Glossary of Terms
Over 600+ carefully defined terms, volume, geometry, mathematics, physics, engineering, finance, health, loans, mortgages, and salary.
Terms
Abscissa
The x-coordinate in a Cartesian coordinate system, representing the horizontal distance from the y-axis.
Absolute Value
The distance of a number from zero on the number line, always expressed as a non-negative value.
Acute Angle
An angle that measures less than 90 degrees.
Acute Triangle
A triangle where all three interior angles are less than 90 degrees.
Addend
Any number that is added to another number in an addition operation.
Addition
The arithmetic operation of combining two or more numbers to find their total.
Adjacent Angles
Two angles that share a common vertex and side but do not overlap.
Adjacent Sides
Sides of a polygon that meet at a common vertex.
Algebra
A branch of mathematics dealing with symbols and the rules for manipulating them to solve equations.
Algorithm
A step-by-step procedure or formula for solving a problem or performing a computation.
Alternate Angles
Angles formed when a transversal cuts two lines, lying on opposite sides of the transversal.
Altitude
The perpendicular distance from the base of a shape to its top or apex.
Angle
The figure formed by two rays sharing a common endpoint, measured in degrees or radians.
Angle Bisector
A ray that divides an angle into two equal angles.
Annulus
The region between two concentric circles, shaped like a ring.
Antecedent
The first term in a ratio or the 'if' part of a conditional statement.
Apex
The highest point or vertex of a cone, pyramid, or other shape.
Arc
A portion of the circumference of a circle or other curve.
Archimedes' Principle
A principle stating that the buoyant force on an object equals the weight of the fluid displaced.
Area
The measure of a two-dimensional surface, expressed in square units.
Arithmetic
The branch of mathematics dealing with basic operations: addition, subtraction, multiplication, and division.
Arithmetic Mean
The average of a set of numbers, calculated by dividing the sum by the count.
Arithmetic Sequence
A sequence where the difference between consecutive terms is constant.
Array
An ordered arrangement of objects, numbers, or symbols in rows and columns.
Associative Property
The property stating that the grouping of numbers in addition or multiplication does not affect the result.
Asymptote
A line that a curve approaches but never touches as it extends to infinity.
Atom
The basic unit of a chemical element, consisting of protons, neutrons, and electrons.
Average
A single value representing the central tendency of a set of numbers, typically the arithmetic mean.
Axes
The reference lines in a coordinate system, typically labeled x and y.
Axis of Symmetry
A line that divides a shape into two mirror-image halves.
Bar Chart
A graphical representation of data using rectangular bars of varying heights.
Bar Graph
A chart with rectangular bars representing data values, often used for comparing categories.
Base
The bottom face of a three-dimensional shape or the number that is raised to a power.
Base Angles
In an isosceles triangle, the two angles opposite the equal sides.
Bearing
A direction measured clockwise from north, typically used in navigation.
Billion
A number equal to 10^9 (1,000,000,000) in the short scale.
Binary
A base-2 number system using only digits 0 and 1, fundamental to computing.
Binary Operation
An operation that combines two elements to produce a third element.
Binomial
A polynomial with exactly two terms, such as 2x + 3.
Bisect
To divide something into two equal parts, typically an angle or line segment.
Bisector
A line or ray that divides an angle or line segment into two equal parts.
Box Plot
A graphical method for displaying the distribution of a dataset based on quartiles.
Bracket
A symbol used in mathematics to group numbers or expressions, such as [ ], ( ), or { }.
Breadth
The width or measurement of a shape from side to side.
Buoyancy
The upward force exerted by a fluid on an object immersed in it.
Calculus
The branch of mathematics dealing with rates of change and accumulation of quantities.
Capacity
The maximum amount that a container can hold, measured in units like liters or gallons.
Capsule
A three-dimensional shape consisting of a cylinder with hemispherical ends.
Cartesian Coordinates
A coordinate system using two or three perpendicular axes to specify points in space.
Center
The point equidistant from all points on a circle or sphere.
Centimeter
A metric unit of length equal to one-hundredth of a meter.
Central Angle
An angle formed by two radii of a circle, with its vertex at the circle's center.
Centroid
The point where the medians of a triangle intersect; the center of mass.
Chain Rule
A formula in calculus for computing the derivative of the composition of two functions.
Chord
A line segment connecting two points on a curve, particularly a circle.
Circle
A closed curve where all points are equidistant from a fixed center point.
Circumference
The distance around a circle, equal to 2π times the radius.
Circumradius
The radius of the circumscribed circle around a polygon.
Coefficient
A numerical or constant factor multiplying a variable in an algebraic expression.
Cofunction
Trigonometric functions that are complements of each other, such as sine and cosine.
Collinear
Points that lie on the same straight line.
Combination
A selection of items from a set where order does not matter.
Complementary Angles
Two angles whose measures sum to 90 degrees.
Complex Number
A number of the form a + bi, where a and b are real numbers and i is the imaginary unit.
Composite Number
A positive integer with more than two factors.
Compound Interest
Interest calculated on the initial principal and accumulated interest.
Concave
A shape that curves inward, like the inside of a bowl.
Cone
A three-dimensional shape that tapers smoothly from a flat base to a point called the apex.
Conic Section
A curve obtained by intersecting a cone with a plane, including circles, ellipses, parabolas, and hyperbolas.
Conjugate
The pair of complex numbers a+bi and a-bi.
Consecutive
Following one after another in order without gaps.
Constant
A fixed value that does not change in an expression or equation.
Construction
In geometry, the process of drawing shapes using a compass and straightedge.
Continuous
A function whose graph has no breaks or gaps.
Contradiction
A statement that is false under all possible truth values.
Convergent
A sequence or series that approaches a finite limit.
Convex
A shape that curves outward; all interior angles are less than 180 degrees.
Coordinate
A set of numbers that defines the position of a point in space.
Coplanar
Points or lines that lie in the same plane.
Corresponding Angles
Angles that are in the same relative position at each intersection.
Cosecant
A trigonometric function equal to the reciprocal of the sine function (csc θ = 1/sin θ).
Cosine
A trigonometric function equal to the ratio of the adjacent side to the hypotenuse in a right triangle.
Cotangent
A trigonometric function equal to the reciprocal of the tangent function (cot θ = 1/tan θ).
Counterexample
An example that disproves a statement or hypothesis.
Cube
A three-dimensional shape with six equal square faces.
Cube Root
A number that, when multiplied by itself twice, gives the original number (³√a).
Cubic
A polynomial of degree 3, or a shape having three-dimensional volume.
Cubic Unit
A unit of measurement for volume, such as cubic meters or cubic inches.
Cylinder
A three-dimensional shape with two parallel circular bases connected by a curved surface.
Data
Collected information, often numerical, used for analysis and drawing conclusions.
Decagon
A polygon with ten sides and ten angles.
Decimeter
A metric unit of length equal to one-tenth of a meter (10 centimeters).
Decreasing
A function or sequence that decreases as the input or index increases.
Deductive Reasoning
Reasoning from general premises to specific conclusions.
Degree
A unit of measurement for angles, with 360 degrees in a full circle.
Degree of a Polynomial
The highest exponent of the variable in a polynomial expression.
Denominator
The bottom number in a fraction, indicating the total number of equal parts.
Density
Mass per unit volume of a substance, typically measured in g/cm³ or kg/m³.
Dependent Variable
A variable that depends on the value of another variable in a function.
Derivative
In calculus, the rate at which a function changes at a given point.
Diagonal
A line segment connecting two non-adjacent vertices of a polygon.
Diameter
The distance across a circle or sphere through its center, equal to twice the radius.
Difference
The result of subtracting one number from another.
Differentiable
A function that has a derivative at a given point.
Differential
An infinitesimal change in a variable or function.
Differential Equation
An equation relating a function to its derivatives.
Digit
A numerical symbol from 0 to 9 used in representing numbers.
Dilation
A transformation that changes the size of a figure proportionally.
Dimension
A measure of extent in a particular direction; the number of coordinates needed to specify a point.
Direct Proportion
A relationship where two quantities increase or decrease together at a constant ratio.
Discriminant
In a quadratic equation, the term b² - 4ac that determines the nature of the roots.
Disjoint
Sets that have no elements in common.
Distance
The length between two points in space.
Distributive Property
A property stating that a(b + c) = ab + ac.
Divergence
A sequence or series that does not converge to a finite limit.
Dividend
The number to be divided in a division operation.
Division
The arithmetic operation of finding how many times one number contains another.
Divisor
The number by which another number is divided.
Domain
The set of all possible input values for a function.
Dodecagon
A polygon with twelve sides and twelve angles.
Dodecahedron
A three-dimensional shape with twelve regular pentagonal faces.
e (Euler's Number)
A mathematical constant approximately equal to 2.71828, the base of natural logarithms.
Eccentricity
A measure of how much a conic section deviates from being circular.
Edge
A line segment where two faces of a polyhedron meet.
Element
An individual object or member of a set.
Ellipse
A conic section shaped like an elongated circle, where the sum of distances to two foci is constant.
Ellipsoid
A three-dimensional shape resembling a stretched sphere, with three unequal semi-axes.
Empty Set
A set with no elements, denoted by ∅ or {}.
Endpoint
The point at either end of a line segment or ray.
Equality
A statement that two expressions have the same value.
Equation
A mathematical statement that two expressions are equal.
Equiangular
A polygon with all interior angles equal.
Equidistant
Points that are at the same distance from a given point or set of points.
Equilateral
A polygon with all sides equal in length.
Equilateral Triangle
A triangle with all three sides and all three angles equal.
Equivalent
Having the same value or meaning.
Error
The difference between a measured value and the true value.
Euclidean Geometry
The study of geometry based on the postulates of Euclid.
Euler's Formula
A formula relating the number of vertices, edges, and faces of a polyhedron: V - E + F = 2.
Evaluate
To find the value of an expression by substituting values for variables.
Even Number
An integer divisible by 2 without a remainder.
Exponent
A number indicating how many times a base is multiplied by itself.
Exponential
A function where the variable appears as an exponent.
Expression
A mathematical phrase consisting of numbers, variables, and operations.
Exterior Angle
An angle formed by one side of a polygon and the extension of an adjacent side.
Extrapolation
Estimating values beyond the range of known data.
Face
A flat surface on a three-dimensional shape.
Factor
A number that divides another number evenly.
Factorial
The product of all positive integers from 1 to n, denoted as n!.
Fibonacci Sequence
A sequence where each number is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13...
Figure
A geometric shape or diagram.
Finite
Having a countable or limited number of elements.
Finite Element Method
A numerical technique used to estimate the volume of complex or irregular shapes.
Floor
The largest integer less than or equal to a given number.
Focus
A fixed point used in defining conic sections, such as ellipses and parabolas.
Formula
A mathematical equation or rule used to calculate a specific quantity.
Fraction
A number expressed as a ratio of two integers, written as a/b.
Frequency
The number of times a value occurs in a dataset.
Function
A relation where each input has exactly one output.
Fundamental Theorem of Calculus
A theorem linking differentiation and integration, showing they are inverse operations.
Frustum
The portion of a solid (such as a cone or pyramid) between two parallel planes.
Galileo's Law
The principle that all objects fall at the same rate in a vacuum, regardless of their mass.
Geometric Mean
The nth root of the product of n numbers, often used for growth rates.
Geometric Progression
A sequence where each term is multiplied by a constant ratio.
Geometry
The branch of mathematics concerned with shapes, sizes, and properties of space.
Gradient
A vector that points in the direction of the greatest rate of increase of a function.
Graph
A visual representation of data or a mathematical function.
Greater Than
A comparison operator indicating that one value is larger than another (>).
Greatest Common Divisor
The largest positive integer that divides two or more numbers without remainder.
Half-Life
The time required for a quantity to reduce to half its initial value, often used in radioactive decay.
Heptagon
A polygon with seven sides and seven angles.
Hexagon
A polygon with six sides and six angles.
Hexahedron
A three-dimensional shape with six faces, such as a cube.
Height
The vertical distance from the base to the top of a shape.
Hendecagon
A polygon with eleven sides and eleven angles.
Histogram
A graphical representation of the distribution of numerical data.
Hyperbola
A conic section consisting of two separate curves, defined by the difference of distances to two foci.
Hypotenuse
The longest side of a right triangle, opposite the right angle.
Hypothesis
A proposed explanation or assumption to be tested in research.
Icosahedron
A polyhedron with twenty triangular faces.
Imaginary Number
A number expressed as a real number multiplied by the imaginary unit i, where i² = -1.
Improper Fraction
A fraction where the numerator is greater than or equal to the denominator.
Increasing
A function or sequence that increases as the input or index increases.
Independent Variable
A variable that is manipulated or changed in an experiment.
Inductive Reasoning
Reasoning that derives general principles from specific observations.
Inequality
A mathematical statement comparing two values using symbols such as <, >, ≤, or ≥.
Infinite
Having no limit or end; unbounded.
Inscribed Angle
An angle formed by two chords with the vertex on the circle.
Integer
A whole number that can be positive, negative, or zero.
Integral
In calculus, a mathematical object representing the area under a curve or the accumulation of quantities.
Integral Calculus
A branch of mathematics used to calculate volumes of shapes with varying cross-sections.
Intercept
The point where a line or curve crosses an axis.
Interior Angles
Angles formed inside a polygon by its sides.
Interpolation
Estimating values within the range of known data.
Intersection
The set of elements common to two or more sets.
Interval
A range of values between two numbers.
Inverse Function
A function that reverses the effect of another function.
Inverse Proportion
A relationship where one quantity increases as another decreases.
Irregular Shape
A shape that does not have a standard geometric form, often requiring advanced methods to calculate its volume.
Isosceles Triangle
A triangle with at least two sides of equal length.
Isosceles Trapezoid
A trapezoid with the non-parallel sides equal in length.
Join
A set operation that combines elements from two sets.
Jordan Curve
A simple closed curve that divides a plane into an interior and exterior region.
Kilogram
The base unit of mass in the International System of Units (SI), equal to 1000 grams.
Kilometer
A metric unit of length equal to 1000 meters.
Kite
A quadrilateral with two pairs of adjacent sides equal in length.
Lateral Area
The surface area of a three-dimensional shape excluding its base(s).
Law of Cosines
A formula relating the sides of a triangle to the cosine of one of its angles.
Law of Sines
A formula relating the sides of a triangle to the sine of their opposite angles.
Least Common Multiple
The smallest positive integer that is a multiple of two or more numbers.
Leg
In a right triangle, either of the two sides that form the right angle.
Lemma
A proven statement used as a stepping stone to prove a larger theorem.
Length
The measurement of something from end to end.
Less Than
A comparison operator indicating that one value is smaller than another (<).
Like Terms
Terms in an algebraic expression that have the same variables and exponents.
Limit
The value that a function approaches as the input approaches a given value.
Line
A straight one-dimensional figure with no thickness, extending infinitely in both directions.
Line Graph
A graph that uses lines to connect data points, showing trends over time.
Line of Symmetry
A line that divides a shape into two mirror-image halves.
Line Segment
A part of a line bounded by two distinct endpoints.
Linear
Having a straight-line relationship or representation.
Linear Equation
An equation whose graph is a straight line.
Linear Function
A function whose graph is a straight line.
Liquid
A state of matter that flows and takes the shape of its container, with a definite volume but no fixed shape.
Liter
A metric unit of volume equal to 1 cubic decimeter or 1000 cubic centimeters.
Logarithm
The exponent to which a base must be raised to produce a given number.
Logic
The study of correct reasoning and argumentation.
Mass
A measure of the amount of matter in an object, typically measured in kilograms or grams.
Matrix
A rectangular array of numbers, symbols, or expressions arranged in rows and columns.
Mean
The average of a set of numbers, calculated by dividing the sum by the count.
Median
The middle value in a set of numbers when arranged in ascending or descending order.
Meter
The base unit of length in the International System of Units (SI).
Midpoint
A point that divides a line segment into two equal parts.
Minus
A symbol (-) indicating subtraction or a negative number.
Mode
The value that appears most frequently in a dataset.
Molarity
A measure of the concentration of a solute in a solution, expressed in moles per liter.
Molecule
A group of atoms bonded together, representing the smallest fundamental unit of a chemical compound.
Multiplicand
A number that is multiplied by another number.
Multiplication
The arithmetic operation of repeated addition.
Multiplier
A number by which another number is multiplied.
Multiplying
The process of combining groups of equal size to find the total.
Natural Number
A positive integer, typically starting from 1.
Negative Number
A number less than zero.
Nested
One element contained within another, often used in programming and mathematics.
Newton
The SI unit of force, named after Isaac Newton.
Nonagon
A polygon with nine sides and nine angles.
Nonlinear
Not having a straight-line relationship or representation.
Normal
A line perpendicular to a surface or another line.
Null Set
A set with no elements, also known as the empty set.
Numerator
The top number in a fraction, indicating the number of parts being considered.
Numerical
Relating to numbers or expressed as numbers.
Obtuse Angle
An angle that measures between 90 and 180 degrees.
Obtuse Triangle
A triangle with one angle greater than 90 degrees.
Octagon
A polygon with eight sides and eight angles.
Octahedron
A polyhedron with eight triangular faces.
Odd Number
An integer that is not divisible by 2.
Operation
A mathematical process such as addition, subtraction, multiplication, or division.
Opposite Angles
Angles in a quadrilateral that do not share a side.
Order
The arrangement of elements in a sequence or the degree of a polynomial.
Ordinate
The y-coordinate in a Cartesian coordinate system, representing the vertical distance from the x-axis.
Origin
The point (0,0) in a Cartesian coordinate system.
Outlier
A data point that differs significantly from other observations in a dataset.
Parabola
A conic section defined as the set of points equidistant from a focus and a directrix.
Parallelogram
A quadrilateral with two pairs of parallel sides.
Parentheses
Symbols ( ) used to group numbers or expressions in mathematics.
Partition
A division of a set into non-overlapping subsets.
Percentage
A number expressed as a fraction of 100.
Perimeter
The distance around the boundary of a two-dimensional shape.
Permutation
An arrangement of items where order matters.
Perpendicular
Two lines or line segments that intersect at a right angle (90 degrees).
Pi (π)
A mathematical constant representing the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.
Plane
A flat two-dimensional surface extending infinitely in all directions.
Plane Figure
A two-dimensional shape that lies in a plane.
Plus
A symbol (+) indicating addition or a positive number.
Point
A location in space with no dimensions.
Polygon
A closed plane figure with straight sides.
Polyhedron
A three-dimensional shape with flat polygonal faces, straight edges, and vertices.
Polynomial
A mathematical expression consisting of variables and coefficients, involving operations of addition, subtraction, and multiplication.
Positive Number
A number greater than zero.
Power
A number multiplied by itself a specified number of times, represented by an exponent.
Powers of Ten
Numbers that are products of multiplying 10 by itself.
Prime Number
A positive integer greater than 1 with exactly two factors: 1 and itself.
Principal
The original amount of money borrowed or invested, excluding interest.
Prism
A three-dimensional shape with two parallel, congruent polygonal bases connected by rectangular faces.
Probability
A measure of the likelihood that an event will occur.
Product
The result of multiplying two or more numbers.
Proof
A logical argument demonstrating the truth of a mathematical statement.
Proper Fraction
A fraction where the numerator is less than the denominator.
Proportion
An equation stating that two ratios are equal.
Protractor
A tool used to measure angles in degrees.
Pyramid
A three-dimensional shape with a polygonal base and triangular faces that meet at a point (apex).
Pythagorean Theorem
A theorem stating that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (a² + b² = c²).
Quadrant
One of four regions into which a coordinate plane is divided by the x-axis and y-axis.
Quadratic
A polynomial of degree 2.
Quadratic Equation
An equation of the form ax² + bx + c = 0, where a ≠ 0.
Quadrilateral
A polygon with four sides and four angles.
Qualitative
Relating to or involving quality or kind rather than quantity.
Quantitative
Relating to or involving measurement or quantity.
Quantum
A discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents.
Quartile
One of the three points that divide a dataset into four equal groups.
Quotient
The result of dividing one number by another.
Radian
A unit of angular measurement equal to the angle subtended at the center of a circle by an arc equal in length to the radius.
Radius
The distance from the center of a circle or sphere to its edge.
Range
The difference between the largest and smallest values in a dataset.
Rate
A ratio comparing two quantities with different units.
Ratio
A comparison of two quantities, often expressed as a fraction.
Rational Number
A number that can be expressed as the ratio of two integers.
Ray
A part of a line that starts at a point and extends infinitely in one direction.
Real Number
A number that can be found on the number line, including rational and irrational numbers.
Reciprocal
The multiplicative inverse of a number; 1 divided by the number.
Rectangle
A quadrilateral with four right angles and opposite sides equal.
Rectangular Prism
A three-dimensional shape with six rectangular faces.
Rectangular Tank
A box-shaped container with six rectangular faces.
Recursion
The process of defining a function or sequence in terms of itself.
Reflection
A transformation that produces a mirror image of a shape.
Regular Polygon
A polygon where all sides and angles are equal.
Relation
A set of ordered pairs, or a connection between two sets of values.
Remainder
The number left over after division.
Rhombus
A parallelogram with all sides equal in length.
Right Angle
An angle that measures exactly 90 degrees.
Right Triangle
A triangle with one right angle (90 degrees).
Roman Numerals
A numeral system using letters from the Roman alphabet: I, V, X, L, C, D, M.
Root
A solution to an equation, or the number that when multiplied by itself a given number of times equals a specified value.
Rotation
A transformation that turns a shape around a fixed point.
Round
To approximate a number to a specified degree of accuracy.
Row
A horizontal arrangement of items or data.
Scalar
A quantity that has only magnitude, not direction.
Scale
A ratio used to represent the relationship between a drawing and the actual object.
Scalene Triangle
A triangle with all three sides of different lengths.
Scientific Notation
A method of writing very large or very small numbers using powers of 10.
Secant
A line that intersects a circle at two points.
Sector
The region of a circle bounded by two radii and the intercepted arc.
Segment
A part of a circle bounded by an arc and its chord.
Semicircle
Half of a circle, formed by a diameter.
Sequence
An ordered list of numbers following a pattern.
Series
The sum of the terms of a sequence.
Set
A collection of distinct objects or elements.
Side
A line segment forming part of a polygon.
Sign
A symbol indicating positive or negative value.
Significant Figures
The digits in a number that carry meaning contributing to its precision.
Similar Figures
Figures that have the same shape but not necessarily the same size.
Simplify
To reduce an expression to its most basic form.
Sine
A trigonometric function equal to the ratio of the opposite side to the hypotenuse in a right triangle.
Slope
A measure of the steepness of a line, calculated as rise over run.
Solid
A three-dimensional shape or state of matter with definite shape and volume.
Sphere
A perfectly round three-dimensional shape where every point on the surface is equidistant from the center.
Spherical Cap
A portion of a sphere cut off by a plane.
Square
A quadrilateral with four equal sides and four right angles.
Square Pyramid
A three-dimensional shape with a square base and four triangular faces meeting at an apex.
Square Root
A number that when multiplied by itself gives the original number (√a).
Standard Deviation
A measure of the dispersion of a set of data points around the mean.
Statistics
The branch of mathematics dealing with data collection, analysis, interpretation, and presentation.
Straight Angle
An angle that measures exactly 180 degrees.
Subset
A set that is contained within another set.
Subtraction
The arithmetic operation of finding the difference between two numbers.
Subtrahend
The number to be subtracted in a subtraction operation.
Sum
The result of adding two or more numbers.
Surface Area
The total area of the outer surfaces of a three-dimensional shape.
Symbol
A character or sign used to represent a number, operation, or relation.
Symmetric
Having a balanced or mirrored arrangement.
Symmetry
The property of a shape that allows it to be divided into two identical halves.
Synthetic Division
A method for dividing polynomials by linear factors.
Tangent
A line that touches a curve at exactly one point, or a trigonometric function equal to the ratio of sine to cosine.
Tetrahedron
A polyhedron with four triangular faces.
Theorem
A statement that has been proven to be true using logic and prior results.
Theory
A well-substantiated explanation of some aspect of the natural world.
Trapezoid
A quadrilateral with at least one pair of parallel sides.
Trend
A general direction in which something is changing or developing.
Triangle
A polygon with three sides and three angles.
Trigonometry
The branch of mathematics dealing with the relationships between sides and angles of triangles.
Trinomial
A polynomial with exactly three terms.
Trisect
To divide into three equal parts.
Tube
A hollow cylinder.
Ultimate
The final or most significant result in a calculation or process.
Uncertainty
The lack of exact knowledge about a measured quantity.
Union
The set of elements that are in at least one of two or more sets.
Unit
A standard quantity used for measurement, such as meters, liters, or kilograms.
Unit Circle
A circle with radius 1, centered at the origin of a coordinate system.
Unit Fraction
A fraction with a numerator of 1.
Univariate
Involving a single variable.
Universal Set
The set containing all elements under consideration.
Unknown
A variable whose value is to be determined in an equation.
Upper Bound
A number that is greater than or equal to all elements in a set.
Valid
A statement or argument that is logically sound and well-founded.
Variable
A symbol, usually a letter, that represents an unknown value or a quantity that can change.
Variance
A measure of how far a set of numbers are spread out from the mean.
Vector
A quantity having both magnitude and direction, often represented by an arrow.
Venn Diagram
A diagram using overlapping circles to show relationships between sets.
Vertex
A point where two or more lines or edges meet; a corner of a polygon or polyhedron.
Vertical
Perpendicular to the horizontal; upright.
Vertical Angles
Angles formed by two intersecting lines, opposite each other and equal in measure.
Volume
The amount of three-dimensional space occupied by an object or substance, typically measured in cubic units.
Volume Conversion
The process of converting a volume from one unit of measurement to another.
Weight
A measure of the force of gravity on an object, often confused with mass.
Weighted Average
An average where each value is multiplied by a weight before being summed and divided.
Whole Number
A number without fractions or decimals, including zero and positive integers.
Width
The measurement of something from side to side.
With Replacement
A sampling method where an item is returned to the population before the next selection.
Without Replacement
A sampling method where an item is not returned to the population after selection.
Work
The product of force and distance, measured in joules.
Work Hours Calculator
A tool for calculating total hours worked, including overtime and breaks.
x-axis
The horizontal axis in a Cartesian coordinate system.
x-coordinate
The first number in an ordered pair, representing the horizontal position.
x-intercept
The point where a line or curve crosses the x-axis.
XOR (Exclusive OR)
A logical operation that returns true if exactly one of the operands is true.
y-axis
The vertical axis in a Cartesian coordinate system.
y-coordinate
The second number in an ordered pair, representing the vertical position.
y-intercept
The point where a line or curve crosses the y-axis.
Zero
A number with no value, representing nothing or the absence of quantity.
Zero Product Property
If the product of two factors is zero, then at least one of the factors must be zero.
Zero Slope
A horizontal line with a slope of zero.
Zeta Function
A mathematical function used in number theory and physics, especially the Riemann zeta function.
Zettabyte
A unit of digital information equal to 10²¹ bytes or 1 sextillion bytes.
Abacus
A manual calculating device using beads on rods, used for arithmetic operations.
Abelian Group
A group in which the operation is commutative.
Absolute Error
The absolute difference between the measured value and the true value.
Abstract Algebra
The study of algebraic structures such as groups, rings, and fields.
Acceleration
The rate of change of velocity with respect to time.
Accuracy
The degree to which a measurement conforms to the true value.
Ackermann Function
A recursive function that grows extremely fast, used in computability theory.
Addition Formula
A formula for adding two trigonometric expressions.
Additive Inverse
The number that when added to a given number yields zero.
Adjacency Matrix
A square matrix used to represent a finite graph.
Affine Transformation
A mapping that preserves points, straight lines, and planes.
Alexandrov Geometry
A branch of geometry dealing with metric spaces with curvature bounds.
Algebraic Equation
An equation involving algebraic expressions.
Algebraic Number
A number that is a root of a non-zero polynomial with rational coefficients.
Angle Bisector Theorem
A theorem stating the relationship between the sides and angle bisector of a triangle.
Antiderivative
A function whose derivative is another given function.
Approximation
A value that is close to but not exactly equal to the true value.
Arc Length
The distance along a curve or arc.
Associative Law
The law stating that the grouping of numbers in addition or multiplication does not affect the result.
Axiom
A statement accepted as true without proof, used as a starting point for reasoning.
Bayes' Theorem
A theorem relating the conditional probabilities of two events.
Bernoulli Distribution
A probability distribution for a random variable with two possible outcomes.
Bessel Function
A family of solutions to Bessel's differential equation, used in physics and engineering.
Biconditional
A logical statement that is true when both parts have the same truth value.
Bifurcation
A change in the structure of a dynamical system as a parameter varies.
Binary Relation
A relation between two sets, represented as a set of ordered pairs.
Boltzmann Constant
A physical constant relating the average kinetic energy of particles to temperature.
Boolean Algebra
An algebraic structure dealing with truth values and logical operations.
Bounded Function
A function whose output values are within a finite range.
Calculus of Variations
A field of mathematics dealing with optimizing functions of functions.
Cantor Set
A fractal set constructed by removing middle thirds of line segments.
Cauchy Sequence
A sequence whose terms become arbitrarily close to each other.
Central Limit Theorem
A theorem stating that the distribution of sample means approximates a normal distribution.
Chebyshev Polynomial
A polynomial family used in approximation theory and numerical analysis.
Cholesky Decomposition
A matrix decomposition method used for solving linear systems.
Closed Form
An expression that can be evaluated in a finite number of operations.
Combinatorics
The branch of mathematics concerned with counting and arranging objects.
Compact Space
A topological space in which every open cover has a finite subcover.
Complex Analysis
The study of functions of complex variables.
Confidence Interval
A range of values likely to contain an unknown population parameter.
Conjugate Gradient
An algorithm for solving systems of linear equations.
Connected Graph
A graph in which there is a path between every pair of vertices.
Constraint
A condition that must be satisfied in an optimization problem.
Continuity Equation
An equation expressing the conservation of a quantity in a system.
Convex Set
A set where the line segment between any two points is contained in the set.
Correlation
A measure of the linear relationship between two variables.
Covariance
A measure of how two variables change together.
Cramer's Rule
A method for solving systems of linear equations using determinants.
Critical Point
A point where the derivative of a function is zero or undefined.
Curve Fitting
The process of constructing a curve that best fits a set of data points.
Cyclic Group
A group that can be generated by a single element.
Decision Theory
The study of rational decision-making under uncertainty.
Dedekind Cut
A method of constructing the real numbers from rational numbers.
Degree of Freedom
The number of independent variables or parameters in a system.
Delta Function
A generalized function used in physics and mathematics.
Descartes' Rule
A rule for determining the number of positive roots of a polynomial.
Determinant
A scalar value computed from a square matrix with many applications.
Diagonal Matrix
A matrix with non-zero entries only on the main diagonal.
Differential Geometry
The study of geometry using differential calculus.
Digital Signal Processing
The processing of signals using digital techniques.
Dirac Equation
A relativistic quantum mechanical equation for spin-1/2 particles.
Dirichlet Function
A function that is 1 on rational numbers and 0 on irrational numbers.
Discrete Mathematics
The branch of mathematics dealing with discrete objects.
Divergence Theorem
A theorem relating the flux through a surface to the divergence inside.
Dual Number
A number system extending real numbers with a nilpotent element.
Eigenvalue
A scalar associated with a linear transformation.
Eigenvector
A non-zero vector that is scaled by a linear transformation.
Elliptic Curve
A curve defined by a cubic equation, used in cryptography.
Empirical Rule
A rule stating that for normal distributions, 68-95-99.7% of data falls within standard deviations.
Energy
The capacity to do work, measured in joules.
Entropy
A measure of disorder or randomness in a system.
Epimorphism
A surjective homomorphism in category theory.
Ergodic Theory
The study of the long-term average behavior of dynamical systems.
Euclidean Algorithm
An algorithm for computing the greatest common divisor of two numbers.
Eulerian Path
A path in a graph that visits every edge exactly once.
Exponentiation
The operation of raising a base to a power.
Extreme Value Theorem
A theorem stating that a continuous function on a closed interval attains maximum and minimum values.
Fermat's Last Theorem
A theorem stating that no three positive integers a, b, c satisfy a^n + b^n = c^n for n > 2.
Fibonacci Number
A number in the Fibonacci sequence.
Field
A set with two operations (addition and multiplication) satisfying certain properties.
Fourier Transform
A transform that decomposes a function into its frequency components.
Fractional Calculus
A generalization of calculus with non-integer order derivatives.
Fundamental Group
An algebraic structure capturing the essential shape of a topological space.
Gaussian Elimination
A method for solving systems of linear equations.
Generating Function
A series whose coefficients encode information about a sequence.
Geodesic
The shortest path between two points in a curved space.
Gibbs Free Energy
A thermodynamic potential used to determine spontaneity of a process.
Gradient Descent
An optimization algorithm for finding the minimum of a function.
Graph Theory
The study of graphs and their properties.
Green's Theorem
A theorem relating line integrals and double integrals over a region.
Grothendieck Topology
A generalization of topology in category theory.
Hamiltonian Path
A path in a graph that visits every vertex exactly once.
Hilbert Space
A complete inner product space, used in functional analysis.
Homology
A concept in algebraic topology measuring holes in a space.
Hypergeometric Function
A special function defined by a hypergeometric series.
Ideal
A special subset of a ring in abstract algebra.
Integral Transform
A transform that maps a function to another function via an integral.
Isomorphism
A structure-preserving mapping between two mathematical structures.
Jacobi Matrix
A matrix of first-order partial derivatives.
Jordan Form
A canonical form for matrices over an algebraically closed field.
Kalman Filter
An algorithm for estimating the state of a linear dynamical system.
Kernel
The set of elements mapped to zero by a function.
Lagrange Multiplier
A method for finding extrema of a function with constraints.
Laplace Transform
A transform used in engineering and physics to solve differential equations.
Lebesgue Measure
A measure on the real line that generalizes length.
Lie Group
A group that is also a smooth manifold.
Logistic Map
A simple model of population growth that exhibits chaotic behavior.
Lorentz Transform
A transform relating space and time coordinates in relativity.
Lyapunov Function
A function used to prove stability of dynamical systems.
Manifold
A topological space that locally resembles Euclidean space.
Markov Chain
A stochastic process with the Markov property.
Mersenne Prime
A prime number of the form 2^n - 1.
Metric Space
A set with a distance function satisfying certain properties.
Minkowski Space
A four-dimensional space combining three dimensions of space and one of time.
Monte Carlo Method
A computational algorithm that relies on random sampling.
Morphism
A structure-preserving map in category theory.
Nash Equilibrium
A concept in game theory where players' strategies are optimal given others' strategies.
Neural Network
A computational model inspired by biological neural networks.
Noetherian Ring
A ring that satisfies the ascending chain condition on ideals.
Non-Euclidean Geometry
Geometry that does not satisfy Euclid's parallel postulate.
Normal Distribution
A continuous probability distribution characterized by a bell-shaped curve.
Number Theory
The branch of mathematics dealing with integers and their properties.
Numerical Analysis
The study of algorithms for solving mathematical problems numerically.
Operator
A mapping from one vector space to another.
Optimization
The process of finding the best solution to a problem.
Ordinal Number
A number representing the position of an element in a well-ordered set.
Partial Differential Equation
An equation involving partial derivatives of a function.
Partition Function
A function used in statistical mechanics to describe a system.
Pascal's Triangle
A triangular array of binomial coefficients.
Perceptron
A simple neural network used for binary classification.
Permutation Group
A group whose elements are permutations of a set.
Perturbation Theory
A method for finding approximate solutions to problems.
Phase Space
A space describing all possible states of a dynamical system.
Poincare Conjecture
A topological theorem stating that every simply connected 3-manifold is a sphere.
Polytope
A geometric object with flat faces and straight edges.
Power Set
The set of all subsets of a given set.
Principal Component Analysis
A statistical method for reducing data dimensionality.
Probability Density Function
A function describing the likelihood of a random variable taking a given value.
Proximal Operator
An operator used in optimization and signal processing.
Quaternion
A number system that extends complex numbers to four dimensions.
Queueing Theory
The study of waiting lines and service systems.
Ramsey Theory
The study of conditions for the occurrence of order in a structure.
Random Variable
A variable whose values depend on random outcomes.
Rational Function
A function that is the ratio of two polynomials.
Real Analysis
The branch of mathematics studying real numbers and functions.
Relational Algebra
A set of operations for manipulating relational databases.
Representation Theory
The study of representing algebraic structures as linear transformations.
Riemann Sum
A method for approximating the integral of a function.
Riemannian Geometry
The study of curved spaces with a metric.
Ring
An algebraic structure with two operations: addition and multiplication.
Saddle Point
A point in a function where the gradient is zero but not a maximum or minimum.
Schrödinger Equation
A fundamental equation in quantum mechanics.
Semigroup
An algebraic structure with an associative operation.
Sequential Analysis
A statistical method where sample size is not fixed in advance.
Set Theory
The branch of mathematics dealing with sets and their properties.
Singular Value Decomposition
A factorization of a matrix into three matrices.
Spinor
A mathematical object used in quantum mechanics.
Stochastic Process
A collection of random variables indexed by time.
Subspace
A subset of a vector space that is itself a vector space.
Surjective Function
A function where every element in the codomain has a pre-image.
Symplectic Geometry
The study of manifolds with a symplectic form.
Tensor
A mathematical object that generalizes scalars, vectors, and matrices.
Topology
The study of geometric properties preserved under continuous deformations.
Transformation
A mapping from one space to another.
Transpose
The operation of flipping a matrix across its diagonal.
Tree
A connected graph with no cycles.
Triangulation
The process of dividing a shape into triangles.
Trivial
A simple or obvious mathematical result.
Tuple
An ordered list of elements.
Unbounded
Not having a finite limit or bound.
Uniform Convergence
A type of convergence of functions.
Unique Factorization
The property of a domain where every element has a unique prime factorization.
Unitary Matrix
A complex matrix whose conjugate transpose equals its inverse.
Universal Algebra
The study of algebraic structures in a general framework.
Validity
The property of a logical argument being well-founded.
Value
The result of evaluating a function or expression.
Variational Method
A method for finding extrema using variations.
Vector Space
A set of vectors with addition and scalar multiplication.
Vibration
The oscillation of a system about an equilibrium point.
Viscosity
A measure of a fluid's resistance to flow.
Wave Function
A function describing the quantum state of a system.
Wavelet
A function used in signal processing and data compression.
Weight
A measure of the importance or magnitude of a value.
Weierstrass Function
A continuous function that is nowhere differentiable.
Wronskian
A determinant used to determine linear independence of functions.
Zeta Potential
A measure of the electrical potential at the sliding plane of a particle.
401(k)
A qualified employer-sponsored retirement plan that allows employees to save and invest a portion of their paycheck before taxes are deducted.
Annuity
A series of equal payments made at regular intervals over a specified period, often used as a retirement income stream.
Asset
An item of economic value owned by an individual or corporation, such as cash, real estate, or investments.
Balance Sheet
A financial statement that summarizes a company's assets, liabilities, and shareholders' equity at a specific point in time.
Bond
A fixed income instrument that represents a loan made by an investor to a borrower (typically corporate or governmental).
Budget
An estimate of revenue and expenses over a specified future period, used for planning and control.
Capital Gain
The profit from the sale of an asset or investment, calculated as the selling price minus the purchase price.
Cash Flow
The net amount of cash moving into and out of a business, indicating its liquidity and financial health.
Credit Score
A numerical expression of a person's creditworthiness, based on their credit history and used by lenders to assess risk.
Debit
An entry recording a sum owed or an expense; in accounting, an increase in assets or a decrease in liabilities.
Deductible
The amount you pay for covered health care services before your insurance plan starts to pay.
Diversification
A risk management strategy that mixes a wide variety of investments within a portfolio to reduce exposure to any single asset.
Dividend
A portion of a company's earnings distributed to shareholders, typically paid in cash or additional stock.
Equity
The value of an ownership interest in a company or property, calculated as total assets minus total liabilities.
Expense
The cost incurred for a business or personal purpose, reducing net income.
Gross Profit
A company's total revenue minus the cost of goods sold (COGS), indicating profitability before operating expenses.
Income Statement
A financial statement that shows a company's revenues and expenses over a period, resulting in net income or loss.
Index Fund
A type of mutual fund or ETF with a portfolio constructed to match a market index, such as the S&P 500.
Inflation
The rate at which the general level of prices for goods and services is rising, eroding purchasing power.
IRA (Individual Retirement Account)
A tax-advantaged savings account designed to help individuals save for retirement.
Liability
A company's financial debt or obligations that arise during the course of business operations.
Mutual Fund
A pool of money collected from many investors to invest in securities like stocks, bonds, and other assets.
Net Present Value (NPV)
The difference between the present value of cash inflows and outflows over a period, used to evaluate investment profitability.
Net Profit
A company's total earnings after subtracting all expenses, taxes, and costs; also known as the bottom line.
Portfolio
A collection of financial investments like stocks, bonds, commodities, and cash, held by an individual or institution.
Premium
An amount paid periodically to an insurer for coverage, or a price paid for a bond above its face value.
Return on Investment (ROI)
A measure of the profitability of an investment, calculated as (net profit / cost of investment) × 100.
Revenue
The total income generated by a business from its normal activities, such as sales of goods and services.
Roth IRA
An individual retirement account allowing tax-free growth and tax-free withdrawals in retirement, funded with after-tax dollars.
Stock
A share of ownership in a corporation, representing a claim on the company's assets and earnings.
Tax Bracket
A range of incomes taxed at a given rate; as income increases, it may move into a higher tax bracket.
Yield
The earnings generated and realized on an investment over a period, expressed as a percentage of the investment amount.
Aerobic
Exercise that increases the need for oxygen, improving cardiovascular fitness and endurance.
Anaerobic
Exercise that involves short, high-intensity activity where oxygen demand exceeds supply, building muscle strength.
Basal Metabolic Rate (BMR)
The number of calories required to keep your body functioning at rest, accounting for the majority of daily energy expenditure.
Blood Pressure
The force of blood against the walls of arteries, measured as systolic and diastolic pressures.
Body Mass Index (BMI)
A measure of body fat based on height and weight, calculated as weight (kg) / height (m²).
Calorie
A unit of energy from food; the amount of energy needed to raise the temperature of one gram of water by one degree Celsius.
Carbohydrate
A macronutrient providing energy, found in foods like bread, rice, pasta, and fruits.
Cardio
Exercise that raises the heart rate and improves cardiovascular health, such as running, cycling, or swimming.
Cholesterol
A waxy substance found in blood, used for building cells; high levels can increase the risk of heart disease.
Daily Caloric Intake
The total number of calories consumed per day, which should align with energy expenditure for weight management.
Exercise
Physical activity done to improve health and fitness, including aerobic, strength, and flexibility training.
Fat
A macronutrient that provides energy, supports cell function, and helps absorb vitamins; also essential for hormone production.
Flexibility
The ability of a joint to move through its full range of motion, reducing injury risk and improving performance.
Glucose
A simple sugar that is a primary source of energy for the body; blood glucose levels are regulated by insulin.
Heart Rate
The number of heartbeats per minute; resting heart rate is an indicator of cardiovascular fitness.
Hydration
The process of providing adequate water to the body to maintain fluid balance and support bodily functions.
Insulin
A hormone produced by the pancreas that regulates blood glucose levels by facilitating cellular uptake.
Lean Body Mass
The weight of everything in the body except fat, including muscle, bone, and organs.
Macronutrient
Nutrients needed in large amounts: carbohydrates, proteins, and fats, providing energy and structural support.
Maximum Heart Rate
The highest heart rate an individual can safely achieve through exercise, roughly estimated as 220 minus age.
Metabolism
The chemical processes that occur within a living organism to maintain life, including energy conversion and tissue repair.
Mineral
An inorganic nutrient essential for body functions, such as calcium for bones and iron for blood.
Oxygen Saturation
The percentage of hemoglobin saturated with oxygen, indicating how well oxygen is being delivered to tissues.
Protein
A macronutrient essential for building and repairing tissue, making enzymes, and supporting immune function.
Pulse
The rhythmic expansion of an artery as blood is pumped through it, felt as a throbbing sensation.
Resting Heart Rate
The heart rate when a person is at rest; a lower resting rate generally indicates better cardiovascular fitness.
Strength Training
Physical activity designed to improve muscle strength and endurance, often using weights or resistance.
Vitamin
An organic compound essential for normal growth and nutrition, required in small amounts for metabolic processes.
Waist-to-Hip Ratio
The ratio of waist circumference to hip circumference, used as an indicator of health risk and body fat distribution.
Adjustable-Rate Mortgage (ARM)
A mortgage with an interest rate that changes periodically based on a market index, affecting monthly payments.
Amortization Schedule
A table detailing each periodic payment on a loan, showing the amount applied to principal and interest over time.
Annual Percentage Rate (APR)
The annual rate charged for borrowing, including fees and costs, expressed as a percentage of the loan amount.
Closing Costs
Fees paid at the closing of a real estate transaction, including appraisal, title search, and attorney fees.
Escrow
A financial arrangement where a third party holds funds or documents on behalf of two transacting parties until conditions are met.
Fixed-Rate Mortgage
A mortgage with an interest rate that remains constant throughout the loan term, providing predictable payments.
Interest Rate
The proportion of a loan charged as interest to the borrower, typically expressed as an annual percentage.
Loan
A sum of money borrowed from a lender, typically repaid with interest over a specified period.
Mortgage
A loan used to purchase real estate, with the property itself serving as collateral for the debt.
Principal
The original sum of money borrowed in a loan, excluding interest and fees.
Private Mortgage Insurance (PMI)
Insurance required for conventional loans with a low down payment, protecting the lender if the borrower defaults.
Refinancing
Replacing an existing loan with a new one, usually to obtain a lower interest rate or better terms.
Underwriting
The process of evaluating a loan application to determine the borrower's risk and the terms of the loan.
Bonus
An additional payment beyond regular salary, often tied to performance, company profits, or other milestones.
Commission
A payment based on a percentage of sales, commonly used in sales and brokerage roles.
Defined Benefit
A pension plan where benefits are predetermined based on salary history and years of service, providing a fixed payout.
Defined Contribution
A pension plan where contributions are defined, but benefits depend on investment performance, such as a 401(k).
Federal Withholding
The amount of tax withheld from a paycheck for federal income tax, based on the employee's W-4 form.
FICA
Federal Insurance Contributions Act tax, funding Social Security and Medicare, deducted from employees' paychecks.
Gross Income
Total income before any deductions, including wages, bonuses, and other compensation.
Health Insurance Premium
The amount paid for health insurance coverage, often deducted from an employee's paycheck.
Medicare
A federal health insurance program for people aged 65 and older, funded by payroll taxes.
Net Income
Take-home pay after all deductions, including taxes, benefits, and retirement contributions.
Overtime
Work done beyond regular hours, often paid at a higher rate (e.g., 1.5 times the regular hourly wage).
Payroll Tax
Tax withheld from an employee's salary by an employer, including federal, state, and local taxes.
Pension
A retirement plan that provides a fixed sum upon retirement, based on years of service and salary history.
Salary
A fixed regular payment, typically paid monthly or biweekly, for work performed.
Social Security
A federal program providing benefits to retirees, disabled individuals, and survivors, funded by payroll taxes.
State Tax
Tax levied by a state on income, varying by state and often deducted from employee paychecks.
Vesting
The process of earning the right to pension benefits or stock options, typically over a period of service.
Wage
Compensation based on an hourly rate, typically paid for manual or clerical work.