Nilknarf

United States

http://nilknarf.langlab.org

I have a blog at this link.

Mi cabeza no es un vaso por llenar,

Es una luz a ser encendida...

-El Cuarteto de Nos

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“Integral Milking”

integration definite-integrals soft-question recreational-mathematics big-list asked Jun 15 '18 at 22:24

math.stackexchange.com

81 votes

Do numbers get worse than transcendental?

definite-integrals soft-question irrational-numbers transcendental-numbers asked Dec 20 '17 at 15:36

math.stackexchange.com

60 votes

Find three non-constant, pairwise unequal functions $f,g,h:\mathbb R\to \mathbb R$…

functions function-composition asked Jul 10 '17 at 21:08

math.stackexchange.com

49 votes

What numbers can be created by $1-x^2$ and $x/2$?

functions dynamical-systems recreational-mathematics function-and-relation-composition asked Feb 13 '18 at 23:57

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33 votes

Painting the plane, and finding points one unit apart

geometry graph-theory contest-math coordinate-systems asked Oct 10 '17 at 23:31

math.stackexchange.com

30 votes

Recreational math: If $f(f(x))=e^x$, bound the integral $\int_0^1 f(x)dx$

integration definite-integrals recreational-mathematics functional-equations upper-lower-bounds asked May 15 '18 at 23:14

math.stackexchange.com

25 votes

Strange functional equation: $f(x)+f(\cos(x))=x$

real-analysis functional-equations asked Aug 18 '18 at 17:31

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24 votes

Why does $\int_1^\sqrt2 \frac{1}{x}\ln\left(\frac{2-2x^2+x^4}{2x-2x^2+x^3}\right)dx$ equal to $0$?

integration definite-integrals logarithms symmetry asked Nov 20 '18 at 0:42

math.stackexchange.com

23 votes

Series involving Fibonacci Numbers: $\sum_{k=1}^\infty \frac{1}{F_kF_{k+1}}$

sequences-and-series fibonacci-numbers telescopic-series asked Dec 25 '17 at 22:56

math.stackexchange.com

21 votes

Minimum values of the sequence $\{n\sqrt{2}\}$

recurrence-relations irrational-numbers fractional-part almost-periodic-functions asked Dec 15 '17 at 23:42

math.stackexchange.com

Top Answers

127

Is there a symbol for “taking a derivative of something”?

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Can sum of a rational number and its reciprocal be an integer?

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Unexpected examples of natural logarithm

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Find the probability that the thirteenth spade will appear before the thirteenth diamond?

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An astounding identity: $\int_0^{\pi/2}\ln\lvert\sin(mx)\rvert\cdot \ln\lvert\sin(nx)\rvert\, dx$

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what's the real value of $\sqrt2^{\sqrt2^{\large \sqrt2^{\sqrt2^{\unicode{x22F0}}}}}$?

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Prove that $2^{66}-1$ is not a prime number

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Value of an exponential function

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Solving $f(x) = f(x/2) + f(x/3) + x$

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What other ways can I go about finding the solution to this limit: $\lim\limits_{x \to 0} \frac{9^x - 4^x}{2^x - 3^x}$

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Color the cubes, then assemble them to form a larger cube

puzzling.stackexchange.com

Integral Representation of the Dottie Number

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Suggestions for mathematical solitaire against boredom

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Is the set of all integers odd?

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Integrating the formula for the sum of the first $n$ natural numbers

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Calculate $\sum_{n=0}^\infty \frac1{(4n^2 - 1)^2}$

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Seeking Methods to solve $ I = \int_{0}^{\frac{\pi}{2}} \frac{\arctan\left(\sin(x)\right)}{\sin(x)}\:dx$

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Calculate $\int_{-\infty}^\infty \frac{e^{-x^2}}{x^2+a^2}\ dx$.

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Create the numbers 1 - 30 using the digits 2, 0, 1, 9 in this particular order!

puzzling.stackexchange.com

Find the value of $1-\frac{1}{7}+\frac{1}{9}-\frac{1}{15}+\frac{1}{17}-\frac{1}{23}+\frac{1}{25}…$

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$\forall n \in \mathbb{N}: f(n)=0 \Longrightarrow f'(n)=0$?

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Good final exam bonus problem for calculus students?

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Solving an infinite product of consecutive square roots

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Prove that the minimum value of $\sin^n(x)+\cos^n(x)$ is $\frac{1}{2^{\frac{n}{2}-1}}$, if n is even

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Prove $\frac{1}{2}\sum_p \frac{1}{p^2}+\frac{1}{3}\sum_p \frac{1}{p^3}+\cdots$ converges

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Proving that a recursive sequence will eventually reach an even number.

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Integral $\int_{0}^{\infty}x^{-x}dx$

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Evaluate integral, without using complex numbers

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How do I find $x$ if I know $y$

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Problem calculating sum of convergent series of $\sum_{n=2}^{\infty} \frac{1}{n^{2}-1}$

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Nilknarf

“Integral Milking”

Do numbers get worse than transcendental?

Find three non-constant, pairwise unequal functions $f,g,h:\mathbb R\to \mathbb R$…

What numbers can be created by $1-x^2$ and $x/2$?

Painting the plane, and finding points one unit apart

Recreational math: If $f(f(x))=e^x$, bound the integral $\int_0^1 f(x)dx$

Strange functional equation: $f(x)+f(\cos(x))=x$

Why does $\int_1^\sqrt2 \frac{1}{x}\ln\left(\frac{2-2x^2+x^4}{2x-2x^2+x^3}\right)dx$ equal to $0$?

Series involving Fibonacci Numbers: $\sum_{k=1}^\infty \frac{1}{F_kF_{k+1}}$

Minimum values of the sequence $\{n\sqrt{2}\}$