Math

Question 1

Number has 2 positive divisors, 1 and itself

Answer 1

Prime numbers

Question 2

These numbers consist of a real and imaginary part!

Answer 2

Complex numbers

Question 3

What is the transcendental number approximately equal to 3.14159?

Answer 3

Pi

Question 4

Whole numbers, negative numbers, and zero are included in this mathematical set

Answer 4

Integers

Question 5

This is the point where to lines curve, or edges meet

Answer 5

Vertex

Question 6

What branch of mathematics calculates the likelihood of an event occurring

Answer 6

Probability

Question 7

This mathematical constant is the ratio of a circle’s circumference to its diameter .
It’s a irrational number
It is represented by a Greek letter
It appears in many formulas in geometry and calculus

Answer 7

Pi

Question 8

This theorem states that in a right triangle, the square of a hypotenuse is equal to the sum of the squares of the other two sides.
Right triangles
Ancient Greece

Answer 8

Pythagorean Theorem

Question 9

This function, represented by an exclamation mark, multiplies all positive integers up to a given number
Permutations
Combinatorics
This functioned generalized by gamma function
This function gives help to organize numbers in distinctive rows.

Answer 9

Factorial

Question 10

What is the sum of the interior angles of any triangle?
It is measured in degrees
It is the same for all triangles

Answer 10

180 degrees

Question 11

What is the square root of 144?
It is an even number
It is the product of 12x12

Answer 11

12

Question 12

What term refers to the sum of a set of numbers divided by the number of values in the set?
It is also known as mean
It is different then median and mode

Answer 12

Average

Question 13

What U-shaped curve is formed by graphing a quadratic function?
It is symmetric
It can open upward and downward

Answer 13

Parabola

Question 14

What mathematical concept describes quantities that have both magnitude and direction, such as velocity and force?
It is commonly used in physics
It is represented by a arrow
This term refers to organisms which can carry and transmit diseases

Answer 14

Vectors

Question 15

What irrational number represents the ratio of a circle’s circumference to its diameter?
It appears in geometry and trigonometry formulas

Answer 15

Pi

Question 16

What mathematical operation involves raising a number to the power of another number, such as x raised to y?
Squaring cubing are examples of this operation
It is a opposite of taking a logarithm

Answer 16

Exponentiation

Question 17

• Finite power series.
• Include variables and coefficients.
• x² - 1 is an example.
• Degree n → n roots.

Answer 17

Polynomials

Question 18

• Repeated addition.
• Not commutative for matrices.
• Used in exponentiation.
• 2 × 3 = 6.

Answer 18

Multiplication

Question 19

• Product of all positive integers ≤ n.
• Written with an exclamation point.
• Stirling’s approximation.
• 3! = 6, 4! = 24.
• Used in combinations.

Answer 19

Factorial

Question 20

• 3 sides, 3 angles.
• Area: Heron’s formula.
• Angles = 180°.
• Used in Minkowski space.
• Simplest polygon

Answer 20

Triangle

Question 21

• Has 3D symmetry.
• Related to spherical harmonics.
• Angles of triangle on it > 180°.
• Surface area = 4πr².
• Shape of planets.

Answer 21

Sphere

Question 22

• Equal to 3 × 11
• A perfect square
• First reverse divisible number
• Used in numerical magic tricks
• Followed by twin primes

Answer 22

33

Question 23

• Appears in Euler’s identity
• Used in circle circumference: C = 2\pi r
• Equal to 180 degrees in radians
• Approximate value is 3.14 or 22/7
• Estimated in Buffon’s needle problem

Answer 23

Pi

Question 24

• Has an eccentricity of zero
• Equation in polar coordinates: r = constant
• Area is πr²
• Cartesian product gives a torus
• All points are equidistant from a cent

Answer 24

Circle

Question 25

These objects of 5 degrees or higher cannot be solved algebraically. These objects can be factored using difference of cubes or squares Can be multiplied using FOIL

Answer 25

Polynomials

Question 26

Property Infinite continued fraction Roots of polynomial Golden ratio and pi Cannot be represented as quotient of two integers Drichlet

Answer 26

Irrational number

Question 27

• Detected by observatories like Super-Kamiokande and IceCube • Nearly massless and uncharged • Involved in flavor oscillation between subtypes like tau, muon, and electron • Extremely difficult to detect due to rare interactions • Their discovery would prove they are their own antiparticles

Answer 27

Neutrinos

Question 28

• Found in matrices and vector spaces • Equals the number of coordinates required to define a point in space • A tesseract has four of these • Also known as rank in linear algebra • Dimension 3 corresponds to a cube

Answer 28

Dimensions

Question 29

• Known for the fifth postulate in geometry • Explains a unique line through a point • Challenged in hyperbolic geometry by Lobachevsky and Bolyai • Also called the parallel postulate • Part of Euclid’s axioms

Answer 29

Parallel

Question 30

• Differentiation is the inverse of this operation • The indefinite form requires adding the constant C • The trapezoidal rule and Riemann sums approximate it • Finds the area under a curve • Partial fraction decomposition is a method used

Answer 30

Integration

Question 31

• Known for the Pythagorean Theorem • Studied musical intervals and mathematical ratios • According to legend, drowned a student for discovering irrational numbers • The Pythagorean theorem is used to find the hypotenuse of a right triangle • Ancient Greek mathematician

Answer 31

Pythagoras

Question 32

• Describes numbers divisible by 2 • The smallest prime number is the only one with this property • Functions with this property are symmetric about the y-axis • Numbers like 4, 6, and 8 are examples of this property • Related to even integers

Answer 32

Even

Question 33

• Found in languages like C++ • Similar to arrays, but with a dynamic size • Describes objects in linear algebra, manipulated with dot and cross products • Can refer to organisms that transmit diseases • Describes velocity, a vector quantity, unlike speed

Answer 33

Vectors

Question 34

• A circle with the center at the origin of the coordinate plane • Defined by the equation x² + y² = r² • Describes the distance from the center to any point on the circle • All points are equidistant from the center

Answer 34

Math

Question 35

1. Russell’s paradox involves sets that don’t contain themselves. 2. Fermi paradox questions lack of extraterrestrial contact. 3. The Liar’s paradox states, “This statement is false.”

Answer 35

Paradoxes

Question 36

1. Euler showed their reciprocals sum to π²/6. 2. Positive integers with odd numbers of factors (e.g., 1, 4, 9). 3. Equal to an integer multiplied by itself (e.g., n²).

Answer 36

Perfect square

Question 37

1. Raising i⁴ gives one; only natural number with one divisor. 2. Multiplicative identity states any number times one equals itself. 3. Raising a number to zero yields one.

Answer 37

One

Question 38

• Carmichael numbers pass Fermat’s test but aren’t prime. • Sieve of Eratosthenes finds them. • “Twin” primes differ by two. • Only divisible by 1 and itself.

Answer 38

Prime numbers

Question 39

• Sato generalized Ramanujan’s formulas for it. • Smallest positive x where cos(x) = -1. • 1 degree = π/180 radians. • Area of a circle: πr².

Answer 39

Pi

Question 40

• These constructs can be reduced to row-echelon form using Gauss-Jordan elimination. • Their characteristic polynomial yields eigenvalues. • The identity version has ones on the diagonal and zeros elsewhere. • Cramer’s rule finds their determinant.

Answer 40

Matrices

Question 41

• If can be expressed as a linear combination of integers and , it has this relationship by Bezout’s identity. • For coprime numbers, this value is always one. • The Euclidean algorithm computes this largest integer dividing two or more integers.

Answer 41

Greatest common divisor

Question 42

• Replaced with “quantum” in systems with energy levels spaced by . • Describes pendulum motion under small angle approximation. • Paired with harmonic to describe oscillations around a fixed point.

Answer 42

Simple

Question 43

• A matrix with ones on the main diagonal and zeros elsewhere is called this. • Multiplying an element by its inverse yields this value, which is one for multiplication. • Property stating any number times one equals itself.

Answer 43

Identity

Question 44

• Defined recursively as sum of two previous terms, starting 0,1,1,2,3,5… • Closed-form expression known as Binet’s formula. • Ratio of consecutive terms approaches the golden ratio, phi.

Answer 44

Fibonacci sequence

Question 45

• Set of numbers including whole numbers and their negatives. • Symbolized by blackboard bold Z. • Floor function returns greatest integer less than or equal to input. • Solutions to Diophantine equations lie in this set.

Answer 45

Integers

Question 46

• Number of sulfur atoms in the puckered ring allotrope produced by the Frasch process. • Number of hydrogen atoms in propane. • Number of valence electrons in noble gases (except helium). • Number of carbons in octane.

Answer 46

Eight

Question 47

• Include Zeno’s arrow and Russell’s paradox. • Liar paradox states “this sentence is a lie.” • Self-contradictory statements challenging logic.

Answer 47

Paradoxes