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Interesting 15 Bountied Hot Week Month
26 votes
6 answers
2k views

Why is this angle always less than $49°$?

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dfnu
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40 votes
7 answers
2k views

How far can an infinite number of unit length planks bridge a right-angled gap?

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4177318477
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17 votes
6 answers
1k views

What is the correct definition of a limit point in real analysis?

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Xander Henderson♦
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5 votes
8 answers
944 views

How to find the angle created when joining two vertices of four adjacent squares

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Letac Gérard
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11 votes
5 answers
2k views

Why Is the Dual Basis Mathematically Unavoidable?

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Man-I-Fold
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2 votes
6 answers
1k views

Example that the union of an infinite number of closed sets is not necessarily closed.

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Blake Winter
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12 votes
5 answers
545 views

Non-recursive, explicit rational sequence that converges to $\sqrt{2}$

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Mikhail Katz
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16 votes
3 answers
1k views

Why does the leading coefficient of a quadratic trinomial resemble some sort of a slope?

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Lutz Lehmann
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8 votes
9 answers
561 views

Evaluate $\int_0^{\frac\pi2}\frac{\mathrm dx}{a\sin ^2x+b\cos ^2x}$ without using its antiderivative

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Integreek
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18 votes
6 answers
639 views

How to solve $\frac{dy}{dx}=xy^{1/2}, y(0)=0$?

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xpaul
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14 votes
2 answers
2k views

Is this formula for cosine correct? (And is it significant) [closed]

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Claude Leibovici
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23 votes
1 answer
2k views

Continuous extensions of GCD to $\Bbb R^{+}\!\!\times \Bbb R^{+}\!$ still commutative and distributive

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Bill Dubuque
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9 votes
3 answers
1k views

Are all natural numbers (except 1 and 2) part of at least one primitive pythagorean triplet?

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poetasis
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13 votes
2 answers
2k views

Is the transfer principle useless?

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Henry
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11 votes
3 answers
2k views

Can there be a continuous function with infinite derivative everywhere?

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Adam Rubinson
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6 votes
6 answers
841 views

Why are we allowed to classify indeterminate limits with a specific form without proving it formally?

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Daniel Smania
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7 votes
5 answers
292 views

Are there any other special mathematical definitions like $0! =1$ to ensure consistent and valid results?

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T﹏T
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10 votes
5 answers
1k views

Why Does Tao Use Inductive Language When Giving Recursive Definitions?

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Kyle Miller
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6 votes
3 answers
1k views

Find the exact path to get the ball in the hole with 2 bounces

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Oscar Lanzi
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11 votes
4 answers
437 views

Evaluate: $4^9-\binom{8}{1}4^8+\binom{7}{2}4^7-\binom{6}{3}4^6+\binom{5}{4}4^5$

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minh quý lê
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12 votes
2 answers
1k views

What type theory really is?

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Mauro ALLEGRANZA
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26 votes
1 answer
753 views

How should a string be laid on a disk to minimize the expected shortest distance between a random point on the disk and the string?

Mark H's user avatar
Mark H
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4 votes
6 answers
317 views

inequality $\frac{x^2 + y^2}{x + y} \geq \frac{x + y}{2}$ [closed]

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David K
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7 votes
2 answers
1k views

Why does this method work some of the time (but only some?)

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true blue anil
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11 votes
2 answers
418 views

Evaluating $\sum_{m=0}^\infty \sum_{n=0}^\infty \frac{1}{(4m + 1)(4n + 1)(4m + 4n + 3)}$

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Svyatoslav
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5 votes
4 answers
594 views

Solving $x^{x^3}=729$

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RobPratt
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8 votes
2 answers
759 views

Probability that four integers can be partitioned into two sets of equal sum

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JC Q
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9 votes
3 answers
445 views

Generalisation of $\int_0^{\infty} \frac{\tan ^{-1}\left(\tan ^2 x\right)}{x^2}\,dx .$

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Lai
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18 votes
3 answers
411 views

Why does every rose curve contain a regular polygon?

David K's user avatar
David K
  • 111k
8 votes
3 answers
520 views

Is there a tame proof of "No anti-knots?"

Kyle Miller's user avatar
Kyle Miller
  • 20.7k
6 votes
4 answers
945 views

Three pulleys are connected to each other via two ropes. By how many centimeters does point Q move upwards?

Arthur's user avatar
Arthur
  • 206k
14 votes
2 answers
719 views

A sequence based on Euler's totient function that always converges to prime numbers

Michael Hartley's user avatar
Michael Hartley
  • 3,593
17 votes
1 answer
551 views

$\int_0^{\infty}\text{Ai}^4(x)dx = \ln(3)/24 \pi^2$

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caesar_147
  • 3
15 votes
1 answer
318 views

What is $\lim_n \sqrt[n]{1+\cos(n)}$?

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Dermot Craddock
  • 5,294
16 votes
1 answer
482 views

Characterization of holomorphic function whose n-fold composition is the identity

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Gerd
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5 votes
3 answers
435 views

Let $z$ be a complex number. If $|z^2+1| \leq 2$, then show that $|z+2| \geq 1$.

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Martin R
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12 votes
4 answers
841 views

Closed form solution for $ \int\limits_{0}^{1} x^{x} (1-x)^{1-x} dx $

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Dhairya Kumar
  • 190
9 votes
3 answers
652 views

Can you prove equality of two expressions by setting them equal in an equation? [closed]

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Daniel S
  • 93
9 votes
4 answers
367 views

compute $\int\limits_{0}^{1} \frac{\sinh^{-1} \left( \sqrt{\frac{1}{2+x}} \right)}{\sqrt{3 - 2x - x^2}} \, \textrm dx$

Dhairya Kumar's user avatar
Dhairya Kumar
  • 190
6 votes
6 answers
367 views

Seeking other generalisations to the integral $\int_0^{\infty} \frac{\ln \left(x+\frac{1}{x}\right)}{1+x^2}dx$

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Sangchul Lee
  • 186k
9 votes
2 answers
409 views

Does this characterize the product topology?

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Joshua Tilley
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13 votes
1 answer
1k views

Why do these valleys in $LCM(P_n - 1, P_n + 1) \bmod n$ exist and are they random?

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philipxy
  • 129
6 votes
4 answers
428 views

Least $n$ with ${\rm lcm}(n,20,15) = 360$ [duplicate]

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true blue anil
  • 49.7k
5 votes
5 answers
322 views

What is the probability that this random variable is less than 1? [duplicate]

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Dan
  • 40.3k
3 votes
4 answers
510 views

How many elements are present in the subset of a null set?

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Bruno Andrades
  • 5,452
6 votes
2 answers
502 views

Cutting a Möbius strip in thirds. Why are the resulting strips interlinked?

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heropup
  • 146k
10 votes
1 answer
489 views

Does every (possibly infinite dimensional) vector space have an orthogonal Hamel basis?

Bruno Andrades's user avatar
Bruno Andrades
  • 5,452
6 votes
4 answers
373 views

Is there a closed form for integral $\int_0^\infty \frac{\ln(1+x^2)}{x^2+2a x+1}dx $ with $|a|<1$

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Claude Leibovici
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