Name the Mathematician
What half-blind Swiss mathematician derived the following famous identity?
e^{i\pi}+1=0
Leonhard Euler
What is the general antiderivative of the natural log function?
x \ln(x) - x + C
What polygon has an interior angle sum of 540º?
A pentagon
If you flip a two-sided coin four times, how many outcomes have exactly two heads?
6
All polynomials with real coefficients have at least one real solution.
x^2 + 1
What German mathematician proved the Fundamental Theorem of Algebra in their doctoral thesis?
Carl Friedrich Gauß
What is the slope of the line tangent to y^2 = 16 - x^2 at the point (0, 4)?
0
What is the volume of a pipe that is 10 units long, has a radius of 2 units, and a thickness of 1 unit? (I.e., an outer radius of 2 and an inner radius of 2.)
30 pi
How many distinct ways are there to arrange the letters in BANANA?
\frac{6!}{3! 2!} = \frac{720}{12} = 60
All continuous functions are differentiable.
|x|
What highly prolific Hungarian mathematician was addicted to amphetamine and methylphenidate, and when forced to take a month-long break from these drugs declared "mathematics was set back a month."
Paul Erdős
What is the following indefinite integral?
\int \frac{e^{i \pi}}{x^2 + 16} dx
-1/4arctan(x/4) + C
How many platonic solids are there?
Five
How many triangles can be formed whose vertices lie amongst nine points arranged in a three-by-three grid?
((9),(3))-8 = 76
If a quadrilateral has one pair of opposite sides that are parallel, and the other pair is congruent, then the quadrilateral is a parallelogram.
Trapezoid
What 20-year-old French mathematician who revolutionized mathematics while in prison, then a month after his released died in an alleged love duel?
Évariste Galois
What does the following improper integral converge to?
\int_1^\infty \frac{2\pi}{x}\sqrt{1 + \frac{1}{x^4}} dx
\infty
How many edges does an octahedron have?
12
What is the minimum number of people at a party to guarantee there are either three mutual acquaintances or three mutual strangers?
R(3, 3) = 6
A continuous bijection has a continuous inverse.
The function
f : (0, 1) \cup [2, \infty) \to (0, \infty)
given by
f(x) = {(x,if x \in (0,1)),(x-1,if x \in [2, \infty)):}
What self-taught Indian mathematician famously proved the sum of the natural numbers is -1/12?
Srinivasa Ramanujan
What is the derivative of x^\sqrt{x} ?
1/2 x^{sqrt(x) - 1/2}(ln(x) + 2)
In what geometry can pairs of lines enclose a finite area?
Spherical / Elliptical
If we only have points and lines connecting points together, how many points and lines are there in the geometric structure satisfying the axioms written on the board?
There are 7 points and 7 lines. This is called the Fano plane.
If \lim_{n \to \infty} a_n = 0 then \sum_{n=1}^\infty a_n converges
a_n = 1/n