106 Mathematics Trivia Questions and Answers
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Easy Mathematics Trivia Questions
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What does a number's absolute value measure on the number line?
Distance from zero
The absolute value of a real number is its nonnegative distance from zero on the number line.
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What is the space inside a two-dimensional shape called?
Area
Area is the amount of surface a flat shape covers, always given in square units such as square metres. A rectangle's area is its length times its width.
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The Cartesian coordinate system is named after which mathematician?
René Descartes
Cartesian coordinates take their name from René Descartes, whose work linked algebraic equations with geometric positions.
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Which formula gives the area of a circle of radius r?
πr²
The area of a circle is pi times the square of its radius. The other expressions are also area-dimensional: r² is the area of a square of side r, 2πr² can describe a cylinder's lateral area when its height equals r, and 4πr² is a sphere's surface area.
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What is a whole number greater than 1 called if it has factors other than 1 and itself?
A composite number
A composite number is any whole number above 1 that divides evenly by something other than 1 and itself, so 6, 9 and 12 are composite while 7 and 13 are prime. Every composite number can be broken down into a unique product of primes.
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What does it mean for two geometric figures to be congruent?
Same shape and size
Congruent figures have the same shape and size; equal area, perimeter, or angle relationships alone do not establish congruence.
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How many equal square faces does a cube have?
Six
A cube has six identical square faces, along with twelve edges and eight vertices, which is why a standard die carries six numbered sides.
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In a decimal, what place does the first digit after the point occupy?
Tenths
The first digit after a decimal point represents tenths; hundredths, thousandths, and millionths are later decimal places.
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What does a derivative measure?
Instantaneous rate of change
The derivative gives a function's instantaneous rate of change, represented by tangent slope.
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Three packs each hold 4 red and 5 blue pens. Counting 3 x 9 or 3 x 4 plus 3 x 5 gives the same total. Which distribution is that?
Multiplication over addition
The distributive law says multiplication distributes over addition (and subtraction).
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What does division commonly represent?
Sharing into equal groups
Division commonly represents sharing a quantity into equal groups. It can also show how many equal-sized groups fit into a total.
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Which value is closest to Euler's number e?
2.718
Euler's number e is approximately 2.71828, so 2.718 is the closest value listed; e is the base of natural logarithms.
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Which name is associated with the sequence 1, 1, 2, 3, 5, 8...?
Fibonacci
The sequence is named for Leonardo of Pisa, whose nickname Fibonacci became attached to it in modern usage.
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In the worst case, what is the maximum number of colors needed for a planar map so adjacent regions differ?
Four
The Four Color Theorem says every planar map can be colored with no more than four colors so adjacent regions differ.
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What is the top number of a fraction called?
Numerator
In 3/4 the numerator 3 counts how many of the equal parts you have, while the denominator 4 says how many parts the whole was cut into.
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Which Greek letter is commonly used for the golden ratio in art and geometry?
φ
The golden ratio is commonly represented by the Greek letter phi, written φ or Φ depending on convention.
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What is the square of the imaginary unit i?
-1
The imaginary unit is defined by i² = −1.
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Which expression is an irrational number?
π
Pi cannot be expressed as a ratio of integers, whereas the other choices are rational.
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Which operation does a logarithm undo?
Exponentiation
A logarithm is the inverse of exponentiation: it identifies the exponent that produces a specified number.
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What measure of location is most commonly meant by “mean”?
Arithmetic average
“Mean” most commonly refers to the arithmetic average: add all the values and divide by the number of values. It can be strongly influenced by unusually large or small values.
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What is the mode of a data set?
Most frequent value
The mode is the value or category occurring most often in a data set.
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What can multiplication represent?
Repeated addition
Multiplication can represent repeated addition: 4 × 3 means adding 3 four times. It provides a quick way to count equal groups.
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What is the base of the natural logarithm?
e
The natural logarithm has base e, the constant roughly equal to 2.71828. It turns up wherever something grows or decays continuously, from compound interest to radioactive decay, and it is the base that makes the calculus come out cleanest.
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What sign results when two values below zero are multiplied?
A positive number
Multiplying two negative values produces a positive product.
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How many sides does an octagon have?
Eight
Octa- is the Greek prefix for eight, the same root behind octopus and octave. The octagon most people see daily is the American stop sign, given that shape in the 1920s so drivers could recognise it from behind or in poor light.
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A shop takes a quarter off every price. What percentage is that?
25 percent
A quarter is one part in four, and four twenty-fives make a hundred, so a quarter is 25 percent. The same step converts any fraction: divide 100 by the bottom number, then multiply by the top.
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In 8 - 2 x (1 + 2), which part is worked out first?
The addition inside the parentheses
Working it through: 1 + 2 makes 3, then 2 times 3 makes 6, and 8 minus 6 leaves 2. The acronym PEMDAS, or BODMAS in British classrooms, exists so everyone parses an expression like this the same way, rather than simply left to right.
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What array lists the binomial coefficients by row?
Pascal's triangle
Pascal's triangle arranges the binomial coefficients in successive rows. The alternatives are other named triangular arrays.
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How many sides does a pentagon have?
Five
A pentagon has five sides and five interior angles, which in a regular pentagon measure 108 degrees each and add up to 540. The name comes from the Greek pente, meaning five, and gonia, meaning angle.
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What is the name for the total distance around the outside of a shape?
Perimeter
The perimeter is the length of a shape's boundary: walk right around the edge and add up how far you went. A rectangle 3 by 5 has a perimeter of 16. For a circle the same measurement gets its own name, circumference.
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A circle’s circumference divided by its diameter is written with which symbol?
π
The Greek letter π is conventionally used for the ratio of a circle's circumference to its diameter.
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In 47, what place does the 4 occupy?
Tens
In 47 the 4 sits in the tens place and stands for 40, while the 7 stands for seven ones: 40 plus 7. Every step to the left multiplies a digit's value by ten.
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What kind of whole number greater than 1 has no positive factors except 1 and itself?
A prime number
A prime has exactly two positive divisors: 1 and itself. That makes 2 the only even prime, and it is why 1 is excluded because it has just one divisor. Every other whole number above 1 is composite, and can be broken into primes in exactly one way.
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The Pythagorean theorem applies directly to which kind of triangle?
Right
Builders still use a simplified version of it: mark 3 units along one side and 4 along another, and the third side will measure exactly 5 units if that corner is a true right angle. 'Hypotenuse' comes from a Greek word meaning roughly 'stretching under,' describing the side opposite that angle.
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What is the degree of a quadratic polynomial?
2
A quadratic polynomial has degree two, meaning its highest variable exponent is 2.
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What is the interior-angle sum of a quadrilateral?
360 degrees
A quadrilateral can be divided into two triangles, so its interior angles total 360 degrees.
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Which description defines a rational number?
A quotient of two integers with denominator nonzero
A rational number can be written as p/q, where p and q are integers and q is not zero; its decimal expansion terminates or repeats.
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What fraction of a full turn is a right angle?
A quarter turn
A full turn is 360 degrees and a right angle is 90, so a right angle is exactly a quarter of the way round: the angle at the corner of a sheet of paper, or between the hands of a clock at three o'clock.
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Which familiar number has no standard symbol in the Roman numeral system?
Zero
Classical Roman numerals represent quantities such as one, five, and ten but have no standard numeral for zero.
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What feature defines a geometric sequence?
Constant ratio
A geometric sequence is defined by multiplying each term by the same constant ratio to get the next term. Its nth term can be written as a₁rⁿ⁻¹.
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What do similar geometric figures share?
Same shape, possibly different scale
Similar figures have equal corresponding angles and proportional corresponding sides; their scale factor need not be one.
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What is the slope of a horizontal line?
0
Slope is the change in height divided by the change in width. A horizontal line gains no height however far along it you travel, so the top of that fraction is zero and the slope is zero. A vertical line is the mirror case: its width never changes, so the bottom is zero and the slope is undefined.
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Which shape has four equal sides and four right angles?
Square
A square is a quadrilateral with four equal sides and four right angles.
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What does standard deviation describe?
Spread of data
Standard deviation measures the typical spread of observations around their mean.
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A straight line forms an angle of how many degrees?
180 degrees
This is exactly half of a full turn. It is why the interior angles of any triangle always add up to it, and why reversing direction completely is called doing a 180.
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What is the interior-angle sum of a Euclidean triangle?
180 degrees
The interior angles of every Euclidean triangle add to 180 degrees.
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Which polygon has exactly three sides?
Triangle
Fix the length of each side and its shape is locked in place, unlike a four-sided frame, which can flex into a parallelogram at the very same lengths. That rigidity is why bridges and roof trusses are built from triangular frames.
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Which mathematician's name is attached to the familiar overlapping-circle diagram?
John Venn
John Venn introduced the diagrams now called Venn diagrams for representing logical relationships among sets.
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In standard mathematics, how is zero classified by sign?
Neither positive nor negative
Zero sits exactly on the boundary between the positive and negative numbers and belongs to neither group. It is the only real number that is equal to its own negative.
Medium Mathematics Trivia Questions
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Ada Lovelace's notes set out an algorithm for which machine?
The Analytical Engine
Her 1843 notes on Charles Babbage's Analytical Engine include a step-by-step method for computing Bernoulli numbers, widely called the first published computer program. The machine itself was never built in her lifetime.
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A "bell curve" is the everyday name for which statistical distribution?
Normal distribution
The normal distribution has a symmetric bell-shaped curve, with most values clustered near the average and fewer the further out you go. Heights, measurement errors and exam scores tend to follow it closely.
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Which formula gives the area of a triangle with base b and height h?
bh/2
A triangle's area is half the product of its base and perpendicular height.
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On a standard graph, the vertical axis normally carries which kind of variable?
The dependent variable
By convention the vertical y-axis carries the dependent variable, the quantity being measured, while the horizontal x-axis carries the independent variable that is set or changed. A plot of temperature through the day therefore puts time along the bottom and temperature up the side.
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Which ancient Greek mathematician wrote Elements?
Euclid
Euclid wrote Elements, a systematic treatise that shaped the study of geometry for centuries.
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Which of these equations is Euler's identity?
e^(iπ) + 1 = 0
Euler's identity, e^(iπ) + 1 = 0, ties five of the most important numbers in mathematics into a single line: e, i, π, 1 and 0. It falls out of the more general formula e^(ix) = cos x + i sin x when x is π.
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For a convex polyhedron, what value does V − E + F equal?
2
Euler's formula states that the number of vertices V minus edges E plus faces F equals 2 for a convex polyhedron.
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Which statistic tells a casino what it will make per play, averaged over the long run?
Expected value
Expected value multiplies every possible outcome by its probability and adds the results, so a rare jackpot counts only in proportion to how rarely it lands. It is why a game with a house edge of a couple of percent still earns a predictable amount per play once the plays run into the millions.
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What feature is characteristic of a fractal?
Self-similar structure
Fractals are characterized by self-similar structure, meaning their patterns repeat at smaller scales. This property can be seen in natural forms such as branching trees and Romanesco broccoli.
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Which two ideas are linked by the fundamental theorem of calculus?
Derivatives and integrals
The theorem states, in two complementary forms, that differentiation and integration are inverse processes.
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Which mathematician is often called the “Prince of Mathematicians”?
Carl Friedrich Gauss
Carl Friedrich Gauss is widely known by the sobriquet Prince of Mathematicians for his influential work across mathematics.
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What number name means 1 followed by 100 zeros?
A googol
A googol is 10^100, or 1 followed by 100 zeros.
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Which side of a right triangle is opposite the right angle?
Hypotenuse
The hypotenuse is the side opposite the right angle and is the longest side of a right triangle.
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Two events are independent, meaning neither one affects the other. What is the chance that both happen?
Their two chances multiplied together
When one event tells you nothing about the other, the chance of both is the product of the two chances. Two fair coins both landing heads is one half times one half, which is one in four.
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Hilbert's Hotel, an imaginary hotel with infinitely many rooms, is used to illustrate what?
A hotel with every room full can still take in more guests
Move the guest in room 1 to room 2, room 2 to room 3, and so on through every room. Room 1 is now empty even though every room had someone in it, which is the way an infinite collection stops behaving like a finite one.
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In calculus, what does a definite integral of a function between two points measure?
The signed area between the graph and the x-axis
A definite integral adds up the area between a curve and the x-axis across an interval, counting anything below the axis as negative. Slope at a point is what a derivative gives instead.
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What does the law of large numbers describe?
Sample average approaches expected value
As independent trials increase, the sample average tends to approach the expected value; individual outcomes do not have to converge.
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How many continuous surfaces can you trace on a Möbius strip?
One
A half-twist joins the strip into one continuous, one-sided surface rather than two separate sides. Its single boundary edge is a different property.
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What is the name for arithmetic in which numbers wrap around after reaching a fixed value, as hours do on a clock face?
Modular arithmetic
In modular arithmetic you keep only the remainder after dividing by a fixed number, so on a 12-hour clock nine o'clock plus five hours is two. The same wrap-around underlies the days of the week, musical octaves and most modern cryptography.
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In the order of operations, what does the M in BODMAS stand for?
Multiplication
BODMAS is brackets, orders, division, multiplication, addition, subtraction. The American version PEMDAS says the same thing in different words.
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What distinguishes a permutation from a combination?
In a permutation the order of the items matters
A permutation counts arrangements, so ABC and CBA are two different permutations of the same three letters. A combination counts only which items were chosen, so ABC and CBA are the same combination. That is why three letters give six permutations but only one combination.
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How many Platonic solids are there?
Five
The five Platonic solids are the tetrahedron, cube, octahedron, dodecahedron, and icosahedron.
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Measured in radians, how big is one complete turn?
2π radians
One radian is the angle you get when the arc along the circle is exactly as long as the radius. A circle's circumference is 2π times its radius, so a full turn is 2π radians, roughly 6.28.
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Which geometric transformation flips a figure across a line?
Reflection
A reflection maps each point to the opposite side of a line at the same perpendicular distance.
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A straight line that cuts across a circle, crossing its edge at two points and carrying on beyond, is called what?
Secant
A secant is the whole line through two points of a circle. A chord is only the segment between those two points, and a tangent touches the circle at just one.
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Which expression gives the volume of a sphere of radius r?
4πr³/3
The volume of a sphere is four-thirds pi times the radius cubed. The alternatives correspond to a cube of side r, a cylinder of radius and height r, and a hemisphere of radius r.
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Which Roman numeral represents 40?
XL
XL means 50 minus 10, or 40, in Roman numeral notation.
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In mathematics, what does 0! (zero factorial) equal?
1
Zero factorial equals 1. It follows from the empty-product convention, where multiplying no numbers together gives 1, and it is what keeps the formulas for permutations and combinations working at their edge cases.
Hard Mathematics Trivia Questions
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In a normal distribution, roughly what percentage lies within one standard deviation of the mean?
About 68%
For a normal distribution, the interval from one standard deviation below to one above the mean contains about 68% of observations.
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Which ancient Greek mathematician trapped pi between polygons of 96 sides to estimate its value?
Archimedes
In Measurement of a Circle, Archimedes squeezed the circle between inscribed and circumscribed 96-sided polygons, showing that pi lies between 3 10/71 and 3 1/7.
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Which paradox says that a solid ball can be decomposed and reassembled into two balls of the same volume?
Banach–Tarski paradox
The Banach–Tarski paradox uses non-measurable sets and the axiom of choice to show that one solid ball can be decomposed and rearranged into two balls of the same volume.
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Which theorem relates prior probability, likelihood, and posterior probability?
Bayes' theorem
Bayes' theorem expresses how a prior probability is updated using new evidence and its likelihood.
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What count underlies the coefficients in a binomial expansion?
Number of combinations
The coefficients in a binomial expansion count the number of ways to choose elements from a set, which is why they are called binomial coefficients. These numbers form Pascal’s triangle when arranged by successive expansions.
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A cardboard triangle balances on a pinhead at one single point. That point is where which three lines meet?
Its medians
The balance point is the centroid, where the three medians cross, each median running from a corner to the midpoint of the opposite side. The centroid sits two-thirds of the way along every median, measured from the corner.
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Which triangle center is equally distant from all three vertices?
Circumcenter
The circumcenter is the intersection of a triangle's perpendicular bisectors and is equally distant from its three vertices.
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Which statement is logically equivalent to "If P, then Q"?
If not Q, then not P
Swapping the two halves and negating both gives the contrapositive, which is true in exactly the same cases as the original statement. Only swapping them gives the converse and only negating them gives the inverse, and neither of those follows from the original: "if it is raining, the ground is wet" does not mean wet ground proves rain.
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Which classical construction problem is also known as the Delian problem, after an oracle's demand during a plague?
Doubling the cube
Known as the Delian problem, it asks for a cube of twice a given volume. Pierre Wantzel proved in 1837 that no straightedge-and-compass construction can do it.
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What does the Euclidean algorithm find efficiently?
Greatest common divisor
The Euclidean algorithm finds the greatest common divisor through repeated division.
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Who wrote Liber Abaci, which helped popularize Hindu-Arabic numerals in Europe?
Fibonacci
Fibonacci, the name used for Leonardo of Pisa, wrote Liber Abaci and helped spread Hindu-Arabic numerals in medieval Europe.
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Which functions form the basic terms of a Fourier series?
Sines and cosines
A Fourier series rebuilds a repeating signal by adding sines and cosines whose frequencies are whole-number multiples of one fundamental. Given enough terms at the right strengths, even a sharp-cornered square wave comes out.
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Which theorem guarantees that every nonconstant polynomial has a root in the complex numbers?
Fundamental theorem of algebra
The fundamental theorem of algebra states that every nonconstant polynomial with complex coefficients has at least one complex root.
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Which theorem states that every integer greater than 1 has a unique prime factorization?
Fundamental theorem of arithmetic
The fundamental theorem of arithmetic says that every integer greater than 1 can be written as a product of primes in only one way apart from order.
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Which 1931 result proved that any consistent formal system strong enough for arithmetic contains true statements it cannot prove?
Gödel's incompleteness theorem
Kurt Gödel showed in 1931 that no consistent, effectively axiomatized system capable of basic arithmetic can prove every true statement of arithmetic.
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What does Goldbach's conjecture propose?
Every even integer greater than 2 is sum of two primes
Goldbach’s conjecture proposes that every even integer greater than 2 can be written as the sum of two prime numbers. It remains unproven, although it has been verified for enormous ranges of numbers.
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Which expression equals the positive golden ratio?
(1 + √5)/2
The positive golden ratio is (1 + √5)/2, approximately 1.618. It appears in the geometry of regular pentagons and other fivefold symmetrical shapes.
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Which problem asks whether a general algorithm can determine if any computer program will eventually stop?
Halting problem
The halting problem asks whether a program will eventually stop, and Alan Turing proved that no general algorithm can decide this for every program and input.
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Which Alexandrian scholar taught mathematics and philosophy until being killed by a mob in 415 CE?
Hypatia
Hypatia led the Neoplatonic school at Alexandria, edited and taught the mathematical works of others, and was respected as an astronomer. In 415 CE she was seized and killed by a mob during a violent power struggle in the city. Her father was Theon of Alexandria, himself a mathematician.
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Which conjecture concerns the densest packing of equal spheres in three-dimensional space?
Kepler conjecture
The Kepler conjecture states that no arrangement of equal spheres in three-dimensional space is denser than the familiar cannonball packing. Thomas Hales announced a proof in 1998.
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What term describes a square matrix with a zero determinant?
Singular
A square matrix with a determinant of zero is called singular. Singular matrices do not have an inverse.
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What is the name of the valid inference P→Q, P, therefore Q?
Modus ponens
Modus ponens infers Q from P and the implication P→Q; it is also called affirming the antecedent.
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What kind of number is pi, beyond being irrational?
Transcendental
A transcendental number is not the solution of any polynomial equation with whole-number coefficients, so no finite piece of algebra can pin it down. Lindemann proved pi transcendental in 1882, and that settled a problem the Greeks left open: a circle cannot be squared with compass and straightedge.
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Which mathematician corresponded with Blaise Pascal on problems of probability?
Pierre de Fermat
Pierre de Fermat and Blaise Pascal exchanged the 1654 correspondence that helped establish mathematical probability theory.
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Which conjecture about the three-sphere was proved by Grigori Perelman?
Poincaré conjecture
The Poincaré conjecture stated that every simply connected closed three-dimensional manifold is homeomorphic to the three-sphere. Grigori Perelman proved it, then turned down both the Fields Medal and the million-dollar Millennium Prize.
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Which famous conjecture proposes that all nontrivial zeros of the zeta function have real part one-half?
Riemann hypothesis
Bernhard Riemann proposed it in 1859 while studying how prime numbers are distributed. It is one of the seven Millennium Prize Problems, and the Clay Mathematics Institute has offered one million dollars for a proof since 2000.
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Which mathematician introduced the equals sign in the 16th century?
Robert Recorde
Robert Recorde introduced the equals sign in The Whetstone of Witte, published in 1557, choosing two parallel lines because no two things can be more equal.
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Who recognized 1729 as the smallest number expressible as the sum of two positive cubes in two different ways?
Srinivasa Ramanujan
Told by G. H. Hardy that the number of his taxicab, 1729, seemed dull, Ramanujan answered at once that it is the smallest number that is the sum of two cubes in two ways: 1 + 1728 and 729 + 1000.
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Topologists say a coffee mug and a doughnut are the same shape because one can be stretched into the other. What is such a transformation called?
A homeomorphism
In topology a shape may be stretched, squashed or bent, but never cut or glued. A mug and a doughnut each have exactly one hole, so a continuous deformation with a continuous inverse, called a homeomorphism, turns one into the other. This is why topology is nicknamed rubber-sheet geometry.
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