data); its associated graph, e.g. a histogram, is also commonly referred to as the frequency distribution (although it is implicitly understood to be only the graphical representation of the distribution rather than the literal "frequency distribution" itself) see section 4.1 practice problem (America's Nat'l Parks)

  • G

  • geometric mean:  a type of average (measure of central tendency), which is defined as the "n-th" root of the product of all the values in a set of numerical data (where n = # of values in the data set)
  • Greek Alphabet:  24-character alphabet which is used to write the Greek language; it is often considered the oldest extant alphabet, having been used since circa the 8th or 9th century B.C.E. (click here to view the alphabet w/pronunciation key)

  • H

  • harmonic mean:  a type of average (measure of central tendency) which is defined as the quotient of n divided by the sum of the reciprocals of all the values in a set of numerical data (where n = # of values in the data set)
  • hectare (ha):  a Metric System unit of land area defined as 1 square hectometer (and which is equivalent to 10,000 square meters)
  • hectometer (hm):  a Metric System unit of length defined as 100 meters
  • Heron's Formula:  formula for finding the Area of a triangle when the lengths of all three sides (a, b, and c) are known.  It involves a (square root) computation using the semiperimeter, which is defined as one-half of the Perimeter (i.e., s = ½P where P = a + b + c)...
    Heron's Formula for the Area of a Triangle
  • hexagon:  a six-sided polygon
  • histogram  a bar-chart or graph depicting with (vertically-directed) rectangles the frequency distribution of the elements in a set of data; the height of each rectangle represents the known frequency for the given data element (in the raw data) or the collective frequency of data elements occuring in a specific category (of the group data)
  • hypotenuse: the side opposite of the right angle in a right triangle, it is always the longest of the three sides; in standard triangle notation (where the sides are labeled a, b and c) it is generally the side of length c

  • I

  • Infinity: () quantity whose value is unbounded
  • Integers:  set of numbers which include all of the Whole numbers combined with the set of negative values of the Natural numbers; frequently represented as I = {...,-3,-2,-1,0,1,2,3,...}
  • interpolate:  to find an intermediate value between two known values (in a set of values), based on a specific pattern, e.g., a proportional amount (used in linear interpolation), of the original values...   [Linear Interpolation Calculator]
  • irrational numbers:  subset of real numbers whose decimal representations neither repeat nor terminate; may also be defined as the subset of real numbers which are not rational numbers (e.g., both 2 and π are irrational)
  • isosceles:  having a pair of base angles which are congruent, usually in reference to a triangle but also sometimes with reference to a trapezoid (as respectively depicted in the illustration, shown at right); moreover, the two corresponding sides are equal in length

  • J

  • judicious:  characterized by good sense or judgment; proceeding from keen insight and pragmatic priority for a desirable result

  • K


    L

  • laissez-faire: (french)  philosophical policy of tolerance toward and non-interference with other's affairs


  • mean:  a type of average (measure of central tendency); see either arithmetic mean, geometric mean, harmonic mean, or quadratic mean
  • median:  middle number in a set of numerical data when when it is arranged in (either ascending or descending) order; for data sets with an even number of data values then the middle value is a hypothetical value which lies halfway between the two middle values
  • mind mapping:  an alternative method of notetaking, one which uses an artistic (stream of consciousness) approach...  Explore!
  • mode:  the most frequent number(s), which must occur more than once; there may not be a mode or there may be more than one (see bimodal)
  • modeling: (mathematical)  describing a physical phenomenon by logical principles characterized with quantitative relationships, e.g., formulas, whose parameters may be measured (or experimentally determined)...  Explore!

  • N

  • Natural numbers:  set of counting numbers; frequently represented as N = {1,2,3,...}
  • nomenclature:  a set or system of names or terms, as those used in a specific science, art, industry, etc.
  • non-sequitur:  a conclusion which does not (logically) follow from its supporting arguments (premises)
  • normal distribution:  a statistical distribution of data values in which the (arithmetic) mean, median, and mode are each equal; the graph is a bell-shaped curve symmetric about the vertical line through its peak and wherein the percentage of data values within one standard deviation of the mean is about 68.26%, the percentage of data values within two standard deviations of the mean is about 95.44%, and about 99.75% of the data values are within three standard deviations of the mean...

  • O

  • oblique:  characterized by an angle which is not a right angle
  • obtuse:  characterized by an angle whose measure is between 90 and 180 (non-inclusive of these two limiting values themselves)
  • octagon:  an eight-sided polygon

  • P

  • parallelogram:  a quadrilateral whose (two) pairs of opposing sides are both parallel and whose (two) pairs of opposing interior angles are congruent; although a rectangle is a special case of the parallelogram, it usually refers to a quadrilateral whose interior angles are not right (90) angles
  • pentagon:  a five-sided polygon
  • perimeter:  the distance around a polygon, often denoted by (the uppercase letter) P
  • perpendicular:  characterized by an angle of intersection which is a right angle, typically in reference to a two-dimensional figure; in higher dimensions this property is usually referred to as "orthogonality" (being orthogonal)
  • pi:  the (irrational, transcendental) number defined as the circumference of a circle divided by its diameter, conventionally denoted by the (lowercase Greek letter) π.  It is approximately equal to
    3.14159265358979323846264338327950288419716939937510
    and has been calculated to over 200 billion decimal places!  More about π?
  • polygon:  a closed, two-dimensional figure of three or more sides, each of which are (straight) line segments; see triangle, quadrilateral, pentagon, hexagon, etc.
  • polyhedron:  a three-dimensional solid whose exterior consists solely of polygons (i.e., flat faces and straight edges); the plural form is "polyhedra"
  • prism:  a three-dimensional object (solid) with at least two parallel faces AND with consistent cross-sectional Areas (i.e., the two-dimensional sections are ALL congruent)
  • Pythagorean Theorem:  a historically renowned formula relating the three sides of a right triangle.  If a and b represent the lengths of the two shorter sides (a.k.a. legs) and c represents the length of the longest side (a.k.a. the hypotenuse), then --
    a2  +  b2  =  c2

  • Q

  • QED:  (latin) literally, "quod erat demonstrandum" meaning that which was to be demonstrated, used to formally earmark the end of a logical or mathematical proof
  • quadratic mean:  a type of average (measure of central tendency), which is defined as the square root of the quotient of the sum of the squares of all the values in a set of numerical data divided by n (where n = # of values in the data set)
  • quadrilateral:  a four-sided polygon; examples include squares, rectangles, parallelograms, trapezoids, etc.

  • R

  • radian:  a unit of angle measure defined as the measure of an angle whose intercepted arc is equal to the radius of the circle when the angle's vertex is positioned at the center of the circle.  Consequently, 2π radians = 360 and thus one radian is 180/π degrees or approx. 57.3.  The unit of radians is most typically used in trigonometry and frequently the unit is omitted such that the value of the angle's measure is, by convention, merely understood to be radians (i.e., in the absence of any other indicated unit such as degrees, minutes, and/or seconds)...
  • radius:  a line segment which extends from the center of a circle to any point of the circle itself
  • rational numbers:  set of numbers formed by the ratio (i.e., fraction) of two Integers where zero in the denominator is not permitted (division by zero is undefined); frequently represented as Q = {a/b | a I, b I, b 0}
  • regular polygon:  an equilateral polygon; i.e., one whose sides are each identical in length AND whose interior angles all have the same measure
  • relative (percentage) error:  ratio of the absolute error to the actual (or true) value, where the absolute error is the difference between the estimate (or measured value) and the actual (or true); this ratio is then typically expressed as a percent...
    err%  =    estimate - actual value 

    actual value
  • right triangle:  a triangle which contains a "right" angle (whose measure is 90); in the conventional "a, b, c" labeling of the three sides, the side of length "c" will represent the hypotenuse

  • S

  • scalene:  having all sides unequal, usually in reference to a triangle
  • SI:  Systeme International (french) = International System
  • similar figures:  any two-dimensional figures (usually in reference to polygons) which are identical in shape but different in size (contrast with congruent figures)
  • similar objects:  any three-dimensional objects (usually in reference to polyhedra) which are identical in shape but different in size (contrast with congruent objects)
  • square root:  the square root of any quantity x, denoted as either  xor x1/2, is defined as the value of y where y 2 =  x
  • standard deviation:  numerical measure of the variation or dispersion in a set of numerical data, which is defined as square root of the quotient of the sum of the squares of all the deviations from the arithmetic mean divided by n for a population or by n - 1 for a sample (where n = # of values in the data set); the (lower-case Greek letter, "sigma") σ is typically used to denote the value for a population while "s" denotes the value for a sample
  • straight angle:  an angle whose initial and terminal sides form a straight line, its measure being 180 (or π radians)
  • subtend:  to extend under or to be opposite of
  • supplementary angles:  two (adjacent) angles which form a straight angle; i.e., the sum of their angle measures is 180
  • surmise:  infer from incomplete evidence or knowledge; imagine to be the case, true or probable
  • symmetric:  similar in size, shape and the relative position of corresponding parts; proportioned in a manner such that half of the figure/object is the "mirror-image" of the other half, e.g., a circle is symmetric about its diameter, a rectangle is symmetric about a diagonal, etc.

  • T

  • tangent:  (1) a line which touches or intersects a curve at one point in the immediate vicinity of the point (in the case of a circle, it touches the curve only once); (2) a trigonometric ratio defined, in terms of a right triangle, as the length of the opposite side divided by the length of the adjacent side (w.r.t. a specified angle)
  • transcendental numbers:  subset of real numbers whose value cannot be expressed as the solution to a polynomial equation -- hence they cannot be a square root, cube root, etc. (even though they are irrational numbers); examples of transcendental numbers include both "π" and "e" Trapezoid figure
  • trapezoid:  a quadrilateral possessing, at least, two parallel sides (as depicted in the illustration, shown at right)
  • triangle:  a three-sided polygon

  • U

  • unit price:  cost per unit for a specific good or service (e.g., the price of gasoline might be $2.25 per gallon)    see section 1.2

  • V

  • vertex:  shared endpoint of two rays (or line segments) which form an angle; "vertices" is the plural of "vertex"
  • vertical angles:  pair of opposing angles whose (common or shared) vertex is the intersection point of two straight lines; the measures of any pair of vertical angles are always equal

  • W

  • Whole numbers:  set of numbers which include zero (0) and all of the Natural Numbers; frequently represented as W = {0,1,2,3,...}

  • X


    Y


    Z

  • z-score:  the value assigned or computed to a raw data (x) value by subtracting the arithmetic mean () from it and then dividing the difference by the standard deviation (σ); i.e.,   zi = (xi - ) / σ

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