Math Concepts

Question 1

Systems are generally tested for this property by calculating the largest Lyapunov exponent and seeing if it is positive.

Answer 1

Chaos Theory

Question 2

De Morgan’s laws state that this operation performed on the union of two sets is equal to the intersection of this operation performed on each of the sets.

Answer 2

Complementary

Question 3

Basic arithmetic operation of combining two or more numbers to obtain their sum.

Answer 3

Addition

Question 4

Its equation is x squared plus y squared equals r squared.

Answer 4

Circle

Question 5

For a Cartesian space it is the number of coordinates needed to specify a point.

Answer 5

Dimension

Question 6

This quantity for a smooth manifold is the number of independent variables needed to parametrize it, and for a vector space this quantity is the cardinality of the largest linearly independent subset.

Answer 6

Dimension

Question 7

If a function whose values are numbers of this type is differentiable at every point of its domain, then it is known as a holomorphic function.

Answer 7

Complex Numbers

Question 8

This operation can be performed on a complex function if both its real and imaginary parts are harmonic, or equivalently =, that it satisfies the Cauchy-Riemann equations, a condition called holomorphicity.

Answer 8

Derivative

Question 9

A geometric problem that involves dividing an angle into three equal parts using only a compass and straightedge.

Answer 9

Angle Trisection

Question 10

Written as A given B equals probability of B given A times probability of B given A times probability of A over probability of B.

Answer 10

Bayes’ Theorem

Question 11

Characterized by the famous “butterfly effect”, where small changes in initial conditions can lead to significant differences in outcomes.

Answer 11

Chaos Theory

Question 12

The Scharz-Christoffel mapping is applied on sets of these numbers, as are all conformal mappings.

Answer 12

Complex Numbers

Question 13

The study of random variables that do not have this property is called free probability.

Answer 13

Commutative/Commutative Property

Question 14

For an orthogonal projection, the kernel and image have this relationship.

Answer 14

Complementary

Question 15

In the calculus of variations, the smallest value of this quantity for distinct objects is the geodesic.

Answer 15

Distance

Question 16

Contrasted with concave.

Answer 16

Convexity

Question 17

This function is on the main diagonal of a two-dimensional rotation matrix.

Answer 17

Cosine function/Cosine

Question 18

Has a volume equal to one-third pi time r squared times h.

Answer 18

Cone

Question 19

Applying this operation to a constant give zero since it gives the instantaneous rate of change.

Answer 19

Derivative

Question 20

It is the base for solutions to the differential equation y-prime equals y, and the derivative of this number to the power x is equal to itself.

Answer 20

e/Euler’s Number

Question 21

According to the inverse function theorem, a function which has continuity and this property is homeomorphic.

Answer 21

Differentiable

Question 22

This value gives the ratio of the area of a shape after a linear transformation to the original area.

Answer 22

Determinant

Question 23

Its namesake law is a generalization of the Pythagorean Theorem.

Answer 23

Cosine function/Cosine

Question 24

This number is equal to approximately 2.718.

Answer 24

e/Euler’s Number

Question 25

Both communitive and associative

Answer 25

Addition and Multiplication

Question 26

This line segment is the longest possible chord of a circle, since it passes through the center.

Answer 26

Diameter

Question 27

This value equals zero when a homogeneous equation has a nontrivial solution.

Answer 27

Determinant

Question 28

Name this operation taken on matrices and symbolized by straight lines.

Answer 28

Determinant

Question 29

The difference between them and their totient is at least two.

Answer 29

Composite Number

Question 30

This type of equation relates a function to its rate of change.

Answer 30

Differential Equations

Question 31

A double angle identity for this function is that with an input of two theta, it equals the quantity on minus the tangent squared of theta over the quantity one plus the tangent squared of theta.

Answer 31

Cosine function/Cosine

Question 32

Arbitrarily long sequences of these numbers can be found by starting at n-factorial plus n, and there is no jump in the function pi of x at each of them.

Answer 32

Composite Number

Question 33

Solutions from Cramer’s rule can be found by taking the quotient of two values for this quantity that can be found by expanding along a row.

Answer 33

Determinant

Question 34

Although every differentiable function has this property, the opposite does not hold- as exemplified by the Weirestrass function being not differentiable, despite having this property.

Answer 34

Continuity

Question 35

The impossibility of trisecting an arbitrary angle using only those two tools.

Answer 35

Angle Trisection

Question 36

The covering variety of this property is always less than or equal to the large inductive variety.

Answer 36

Dimension

Question 37

An algorithm named for Euclid can be used to find the GCD, or to perform this operation on integers. (The Euclidean Algorithm)

Answer 37

Division

Question 38

Can be used to solve the Monty Hall problem.

Answer 38

Bayes’ Theorem

Question 39

Identify this property that applies to addition and multiplication in which x plus y equals y plus x.

Answer 39

Commutative/Commutative Property

Question 40

Used to calculate the posterior probability and relates the actual probability of an event to the measured probability in a test.

Answer 40

Bayes’ Theorem

Question 41

Refers to the measurement of the extent or size of a two-dimensional space or shape.

Answer 41

Area

Question 42

Matrices with the property described by this term are both upper triangular and lower triangular, and their only nonzero elements form a line between the upper left and lower right corners.

Answer 42

Diagonal

Question 43

Give this term for lines which are neither horizontal nor vertical.

Answer 43

Diagonal

Question 44

An interval with this property contains its limit points, which means that it includes both of its endpoints.

Answer 44

Closed

Question 45

The nth Catalan number can be found using one over n plus one times one of these numbers.

Answer 45

Binomial Coefficients

Question 46

Integrating functions of this type gives a quartic equation, while differentiating them gives a quadratic.

Answer 46

Cubic

Question 47

The process of finding a derivative is called what?

Answer 47

Differentiation

Question 48

This term refers to angles whose values sum to 90.

Answer 48

Complementary

Question 49

These numbers are crossed out in the Sieve of Eratosthenes, because they are divisible by a lower, circled number.

Answer 49

Composite Number

Question 50

Prince Rupert’s problem deals with two of these and it is an equilateral zonohedron.

Answer 50

Cube

Question 51

The tesseract is a higher-dimensional analogue of this shape.

Answer 51

Cube

Question 52

What measurement is equal to twice the circle’s radius.

Answer 52

Diameter

Question 53

One type of this operation occurs when there are multiple variables, and it is called partial.

Answer 53

Derivative

Question 54

One of these is named after Dijkstra

Answer 54

Algorithm

Question 55

In the standard normal density function, this number is raised to the minus x squared over two power.

Answer 55

e/Euler’s Number

Question 56

Big-O used to express the amount of time and space these procedures use.

Answer 56

Algorithm

Question 57

Can be calculated using Brettschneider’s formula.

Answer 57

Area of a Quadrilateral

Question 58

This is an even trigonometric function which is the reciprocal of secant and the cofunction of sine.

Answer 58

Cosine function/Cosine

Question 59

This is evaluated to find a characteristic equation, which is solved to find eigenvalues.

Answer 59

Determinant

Question 60

The midpoint of each side of a triangle, the foot of each altitude, and the midpoint of each line segment stretching from the vertex of the orthocenter are the nine points used to define one of these shapes (This type would be called the nine-point one).

Answer 60

Circle

Question 61

Families of these geometric shapes orthogonal to one another are named for Apollonius of Perga.

Answer 61

Circle

Question 62

Edward Larenz pioneered this field of math by concluding that weather is nearly impossible to predict accurately due to its sensitivity to initial conditions.

Answer 62

Chaos Theory

Question 63

This quantity raised to the power of i pi is equal to negative one.

Answer 63

e/Euler’s Number

Question 64

Groups with this property have only normal subgroups and are called abelian.

Answer 64

Commutative/Commutative Property

Question 65

A “synthetic” version of this operation can be used on polynomials.

Answer 65

Division

Question 66

Real functions have this property is for all x in the domain, the limit of the function as it approaches x equals the function’s value at that point.

Answer 66

Continuity

Question 67

For a group of sets of this type in the plane, if any three of the sets intersect, then they all intersect by Helly’s Theorem.

Answer 67

Convexity

Question 68

The classic problem of “squaring” this shape was shown to be impossible when pi was proven to be transcendental.

Answer 68

Circle

Question 69

It has thirteen axes of symmetry and eleven different nets.

Answer 69

Cube

Question 70

One theorem named for Thales concerns right angles formed by three points on this shape.

Answer 70

Circle

Question 71

This mathematical operation is the inverse of the integral.

Answer 71

Derivative

Question 72

One method of calculating this operation involves expansion by minors, which takes into account that this function is alternation multilinear.

Answer 72

Determinant

Question 73

DeMoivre’s theorem (calculating roots of this number) can be used when raising this type of number to a power.

Answer 73

Complex Numbers

Question 74

The hyperbolic version of this function defines a catenary, and equals half the quantity e to the x plus e to the negative x.

Answer 74

Cosine function/Cosine

Question 75

Surface area is twenty-four times its radius squared and its volume is eight times its radius cubed.

Answer 75

Cube

Question 76

A well-known Axiom A diffeomorphism in this field of study is the Smale horseshoe.

Answer 76

Chaos Theory

Question 77

The primary difference between a group and a quasi-group is that a quasi-group lacks this property.

Answer 77

Associative Property

Question 78

Pressure is defined as force per units of this quantity.

Answer 78

Area

Question 79

One of these things is classified as homogeneous if it does not contain any functions in terms of x that are not multiplied by other functions, which means that it has no constant terms.

Answer 79

Differential Equations

Question 80

Name these “coefficients” that describe the number of ways to choose k things from n possibilities, or n choose k.

Answer 80

Binomial Coefficients

Question 81

Finite intervals that include both endpoints are known by this term and denoted with square brackets.

Answer 81

Closed

Question 82

ABC conjecture considers A+B=C (the largest of these numbers is this function of the other two)

Answer 82

Addition

Question 83

This theory features fractal entities called strange attractors, such as one named after Edward Larenz.

Answer 83

Chaos Theory

Question 84

Can be found “under a curve” via integration.

Answer 84

Area

Question 85

CLRS textbook is an introduction to these things

Answer 85

Algorithm

Question 86

It’s the inverse of multiplication

Answer 86

Division

Question 87

Three-dimensional analogue of a square.

Answer 87

Cube

Question 88

Unit one of these is described by x squared plus y squared equals 1. (and has an area of pi)

Answer 88

Circle

Question 89

The generalized Poincare conjecture sorts of manifolds into top, piecewise linear, or having this property.

Answer 89

Differentiable

Question 90

If f has this property, then f of a is always equal to the limit of f of x as x approaches a.

Answer 90

Continuity

Question 91

The Euclidean Algorithm gives the largest integer that can be used for this action on two different integers.

Answer 91

Division

Question 92

Functions with the complex version of this property have du dx equal dv dy and du dy equal negative dv dx, which are known as the Cauchy-Riemann equations.

Answer 92

Differentiable

Question 93

This operation produces fractions.

Answer 93

Division

Question 94

Subtraction possesses the “anti” form of this property.

Answer 94

Commutative/Commutative Property

Question 95

This transcendental irrational is the base of the natural logarithm.

Answer 95

e/Euler’s Number

Question 96

Two disjoint open sets of this type can always be separated by a hyperplane.

Answer 96

Convexity

Question 97

Its result is called a quotient.

Answer 97

Division

Question 98

Gauss was the first person to illustrate this theorem, which requires that its inputs be relatively prime, using a system of modular congruences.

Answer 98

Chinese Remainder Theorem

Question 99

Several theorems about these numbers can be proven using the maximum modulus principle.

Answer 99

Complex Numbers

Question 100

Carmichael numbers are numbers of this type that satisfy Fermat’s Little Theorem.

Answer 100

Composite Number

Question 101

Repetition of this function is denoted by a capital sigma.

Answer 101

Addition

Question 102

Positive in the first and fourth quadrants, in a right triangle it is the adjacent leg over the hypotenuse.

Answer 102

Cosine function/Cosine

Question 103

This operation applied to a composition of two functions is this operation applied to the second according to the chain rule.

Answer 103

Differentiation

Question 104

Name this shape whose slices are used to generate ellipses, parabolas, and hyperbolas.

Answer 104

Cone

Question 105

The sign of this operation tells whether a linear transformation preserves orientation.

Answer 105

Determinant

Question 106

This measure is 2 for polygons and 3 for solids.

Answer 106

Dimension

Question 107

The shoestring methos for finding the area of a polygon is based on a formula that uses this operation.

Answer 107

Determinant

Question 108

This value can be used to determine the nature roots of a function.

Answer 108

Discriminant

Question 109

The incomplete beta function can compute the cumulative density function for this object’s namesake probability distribution.

Answer 109

Binomial

Question 110

Given three points on a circle, Thales’ Theorem says that is two of the points can form this, then the three points can form a right angle.

Answer 110

Diameter

Question 111

When this operation can be repeated infinitely, the input function is called smooth.

Answer 111

Differentiation

Question 112

This function is squared in Malus’s law and appears in a law relating the radiant intensity of Lambertian surfaces.

Answer 112

Cosine function/Cosine

Question 113

The general ability to do this action separates fields from commutative rings. The ability to always do this action also separates the mathematical set “Q” from “Z”.

Answer 113

Division

Question 114

On a closed interval, a function of this type will assume all intermediate value.

Answer 114

Continuity

Question 115

This operation finds a function’s instantaneous rate of change, the inverse of integration.

Answer 115

Differentiation

Question 116

Tartaglia taught Cardano a method for solving equations of this type, and eliminating one of their terms is called “depressing” them.

Answer 116

Cubic

Question 117

Taking this operation on a set produces a set which is disjoint from it.

Answer 117

Complementary

Question 118

Reciprocal of a number (x)

Answer 118

1/x

Question 119

A line segment connecting two points on this shape is known as a chord.

Answer 119

Circle

Question 120

Two methods for calculating this value are Dodgson condensation and cofactor expansion.

Answer 120

Determinant

Question 121

Not defined if the second operand is zero.

Answer 121

Division

Question 122

Mathematical operations have this property when the result is always the same set as the operands.

Answer 122

Closed

Question 123

Minkowski’s taxicab geometry created a version of this quantity named for Manhattan.

Answer 123

Distance

Question 124

A metric space is a set in which this notion can be quantified, and on those spaces, this notion must satisfy non-negativity, symmetry, and the triangle inequality.

Answer 124

Distance

Question 125

The law of this function states that, for a triangle ABC, c squared equals a squared plus b squared minus 2 a b times this function of x is the secant of x.

Answer 125

Cosine function/Cosine

Question 126

This word describes a six-faced Platonic solid, or a polynomial of degree three.

Answer 126

Cubic

Question 127

Each ratio in the law of sines is equal to this measurement for the circle circumscribed about the triangle.

Answer 127

Diameter

Question 128

One of these structures is named for Peter Shor

Answer 128

Algorithm

Question 129

The smallest set of this type that encloses a given set is known as that set’s “hull” of this type.

Answer 129

Convexity

Question 130

The fundamental theorem of algebra states that any polynomial has at least one root in this set.

Answer 130

Complex Numbers

Question 131

Refer to step-by-step procedures or sets of rules used to perform tasks.

Answer 131

Algorithm

Question 132

This quantity is the separation between two points in space.

Answer 132

Distance

Question 133

This action either produces rationals from the integers or yields a remainder, and you can’t do it with zero.

Answer 133

Division

Question 134

A function with this property within a closed and bounded interval will attain a minimum and maximum at least once by the extreme value theorem.

Answer 134

Continuity

Question 135

This word describes a method of proof that attempts to write every number in binary, then constructs a number that cannot have been represented in that list; that argument shows that the real numbers are uncountable and was advanced by Cantor.

Answer 135

Diagonal

Question 136

This word denotes polygons whose internal angles are all less than 180 degrees because it lacks an internal reflex angle.

Answer 136

Convexity

Question 137

Like its dual, for whom its symmetries are named, this shape has 24 rotational symmetries.

Answer 137

Cube

Question 138

For the boundary of the Mandelbrot Set, the “fractal” version of this quantity is two, while for a tesseract this quantity is equal to four.

Answer 138

Dimension

Question 139

An ancient problem asks if it is possible to construct a square with area equal to a given one of these shapes using a compass and straightedge (known as “squaring” this shape).

Answer 139

Circle

Question 140

The arc length of a function f from a to b is the integral of square root quantity one plus this operation of f squared.

Answer 140

Differentiation

Question 141

Four x cubed minus three x equals a constant used to determine if the classical version of this task can be done.

Answer 141

Angle Trisection

Question 142

This system is seen in dynamical systems like the logistical map and double pendulum.

Answer 142

Chaos Theory

Question 143

Christoffel symbols are used to calculate the “covariant” form of this operation.

Answer 143

Derivative

Question 144

This property works for multiplication or addition, but not for division or subtraction.

Answer 144

Associative Property

Question 145

This adjective describes the distribution modeling the number of successes in a sample of size n drawn with replacement.

Answer 145

Binomial

Question 146

For a system of linear equations, doping this on collections of coefficients is used to find solutions according to Cramer’s rule.

Answer 146

Determinant

Question 147

This word describes the lowest-degree equation that is guaranteed to have both a finite relative minimum as well as a real root.

Answer 147

Cubic

Question 148

Can be drawn without lifting the pencil.

Answer 148

Continuity

Question 149

A mathematical concept that deals with modular arithmetic and finding solutions to systems of modular equations. Named after mathematician Sun Tzu (Sunzi).

Answer 149

Chinese Remainder Theorem

Question 150

This operation finds the slope of a line tangent to a curve.

Answer 150

Differentiation

Question 151

In conics, if this value is less than 0, a circle or ellipse forms.

Answer 151

Discriminant

Question 152

This number is the limit, as n goes to infinity, of the quantity “1 plus 1-over-n” to the n, which you might run into while calculating compound interest.

Answer 152

e/Euler’s Number

Question 153

It equals zero at critical points, and applying this operation on velocity with respect to time gives acceleration.

Answer 153

Derivative

Question 154

Result of this operation on two vectors can be found with the “parallelogram rule”.

Answer 154

Addition

Question 155

Its derivative can be found via Jacobi’s formula or by summing the values obtained by differentiating one input at a time.

Answer 155

Determinant

Question 156

Any function from a set with the discrete topology will have this property, as the discrete topology includes all elements and thus all subsets are open.

Answer 156

Continuity

Question 157

These objects give the number of ways to select r objects from a group of n.

Answer 157

Binomial Coefficients

Question 158

This property generally does not hold for matrix multiplication, division, or subtraction, while it does hold for the dot product, and holds along with the associative property for addition and multiplication.

Answer 158

Commutative/Commutative Property

Question 159

Unlike quaternions, octonions lack this property for multiplication.

Answer 159

Associative Property

Question 160

The derivative of “this number to the x” is just “this number to the x”.

Answer 160

e/Euler’s Number

Question 161

Those with modulus one can be generated by the function “cis x”, which appears in de Moivre’s formula, and can also be expressed as the rotation matrix.

Answer 161

Complex Numbers

Question 162

This number used as x gives the largest output of the function x raised to the reciprocal of x power.

Answer 162

e/Euler’s Number

Question 163

This term describes curves in the plane with no endpoints that completely surround an area.

Answer 163

Closed

Question 164

Raising one of these to the nth power yield an expansion with n+1 terms, whose coefficients can be found on the rows of Pascal’s Triangle using this algebraic expression’s namesake theorem.

Answer 164

Binomial

Question 165

The Jacobian is the determinant of a matrix whose entries come from performing this operation.

Answer 165

Differentiation

Question 166

Truncating this shape gives a frustum.

Answer 166

Cone

Question 167

This word refers to line segments that connect non-adjacent vertices of a polygon.

Answer 167

Diagonal

Question 168

Found by adding a set of numbers and dividing by the number of values in the set.

Answer 168

Arithmetic Mean

Answer 169

e/Euler’s Number

Question 170

In cylindrical coordinates, the equation z equals r gives one of these shapes.

Answer 170

Cone

Question 171

This set of numbers expressed in the form “a plus b i” where I squared is negative one.

Answer 171

Complex Numbers

Question 172

These numbers are solutions to quadratics with negative discriminant.

Answer 172

Complex Numbers

Question 173

This word also refers to square matrices whose only nonzero elements have a row number equal to their column number.

Answer 173

Diagonal

Question 174

Invertible entities have nonzero value for this operation, which for a two-by-two input is equal to ad minus bc.

Answer 174

Determinant

Question 175

This quantity appears in the denominator of Stirling’s formula for the asymptotics of the factorial function.

Answer 175

e/Euler’s Number

Question 176

The field of analysis named for this often studies holomorphic functions.

Answer 176

Complex Numbers

Question 177

This shape consists of all the points in spherical coordinates for which rho goes from zero to a constant times cosine phi, and phi goes from zero to a constant less than pi over two.

Answer 177

Cone

Question 178

The “directional” form of this operation can be found using the gradient.

Answer 178

Derivative

Question 179

The limit as x approaches 0, of this function minus 1, all over x, equals 0.

Answer 179

Cosine function/Cosine

Question 180

For a function, this value can be calculated by dividing its integral by the width of the interval of the integral.

Answer 180

Arithmetic Mean

Question 181

For a composition of functions, the chain rule can be used to find it.

Answer 181

Derivative

Question 182

If two angles have this property, the sine of one is equal to the cosine of the other.

Answer 182

Complementary

Question 183

In quantum mechanics, certain pairs of linear operators that lack this property, such as position and momentum, are said to be complementary.

Answer 183

Commutative/Commutative Property

Question 184

The quaternions are a generalization of them, and multiplying one by its namesake conjugate yields a real number.

Answer 184

Complex Numbers

Question 185

This term can describe something with a barrier, such as a locked door.

Answer 185

Closed

Question 186

In category theory, a diagram has this property if composing different paths gives the same result.

Answer 186

Commutative/Commutative Property

Question 187

Apollunius’ Problem is the construction of one of these shapes tangent to three others.

Answer 187

Circle

Question 188

This function has a universal attracting fixed point at the Dottie number.

Answer 188

Cosine function/Cosine

Question 189

Used to find the credibility interval.

Answer 189

Bayes’ Theorem

Question 190

The coefficient of the nth term in a Taylor series is the nth order of this operation over n factorial.

Answer 190

Derivative

Question 191

Its hyperbolic analogue describes the shape of a catenary.

Answer 191

Cosine function/Cosine

Question 192

A problem involving this shape’s difficulty arises from the fact that the Delian constant is not Euclidean.

Answer 192

Cube

Question 193

A surface is a manifold with two for this value.

Answer 193

Dimension

Question 194

A measure of central tendency that represents the average value of a set of numbers.

Answer 194

Arithmetic Mean

Question 195

A function has this property if its second derivative is positive on that interval.

Answer 195

Convexity

Question 196

This property states that the order in which consecutive occurrences of certain binary operations are carried out will not affect the result of an expression.

Answer 196

Associative Property

Question 197

One of the problems of antiquity was to double this figure.

Answer 197

Cube

Question 198

Functions that possess the complex version of this property in a disk are called holomorphic.

Answer 198

Differentiable

Question 199

Spheres tangent to one of these and a plane are called Dandelin spheres.

Answer 199

Cone

Question 200

The ordinary types of these use only one independent variable, and some ordinary types are initial value problems.

Answer 200

Differential Equations

Question 201

Proving that a space is a vector subspace requires proving that it has this property.

Answer 201

Closed

Question 202

Has a constant finite curvature.

Answer 202

Circle

Question 203

The Jacobian matrix consists of functions on which one type of this operation has been performed, and it can be used to define a gradient.

Answer 203

Derivative

Question 204

This theorem is often illustrated using groups of soldiers.

Answer 204

Chinese Remainder Theorem

Question 205

On any interval, there is at least one point where this operation is equal to the average slope of a function over that interval, according to the mean-value theorem.

Answer 205

Differentiation

Question 206

Solutions to common types of these are exponential or logistic functions, and the simplest examples can be solved using the separation of variables.

Answer 206

Differential Equations

Question 207

Can be approximated by infinitely altering sides with a process that involves drawing three arcs.

Answer 207

Angle Trisection

Question 208

The entries of Pascal’s triangles are these, which arise when multiplying a two-term polynomial with itself.

Answer 208

Binomial Coefficients

Question 209

Faa di Bruno’s formula can be used to find higher order examples of these operations.

Answer 209

Derivative

Question 210

Multilinear and alternating functions can be written as a constant times this value.

Answer 210

Determinant

Question 211

The absolute value of these numbers is called the modulus.

Answer 211

Complex Numbers

Question 212

A set of points equidistant from a center.

Answer 212

Circle

Question 213

Equal to the length of the adjacent side over the hypotenuse.

Answer 213

Cosine function/Cosine

Question 214

If this value is positive in a quadratic equation, then there are two real solutions, and the formula for finding this value in a quadratic equation is b squared minus four a c.

Answer 214

Discriminant

Question 215

A function that lacks this property everywhere but is continuous is named for Weierstrass.

Answer 215

Differentiable

Question 216

Applying this operation to two functions multiplied together requires using the product rule.

Answer 216

Derivative

Question 217

This property does not hold for subtraction of positive numbers because the difference of two positive numbers can be negative.

Answer 217

Closed

Question 218

If this value is 0 in cubic functions, there is one root of multiplicity 2.

Answer 218

Discriminant

Question 219

Numerator = 1
Denominator = x

Answer 219

1/x

Question 220

A type of polynomial that contains two terms.

Answer 220

Binomial

Question 221

A set is compact if and only if the set is bounded and has this property, according to the Heine-Borel Theorem.

Answer 221

Closed

Question 222

Lucas’s theorem reduces one of these numbers to a product of them modulo p.

Answer 222

Binomial Coefficients

Question 223

This property states that each point in a function’s domain has a derivative.

Answer 223

Differentiable

Question 224

A square has two of these things, and their length is equal to the side length times root 2.

Answer 224

Diagonal

Question 225

Donald Knuth designed one of these for matrices named X.

Answer 225

Algorithm

Question 226

Cromwell’s rule limits the cases where this theorem can be applied.

Answer 226

Bayes’ Theorem

Question 227

In Euclidian geometry, this quantity for points x and y can be represented as the norm of x minus y, which can otherwise be written as the square root of the sum squared differences between each component of two vectors a and b.

Answer 227

Distance

Question 228

This theorem allows probability to change upon the acquisition of new evidence.

Answer 228

Bayes’ Theorem

Question 229

For a cube of side length s, the structure by this name has a length of s root 3.

Answer 229

Diagonal

Question 230

Heron’s formula can be used to find this for triangles using a semi perimeter.

Answer 230

Area

Question 231

Identify these numbers which have a factor besides one and themselves and are therefore not prime.

Answer 231

Composite Number

Question 232

Taking this operation on a set can be denoted with a bar over the set’s name.

Answer 232

Complementary

Question 233

Inverse of subtraction

Answer 233

Addition

Question 234

The LRL vector is usually scaled by the namesake vector of this quantity.

Answer 234

Eccentricity

Question 235

This quantity equals the square root of 1 plus two times the energy times angular momentum squared over the mass times Big G squared.

Answer 235

Eccentricity

Question 236

This quantity multiplies the sine of its namesake anomaly, then is subtracted from that anomaly, in order to calculate the mean anomaly.

Answer 236

Eccentricity

Question 237

For Earth, this quantity is approximately 0.016.

Answer 237

Eccentricity

Question 238

This quantity multiplies the cosine of the angle to the point of closest approach in the denominator of a mathematical description of Kepler’s First Law.

Answer 238

Eccentricity

Question 239

The nonzero value for this quantity explains why the time between equinoxes is not equal.

Answer 239

Eccentricity

Question 240

Name this quantity which represents the ratio of focal length and semimajor axis length for an elliptical orbit, symbolized epsilon.

Answer 240

Eccentricity

Question 241

Curves named after this shape have equation y-squared equals x-cubed plus a times x plus b and were used to help prove Fermat’s Last Theorem.

Answer 241

Ellipses

Question 242

If points A, B, and C are marked on a trammel, and B and C are allowed to move freely on two perpendicular lines, then A will trace out one of these figures.

Answer 242

Ellipses

Question 243

These simplest Lissajous figures are the shapes of the paths of objects trapped in orbit by inverse-square forces like gravity.

Answer 243

Ellipses

Question 244

This figure with positive eccentricity less than one has area equal to pi times the product of its semi-axes, and this figure is the set of all points the sum of whose distances to two foci are constant.

Answer 244

Ellipses

Question 245

Identify this oval-shaped conic section.

Answer 245

Ellipses

Question 246

The volume of a unit sphere in a dimension that is one of these numbers can be written as pi to the k over k factorial.

Answer 246

Even Numbers

Question 247

The function 2x over the quantity x minus 1 squared generates these numbers, which are an ideal in the natural numbers.

Answer 247

Even Numbers

Question 248

The word describing these numbers also names permutations with positive signature.

Answer 248

Even Numbers

Question 249

An unproven statement regarding them is that all but one of them can be written as the sum of two primes.

Answer 249

Even Numbers

Question 250

That statement is Goldbach’s conjecture.

Answer 250

Even Numbers

Question 251

They share their name with functions for which f of negative x equals f of x, and when written in binary this kind of number ends in a 0.

Answer 251

Even Numbers

Question 252

Identify this set of numbers including 0, 2 ,4, 6, and 32, the opposite of odd numbers.

Answer 252

Even Numbers

Question 253

F. Scott Fitzgerald hated this thing because he said it “is like laughing at you own joke.”

Answer 253

Exclamation Mark

Question 254

When this thing follows an integer n, it is asymptotically equal to the square root of two pi n times the quantity n over e to the n, according to an approximation named for James Stirling.

Answer 254

Exclamation Mark

Question 255

In chess two of these things denote an excellent move.

Answer 255

Exclamation Mark

Question 256

Name this symbol which mathematically denotes a factorial.

Answer 256

Exclamation Mark

Question 257

This word preceded by “hyper” describes a function of a equal to the K-function of a+1.

Answer 257

Factorial

Question 258

The formula for the kth Catalan number is this function of 2k divided by this function of k times this function of k+1.

Answer 258

Factorial

Question 259

This function of successive natural numbers forms the denominators of the terms in a Taylor series.

Answer 259

Factorial

Question 260

For zero, this function can be shown to equal one, by equating this function of n to the number of permutations of n objects.

Answer 260

Factorial

Question 261

Name this function which gives the product of all positive integers equal to or less than a specified integer, symbolized by an exclamation point.

Answer 261

Factorial

Question 262

According to a Donald Knuth conjecture, this function along with the square root and floor functions and the number 3 can generate any natural number.

Answer 262

Factorial

Question 263

The Pochhammer Symbol is used to represent its rising and falling types.

Answer 263

Factorial

Question 264

Stirling’s approximation is used to calculate very large terms of this operation.

Answer 264

Factorial

Question 265

The solution to this problem was originally approached using horizontal Iwasawa theory, and a weaker version of this result is derived from Falting’s theorem.

Answer 265

Fermat’s Last Theorem

Question 266

The proof of this theorem relied on Ribet’s work on the epsilon conjecture.

Answer 266

Fermat’s Last Theorem

Question 267

It was proven for all primes less than 100 using Sophie Germain’s theorem.

Answer 267

Fermat’s Last Theorem

Question 268

Its proof relied on a result that states that any elliptic curveover the rationals can be obtained from a rational map, known as the Taniyama-Shimura conjecture.

Answer 268

Fermat’s Last Theorem

Question 269

The originator of this result claimed to have miraculous proof of it that the margin couldn’t contain.

Answer 269

Fermat’s Last Theorem

Question 270

Name this result proven by Andrew Wiles, which states that for n greater than 2, there are no integers x, y, and z such that x to the n plus y to the n equals z to the n.

Answer 270

Fermat’s Last Theorem

Question 271

This statement holds for exponent p in an irregular pair if the pair satisfies Vandiver’s Criteria.

Answer 271

Fermat’s Last Theorem

Question 272

One method of testing whether a number n is one of these involves asking whether 5n squared minus 4 or 5 n squared plus 4 is a perfect square.

Answer 272

Fibonacci Numbers/Sequence

Question 273

One method of generating these numbers is to repeatedly take powers of the two-by-two matrix one-one-one-zero, and the Wall-Sun-Sun primes are defined using these numbers.

Answer 273

Fibonacci Numbers/Sequence

Question 274

The generating function x divided by the quantity 1 minus x minus x squared creates these numbers.

Answer 274

Fibonacci Numbers/Sequence

Question 275

The ratio between successive members of these numbers approaches 1 plus the square root of 5 all over 2, which is known as the golden ratio.

Answer 275

Fibonacci Numbers/Sequence

Question 276

Name this sequence of numbers, a given member of which is a sum of the previous two entries.

Answer 276

Fibonacci Numbers/Sequence

Question 277

This set of numbers begins [1,1,2,3,5,8…]

Answer 277

Fibonacci Numbers/Sequence

Question 278

Three of these numbers cannot form a Pythagorean triplet, and neither can the similar Lucas numbers.

Answer 278

Fibonacci Numbers/Sequence

Question 279

The shallow diagonals in Pascal’s triangle sum to these numbers, which were used by their namesake to describe the population of a group of rabbits.

Answer 279

Fibonacci Numbers/Sequence