On-line Mathematics Dictionary

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abacus An oriental counting device and calculator. Abelian group A group in which the binary operation is commutative, that is, ab=ba for all elements a abd b in the group. abscissa The x-coordinate of a point in a 2-dimensional coordinate system. absolute value The positive value for a real number, disregarding the sign. Written |x|. For example, |3|=3, |-4|=4, and |0|=0. abundant number A positive integer that is smaller than the sum of its proper divisors. acceleration The rate of change of velocity with respect to time. acute angle An angle that is less than 90 degrees addition The process of adding two numbers to obraint heir sum. algebraic equation An equation of the form f(x)=0 where f is a polynomial. algebraic number A number that is the root of an algebraic polynomial. For example, sqrt(2) is an algebraic number because it is a solution of the equation x2=2. alphametic A cryptarithm in which the letters, which represent distinct digits, form related words or meaningful phrases. altitude The altitude of a triangle is the line segment from one vertex that is perpendicular to the opposite side. amicable numbers Two numbers are said to be amicable if each is equal to the sum of the proper divisors of the other. angle The figure formed by two line segments or rays that extend from a given point. annulus The region enclosed by two concentric circles. arc A portion of a circle. area The amount of surface contained by a figure. arithmetic The type of mathematics that studies how to solve problems involving numbers (but no variables). arithmetic mean The arithmetic mean of n numbers is the sum of the numbers divided by n. automorphism An isomorphism from a set onto itslef. average Typically this refers to the arithmetic mean. ball A sphere together with its interior. bar graph A type of chart used to compare data in which the length of a bar represents the size of the data. base In the expression xy, x is called the base and y is the exponent. Bayes's Rule A rule for finding conditional probability. binary number A number written to base 2. binary operation A binary operation is an operation that involves two operands. For example, addition and subtraction are binary operations. bijection A one-to-one onto function. binomial An expression that is the sum of two terms. binomial coefficient The coefficients of x in the expansion of (x+1)n. biquadratic equation A polynomial equation of the 4th degree. bisect to cut in half. bit A binary digit. braces The symbols { and } used for grouping or to represent a set. byte The amount of memory needed to represent one character on a computer, typically 8 bits. Calculator A machine for performing arithemtical calculations. Caliban puzzle A logic puzzle in which one is asked to infer one or more facts from a set of given facts. cardinal number A number that indicates the quantity but not the order of things. catenary A curve whose equation is y = (a/2)(ex/a+e-x/a). A chain suspended from two points forms this curve. ceiling function The ceiling function of x is the smallest integer greater than or equal to x. central angle An angle between two radii of a circle. centroid The center of mass of a figure. The centroid of a triangle is the intersection of the medians. cevian A line segment extending from a vertex of a triangle to the opposite side. Chebyshev polynomials chord The line joining two points on a curve is called a chord. circle The set of points equidistant from a given point (the center). circular cone A cone whose base is a circle. circumcenter The circumcenter of a triangle is the center of the circumscribed circle. circumcircle The circle circumscribed about a figure. circumference The boundary of a circle. cissoid A curve with equation y2(a-x)=x3. coefficient The constant multipliers of the indeterminate variable in a polynomial. For example, in the polynomial x2+3x+7, the coefficients are 1, 3, and 7. common denominator A multiple shared by the denominators of two or more fractions. complementary angles Two angles whose sum is 90o. complex number The sum of a real number and an imaginary number, for example 3+4i where i=sqrt(-1). compute To solve problems that use numbers. concave curved from the inside. cone A three-dimensional solid that rises froma circular base to a single point at the top. congruent figures two geometric figures that are identical in size and shape. conic section The cross section of a right circular cone cut by a plane. An ellipse, parabola, and hyperbola are conic sections. coordinates Numbers that determine the position of a point. coprime Integers m and n are coprime if gcd(m,n)=1. cryptarithm A number puzzle in which an indicated arithmetical operation has some or all of its digits replaced by letters or symbols and where the restoration of the original digits is required. Each letter represents a unique digit. cube A solid figure bounded by 6 congruent squares. cubic equation A polynomial equation of degree 3. cyclic polygon A polygon whose vertices lie on a circle. cylinder A rounded three-dimensional solid that has a flat circular face at each end. data Facts that have been collected but not yet interpreted. decagon A polygon with 10 sides. decimal number A number written to the base 10. decimal point The period in a deimal number separating the integer part from the fractional part. deficient number A positive integer that is larger than the sum of its proper divisors. degree The degree of a term in one variable is the exponent of that variable. For example, the degree of 7x5 is 5. denominator In the fraction x/y, x is called the numerator and y is called the denominator. diagonal In a polygon, the line segment joining a vertex with another (non-adjacent) vertex is called a diagonal. diameter The longest chord of a figure. In a circle, a diameter is a chord that passes through the center of the circle. difference The difference between two numbers is what you get when you subtract one from the other. differential calculus That part of calculus that deals with the opeation of differentiation of functions. digimetic A cryptarithm in which digits represent other digits. digit In the decimal system, one of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. dihedral angle The angle formed by two planes meeting in space. dimension The indication of how far something extends in space. disc A circle together with its interior. distributive law The formula a(x+y)=ax+ay. dividend In the expression "a divided by b", a is the divident and b is the divisor. division A basic arithmetical operation determining how many times one quantity is contained within another. divisor In the expression "a divided by b", a is the divident and b is the divisor. divisor The nonzero integer d is a divisor of the integer n if n/d is an integer. Diophantine equation An equation that is to be solved in integers. dodecagon A polygon with 12 sides. dodecahedron A solid figure with 12 faces A regular dodecahedron is a regular polyhedron with 12 faces. Each face is a rgular pentagon. domain The domain of a function f(x) is the set of x values for which the function is defined. domino Two congruent squares joined along an edge. duodecimal number system The system of numeration with base 12. Egyptian fraction A number of the form 1/x where x is an integer is called an Egyptian fraction. eigenvalue characteristic value elementary function one of the functions: rational functions, trigonometric functions, exponential functions, and logarithmic functions. ellipse A plane figure whose equation isx2/a2+y2/b2=1. ellipsoid A solid figure whose equation is x2/a2+y2/b2+z2/c2=1. empty set The set with no elements in it. enumerable set A countable set. equation A statement that two expressions are equal to each other. equiangular polygon A polygon all of whose interior angles are equal. equichordal point A point inside a closed convex curve in the plane is called an equichordal point if all chords through that point have the same length. equilateral polygon A polygon all of whose sides are equal. equilateral triangle A triangle with three equal sides. escribed circle An escribed circle of a triangle is a circle tangent to one side of the triangle and to the extensions of the other sides. estimate A rough guess at the value of a number. Euler line The Euler line of a triangle is the line connecting the centroid and the circumcenter. Euler's constant The limit of the series 1/1+1/2+1/3+...+1/n-ln n as n goes to infinity. Its value is approximately 0.577216. even function A function f(x) is called an even function if f(x)=f(-x) for all x. even number An integer that is divisible by 2. excenter The center of an excircle. excircle An escribed circle of a triangle. exponent In the expression xy, x is called the base and y is called the exponent. exponential function The function f(x)=ex. expoential function to base a The function f(x)=ax. exradius An exradius of a triangle is the radius of an escribed circle. face angle The plane angle formed by adjacent edges of a polygonal angle in space. factor (noun) An exact divisor of a number. This 7 is a factor of 28. factor (verb) To find the factors of a number. factorial n! (read n factorial) is equal to the product of the integers from 1 to n. Farey sequence The sequence obtained by arranging in numerical order all the proper fractions having denominators not greater than a given integer. Fermat number A number of the form 2^{2^n}+1. Fermat's spiral A parabolic spiral. Fibonacci number A member of the sequence 0, 1, 1, 2, 3, 5,... where each number is the sum of the previous two numbers. figurate numbers polygonal numbers finite group A group containing a finite number of elements. floor function The floor function of x is the greatest integer in x, i.e. the largest integer less than or equal to x. focal chord A chord of a conic that passes through a focus. focal radius A line segment from the focus of an ellipse to a point on the perimeter of the ellipse. foot of altitude The intersection of an altitude of a triangle with the base to which it is drawn. foot of line The point of intersection of a line with a line or plane. formula A concise statement expressing the symbolic relationship between two or more quantities. Fourier series A periodic function with period 2 pi. fraction An expression of the form a/b. frequency The number of times a value occurs in some time interval. frustum For a given solid figure, a related figure formed by two parallel planes meeting the given solid. In particular, for a cone or pyramid, a frustum is determined by the plane of the base and a plane parallel to the base. NOTE: this word is frequently incorrectly misspelled as frustrum. Gaussian curve A normal curve. geoboard A flat board into which nails have been driven in a regular rectangular pattern. These nails represent the lattice points in the plane. geodesic The arc on a surface of shortest length joining two given points. geodesy A branch of mathematics dealing with the shape, size, and curvature of the Earth. geometric mean The geometric mean of n numbers is the nth root of the product of the numbers. geometric progression A sequence in which the ratio of each term to the preceding term is a given constant. geometric series A series in which the ratio of each term to the preceding term is a given constant. geometric solid The bounding surface of a 3-dimensional portion of space. geometry The branch of mathematics that deals with the nature of space and the size, shape, and other properties of figures as well as the transformations that preserve these properties. Gergonne point In a triangle, the lines from the vertices to the points of contact of the opposite sides with the inscribed circle meet in a point called the Gergonne point. gnomon magic square A 3 X 3 array in which the elements in each 2 X 2 corner have the same sum. golden ratio (1+Sqrt[5])/2. golden rectangle A rectangle whose sides are in the golden ratio. graceful graph A graph is said to be graceful if you can number the n vertices with the integers from 1 to n and then label each edge with the difference between the numbers at the vertices, in such a way that each edge receives a different label. grad (or grade) 1/100th of a right angle graph A graph is a set of points (called vertices) and a set of lines (called edges) joinging these vertices. great circle A circle on the surface of a sphere whose center is the center of the sphere. greatest common divisor The greatest common divisor of a sequence of integers, is the largest integer that divides each of them exactly. greatest common factor Same as greatest common divisor. greatest lower bound The greatest lower bound of a set of real numbers, is the largest real number that is smaller than each of the numbers in the set. group A mathematical system consisting of elements from a set G and a binary operation * such that x*y is a member of G whenever x and y are (x*y)*z=x*(y*z) for all x, y, and z there is an identity element e such that e*x=x*e=e for all x each member x in G has an inverse element y such that x*y=y*x=e half-line A ray. half-plane The part of a plane that lies on one side of a given line. Hankel matrix A matrix in which all the elements are the same along any diagonal that slopes from northeast to southwest. harmonic analysis The study of the representation of functions by means of linear operations on characteristic sets of functions. harmonic division A line segment is divided harmonically by two points when it is divided externally and internally int he same ratio. harmonic mean The harmonic mean of two numbers a and b is 2ab/(a + b). hectare A unit of measurement in the metric system equal to 10,000 square meters (approximately 2.47 acres). helix The path followed by a point moving on the surface of a right circular cylinder that moves along the cylinder at a constant ratio as it moves around the cylinder. The parameteric equation for a helix is x=a cos t y=a sin t z=bt heptagon A polygon with 7 sides. hexagon A polygoin with 6 sides. hexagonal number A number of the form n(2n-1). hexagonal prism A prism with a hexagonal base. hexahedron A polyhedron having 6 faces. The cube is a regular hexahedron. hexomino A six-square polyomino. Heronian triangle A triangle with integer sides and integer area. homeomorphism A one-to-one continuous transformation that preserves open and closed sets. homomorphism A function that preserve the operators associated with the specified structure. horizontal line A line parallel to the earth's surface or the bottom of a page. hyperbola A curve with equation x2/a2-y2/b2=1. hyperbolic spiral The curve whose equation in polar coordinates is r*theta=a. hyperboloid A geometric solid whose equation is x2/a2+y2/b2-z2/c2=1 orx2/a2+y2/b2-z2/c2=-1. hypotenuse The longest side of a right triangle. icosahedron A polyhedron with 20 faces. idempotent The element x in some algebraic structure is called idempotent if x*x=x. imaginary axis The y-axis of an Argand diagram. imaginary number A complex number of the form xi where x is real and i=sqrt(-1). imaginary part The imaginary part of a complex number x+iy where x and y are real is y. incenter The incenter of a triangle is the center of its inscribed circle. incircle The circle inscribed in a given figure. inequality The statement that one quantity is less than (or greater than) another. infinite becoming large beyond bound. infinitesimal A variable that approaches 0 as a limit. infinity A reference to a quantity larger than any specific integer. inflection A point of inflection of a plane curve is a point where the curve has a stationary tangent, at which the tangent is changing from rotating in one direction to rotating in the oppostie direction. injection A one-to-one mapping. inscribed angle The angle formed by two chords of a curve that meet at the same point on the curve. integer One of the numbers ..., -3, -2, -1, 0, 1, 2, 3, ... intersect Two figures are said to intersect if they meet or cross each other. irrational number A number that is not rational. isogonal conjugate Isogonal lines of a triangle are cevians that are symmetric with respect to the angle bisector. Two points are isogonal conjugates if the corresponding lines to the vertices are isogonal. isometry A length preserving map. isosceles tetrahedron A tetrahedron in which each pair of opposite sides have the same length. isosceles triangle A triangle with two equal sides. isosceles trapezoid Ain which the two non-parallel sides have the same length. isotomic conjugate Two points on the side of a triangle are isotomic if they are equidistant from the midpoint of that side. Two points inside a triangle are isotomic conjugates if the corresponding cevians through these points meet the opposite sides in isotomic points. joint probability function A function that gives the probability that each of two or more random variables takes at a particular value. joint variation A variation in which the values of one variable depend upon those of 2 or more variables. Jordan curve A simple closed curve. Jordan matrix A matrix whose diagonal elements are all equal (and nonzero) and whose elements above the principal diagonal are equal to 1, but all other elements are 0. joule A unit of energy or work. jump discontinuity A discontinuity in a function where the left and righ-hand limits exist but are not equal to each other. kilometer A unit of length equal to 1,000 meters. kinematics A branch of mechanics dealing with the motion of rigid bodies without reference to their masses or the forces acting on the bodies. kite A quadrilateral which has two pairs of adjacent sides equal. knight's tour A knight's tour of a chessboard is a sequence of moves by a knight such that each square of the board is visited exactly once. knot A curve in space formed by interlacing a piece of string and then joining the ends together. knot a unit of speed in navigation equal to one nautical mile per hour. L-tetromino A tetromino in the shape of the letter L. latera recta plural of lattice rectum. latin square An n X n array of numbers in which only n numbers appear. No number appears more than once in any row or column. latitude The angular distance of a point on the Earth from the equator, measured along the meridian through that point. lattice point A point with integer coordinates. latus rectum A chord of an ellipse passing through a focus and perpendicular to the major axis of the ellipse.Plural: latera recta. least common multiple The least common multiple of a set of integers is the smallest integer that is an exact multiple of every number in the set. least upper bound The least upper bound of a set of numbers is the smallest number that is larger than every member of the set. lemata plural of lemma. lemma A proposition that is useful mainly for the proof of some other theorem. length The straight line distance between two points. Legendre polynomials line A geometrical figure that has length but no width. linear function A function of the form y=ax+b. line graph A chart that shows data by means of points connected by lines. line segment The part of a line between two given distinct points on that line (including the two points). locus The set of all points meeting some specified condition. logic The study of the formal laws of reasoning. lowest common denominator The smallest number that is exactly divisible by each denominator of a set of fractions. loxodrome On a sphere, a curve that cuts all parallels under the same angle. lowest common denominator The smallest multiple shared by the denominators of a set of fractions. lowest terms A fraction is said to be in lowest terms if its numerator and denominator have no common factor. Lucas number A member of the sequence 2, 1, 3, 4, 7,... where each number is the sum of the previous two numbers. L0=2, L1=1, Ln=Ln-1+Ln-2. lune The portion of a sphere between two great semicircles having common endpoints (including the semicircles). magic square A square array of n numbers such that sum of the n numbers in any row, column, or main diagonal is a constant (known as the magic sum). magic tour If a chess piece visits each square of a chessboard in succession, this is called a tour of the chessboard. If the successive squares of a tour on an n X n chessboard are numbered from 1 to n^2, in order, the tour is called a magic tour if the resulting square is a magic square. main diagonal In the matrix [aij], the elements a11, a22, ..., ann. major axis The major axis of an ellipse is it's longest chord. Malfatti circles Three equal circles that are mutually tangent and each tangent to two sides of a given triangle. maximum The largest of a set of values. matrix A rectangular array of elements. mean Same as average. medial triangle The triangle whose vertices are the midpoints of the sides of a given triangle. median The median of a triangle is the line from a vertex to the midpoint of the opposite side. median When a set of numbers is ordered from smallest to largest, the median number is the one in the middle of the list. Mersenne number A number of the form 2p-1 where p is a prime. Mersenne prime A Mersenne number that is prime. midpoint The point M is the medpoint of line segment AB if AM=MB. That is, M is halfway between A and B. minor axis The minor axis of an ellipse is its smallest chord. minimum The smallest of a set of values. mode The most frequently occurring value in a sequence of numbers. modulo The integers a and b are said to be congruent modulo m if a-b is divisible by m. monomial An algebraic expression consisting of just one term. monotone A sequence is monotone if its terms are increasing or decreasing. monic polynomial A polynomial in which the coefficient of the term of highest degree is 1. monochromatic triangle A triangle whose vertices are all colored the same. multinomial An algebraic expression consisting of 2 or more terms. multiple The integer b is a multiple of the integer a if there is an integer d such that b=da. multiplication The basic arithemtical operation of repeated addition. nadir The point on the celestial spehere in the direction downwards of the plumb-line. Nagel point In a triangle, the lines from the vertices to the points of contact of the opposite sides with the excircles to those sides meet in a point called the Nagel point. natural number Any one of the numbers 1, 2, 3, 4, 5, ... . negative number A number smaller than 0. nine point center In a triangle, the circumcenter of the medial triangle is called the nine point center. nine point circle In a triangle, the circle that passes through the midpoints of the sides is called the nine point circle. nomograph A graphical device used for computation which uses a straight edge and several scales of numbers. nonagonal number A number of the form n(7n-5)/2. nonary associated with 9 normal perpendicular null hypothesis The null hypothesis is the hypothesis that is being tested in a hypothesis-testing situation. null set the empty set number line A line on which each point represents a real number. number theory The study of integers. numeral A symbol that stands for a number. numerator In the fraction x/y, x is called the numerator and y is called the denominator. numerical analysis The study of methods for approximation of solutions of various classes of mathematical problems including error analysis. oblate spheroid An ellipsoid produced by rotating an ellipse through 360o about its minor axis. oblique angle an angle that is not 90o oblique coordinates A coordinate system in which the axes are not perpendicular. oblique triangle A triangle that is not a right triangle. obtuse angle an angle larger than 90o but smaller than 180o obtuse triangle A triangle that contains an obtuse angle. octagon A polygon with 8 sides. octahedron A polyhedron with 8 faces. octant any one of the 8 portions of space dtermined by the 3 coordinate planes. odd function A function f(x) is called an odd function if f(x)=-f(-x) for all x. odd number An integer that is not divisible by 2. one to one A function f is said to be one to one if f(x)=f(y) implies that x=y. onto A function f is said to map A onto B if for every b in B, there is some a in A such f(a)=b. open interval An interval that does not include its two endpoints. ordered pair A pair of numbers in which one number is distinguished as the first number and the other as the second number of the pair ordinal number A number indicating the order of a thing in a series ordinate The y-coordinate of a point in the plane. origin The point in a coordinate plane with coordinates (0,0). orthic triangle The triangle whose vertices are the feet of the altitudes of a given triangle. orthocenter The point of intersection of the altitudes of a triangle. palindrome A positive integer whose digits read the same forward and backwards. palindromic A positive integer is said to be palindromic with respect to a base b if its representation in base b reads the same from left to right as from right to left. pandiagonal magic square A magic square in which all the broken diagonals as well as the main diagonals add up to the magic constant. pandigital A decimal integer is called pandigital if it contains each of the digits from 0 to 9. paraboloid A paraboloid of revolution is a surface of revolution produced by rotating a parabola about its axis. parallel Two lines in the plane are said to be parallel if they do not meet. parallelogram A quadrilateral whose opposite sides are parallel. parallelepiped A prism whose bases are parallelograms. parentheses The symbols ( and ) used for grouping expressions. Pascal's triangle A triangular array of binomial coefficients. pedal triangle The pedal triangle of a point P with respect to a triangle ABC is the triangle whose vertices are the feet of the perpendiculars dropped from P to the sides of triangle ABC. Pell number The nth term in the sequence 0, 1, 2, 5, 12,... defined by the recurrence P0=0, P1=1, and Pn=2Pn-1+Pn-2. pentagon A polygon with 5 sides. pentagonal number A number of the form n(3n-1)/2. pentomino A five-square polyomino. percent A way of expressing a number as a fraction of 100. perfect cube An integer is a perfect cube if it is of the form m3 where m is an integer. perfect number A positive integer that is equal to the sum of its proper divisors. For example, 28 is perfect because 28=1+2+4+7+14. perfect power An integer is a perfect power if it is of the form mn where m and n are integers and n>1. perfect square An integer is a perfect square if it is of the form m2 where m is an integer. perimeter The distance around the edge of a multisided figure. perpendicular Two straight lines are said to be perpendicular if they meet at right angles. pi The ratio of the circumference of a circle to its diameter. pie chart A type of chart in which a circle is divided up into portions in which the area of each portion represents the size of the data. place value Within a number, each digit is given a place value depending on it's location within the number. plane A two-dimensional area in geometry. point In geometry, a point represents a position, but has no size. polygon A plane figure with many sides. polyomino A planar figure consisting of congruent squares joined edge-to-edge. positive number A number larger than 0. power A number multiplied by itself a specified number of times. practical number A practical number is a positive integer m such that every natural number n not exceeding m is a sum of distinct divisors of m. prime A prime number is an integer larger than 1 whose only positive divisors are 1 and itself. primitive Pythagorean triangle A right triangle whose sides are relatively prime integers. primitive root of unity The complex number z is a primitive nth root of unity if zn=1 but zk is not equal to 1 for any positive integer k less than n. probability The chance that a particular event will happen. product The result of multiplying two numbers. pronic number A number of the form n(n+1). proper divisor The integer d is a proper divisor of the integer n if 0<d<n and d is a divisor of n. proportion A comparison of ratios. pyramid A three-dimensional solid whose base is a polygon and whose sides are triangles that come to a point at the top. Pythagorean triangle A right triangle whose sides are integers. Pythagorean triple An ordered set of three positive integers (a,b,c) such that a2+b2=c2. QED Abbreviation for quod erat demonstrandum, used to denote the end of a proof. quadrangle A closed broken line in the plane consisting of 4 line segments. quadrangular prism A prism whose base is a quadrilateral. quadrangular pyramid A pyramid whose base is a quadrilateral. quadrant Any one of the four portions of the plane into which the plane is divided by the coordinate axes. quadratfrie square free quadratic equation An equation of the form f(x)=0 where f(x) is a second degree polynomial. That is, ax2+bx+c=0. quadrature The quadrature of a geometric figure is the determination of its area. quadric curve The graph of a second degree equation in two variables. quadric surface The graph of a second degree equation in three variables. quadrilateral A geometric figure with four sides. quadrinomial An algebraic expression consisting of 4 terms. quartic polynomial A polynomial of degree 4. quartile The first quartile of a sequence of numbers is the number such that one quuarter of the numbers in the sequence are less than this number. quintic polynomial A polynomial of degree 5. quotient The result of a division. radian A unit of angular measurement such that there are 2 pi radians in a complete circle. One radian = 180/pi degrees. One radian is approximately 57.3o. radical axis the locus of points of equal power with respect to two circle. radical center The radical center of three circles is the common point of interesection of the radical axes of each pair of circles. radii Plural of radius. radius The length of a stright line drown from the center of a circle to a point on its circumference. radix point The generalization of decimal point to bases of numeration other than base 10. range The set of values taken on by a function. rate A way of comparing two quantities. ratio quotient of two numbers. rational number A rational number is a number that is the ratio of two integers. All other real numbers are said to be irrational. real axis The x-axis of an Argand diagram. real part The real number x is called ther eal part of the complex number x+iy where x and y are real and i=sqrt(-1). real variable A variable whose value ranges over the real numbers. reciprocal The reciprocal of the number x is the number 1/x. rectangle A quadrilateral with 4 right angles. reflex angle An angle between 180o and 360o. remainder The number left over when one number is divided by another. repdigit An integer all of whose digits are the same. repeating decimal A decimal whose digits eventually repeat. repunit An integer consisting only of 1's. rhombus A parallelogram with four equal sides. right angle an angle formed by two perpendicular lines; a 90o angle. right triangle A triangle that contains a right angle. roman numerals A system of numeration used by the ancient Romans. root of unity A solution of the equation xn=1, where n is a positive integer. round-off error The error accumulated during a calculation due to rounding intermediate results. rounding The process of approximating a number to a nearby one. ruled surface A surface formed by moving a straight line (called the generator). rusty compass A pair of compasses that are fixed open in a given position. scalene triangle A triangle with unequal sides. secant A straight lien that meets a curve in two or more points. semi-magic square A square array of n numbers such that sum of the n numbers in any row or column is a constant (known as the magic sum). sequence A collection of numbers in a prescribed order: a1, a2, a3, a4, ... series The sum of a finite or infinite sequence set A collection of objects. similar figures Two geometric figures are similar if their sides are in proportion and all their angles are the same. skeleton division A long division in which most or all of the digits have been replaced by asterisks to form a cryptarithm. slide rule A calculating device consisting of two sliding logarithmic scales. solid A three-dimensional figure. solid of revolution A solid formed by rotation a plane figure about an axis in three-space. solidus The slanted line in a fraction such as a/b dividing the numerator from the denominator. sphere The locus of pointsin three-space that are a fixed distance froma given point (called the center). spherical trigonometry The branch of mathematics dealing with measurements on the sphere. square A quadrilateral with 4 equal sides and 4 right angles. square free An integer is said to be square free if it is not divisible by a perfect square, n2, for n>1. square number A number of the form n2. square root The number x is said to be a square root of y if x2 = y. Stirling numbers subtraction A basic operation of arithemtic in which you take away one number from another. sum The result of adding two or more numbers. supplementary Two angels are supplementary of they add up to 180o. surface area The measure of a surface of a three-dimensional solid indicating how large it is. symmedian Reflection of a median of a triangle about the corresponding angle bisector. tangent A line that meets a smooth curve at a single point and does not cut across the curve. tautology A sentence that is true because of its logical structure. tetrahedron A polyhedron with four faces. tetromino A four-square polyomino. Toeplitz matrix A matrix in which all the elements are the same along any diagonal that slopes from northwest to southeast. torus A geometric solid in the shape of a donut. trace The trace of a matrix is the sum of the terms along the principal diagonal. transcendental number A number that is not algebraic. trapezium A quadrilateral in which no sides are parallel. trapezoid A quadrilateral in which two sides are parallel. tree A tree is a graph with the property that there is a unique path from any vertex to any other vertex traveling along the edges. triangle A geometric figure with three sides. triangular number A number of the form n(n+1)/2. trinomial An algebraic expression consisting of 3 terms. tromino A three-square polyomino. truncated pyramid A section of a pyramid between its base and a plane parallel to the base. twin primes Two prime numbers that differ by 2. For example, 11 and 13 are twin primes. unilateral surface A surface with only one side, such as a Moebius strip. unimodal A finite sequence is unimodal if it first increases and then decreases. unimodular A square matrix is unimodular if its determinant is 1. unit circle A unit circle is a circle with radius 1. unit cube A cube with edge length 1. unit fraction A fraction whose numerator is 1. unit square A unit square is a square of side length 1. unitary divisor A divisor d of c is called unitary if gcd(d,c/d) = 1. unity one variable A symbol whose value can change. velocity The rate of change of position. vertical line A line that runs up and down and is perpendicular to a horizontal line. vigesimal related to intervals of 20. vinculum The horizontal bar in a fraction separating the numerator from the denominator. volume The measure of spce occupied by a solid body. vulgar fraction A common fraction. weak inequality An inequality that permits the equality case. For example, a is less than or equal to b. wff A well-formed formula. whole number A natural number. winding number The number of times a closed curve in the plane passes around a given point in the counterclockwise direction. witch of Agnesi A curve whose equation is x2y=4a2(2a-y). X Roman numeral for 10. x-axis The horizontal axis in the plane. x-intercept The point at which a line crosses the x-axis. X-pentomino A pentomino in the shape of the letter X. y-axis The vertical axis in the plane. y-intercept The point at which a line crosses the y-axis. yard A measure of length equal to 3 feet. year A measure of time equal to the period of one revolution of the earth about the sun. Approximately equal to 365 days. z-intercept The point at which a line crosses the z-axis. zero 0 zero divisors Nonzero elements of a ring whose product is 0. zero element The element 0 is a zero element of a group if a+0=a and 0+a=a for all elements a. zeta function zone The portion of a sphere between two parallel planes.

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