Mathematics Weekly Newsletter
Mathematics Weekly Newsletter

Top new questions this week:

Problems that become easier in a more general form.

When solving a problem, we often look at some special cases first, and then try to work our way up to the general case. It would be interesting to see some counterexamples to this mental process, …

(soft-question) (proof-strategy) (examples-counterexamples) (problem-solving)  
asked by MGA 49 votes
answered by JimmyK4542 51 votes

How far can one see over the ocean?

Since Earth is a sphere, one has only a limited visibility radius. How far is that, actually? This Q&A was inspired by this question, about whether or not Legolas can see the 24km distant Riders …

asked by M.Herzkamp 44 votes
answered by Michael Hardy 45 votes

Geometry problem involving infinite number of circles

What is the sum of the areas of the grey circles? I have not made any progress so far.

(sequences-and-series) (geometry)  
asked by Dan 35 votes
answered by J. J. 30 votes

Mathematical literature to lose yourself in

H.M. Edwards in the preface to his book on the Riemann Zeta Function, summarises his philosophy on learning Mathematics: ...I have tried to say to students of mathematics that they should read the …

(reference-request) (soft-question) (recreational-mathematics) (big-list)  
asked by user14982305 23 votes
answered by InTransit 7 votes

Simulate a 7-sided die with a 6-sided die

What is the most efficient way to simulate a 7-sided die with a 6-sided die? I've put some thought into it but I'm not sure I get somewhere specifically. To create a 7-sided die we can use a …

(probability) (dice)  
asked by neverlastn 23 votes
answered by Chris Culter 5 votes

Which is greater, $20 \uparrow\uparrow\uparrow\uparrow 20$ or $4 \uparrow\uparrow\uparrow\uparrow\uparrow 4$?

This past Wednesday's What-If had this image at the bottom: In particular, I am interested in $20 \uparrow\uparrow\uparrow\uparrow 20$. I immediately thought of Graham's Number, but clearly that …

(number-theory) (recreational-mathematics)  
asked by El'endia Starman 22 votes
answered by Mark S. 10 votes

Where did the negative answer come from?

The question is to evaluate $\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\cdots }}}}$ $$x=\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\cdots }}}}$$ $$x^2=2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\cdots }}}}$$ $$x^2=2+x$$ …

(sequences-and-series) (algebra-precalculus) (limits) (nested-radicals)  
asked by Shabbeh 20 votes
answered by Liu Gang 42 votes

Greatest hits from previous weeks:

How to Determine if a Function is One-to-One

I am looking for the "best" way to determine whether a function is one-to-one, either algebraically or with calculus. I know a common, yet arguably unreliable method for determining this answer would …

(calculus) (algebra-precalculus) (functions)  
asked by spryno724 11 votes
answered by David Mitra 27 votes

Mathematicians ahead of their time?

In every field there's always that person who's just years ahead of their time. For instance, Paul Morphy (born 1837) is said to have retired from chess because he found no one to match his technique …

(soft-question) (math-history) (big-list) (mathematicians)  
asked by hb20007 59 votes
answered by MJD 56 votes

Can you answer these?

Explicit description of small open set containing the rationals

We know that the set $\mathbb{Q}$ of rational numbers has measure zero because it is countable. In fact, if $(q_n)_{n=1,2,\ldots}$ is an enumeration of $\mathbb{Q}$, then …

asked by Harald Hanche-Olsen 7 votes

Sum the series $\sum_{n = 0}^{\infty} (-1)^{n}\{(2n + 1)^{7}\cosh((2n + 1)\pi\sqrt{3}/2)\}^{-1}$

In one of his letters to G. H. Hardy, Ramanujan gave the following sum $$\dfrac{1}{1^{7}\cosh\left(\dfrac{\pi\sqrt{3}}{2}\right)} - \dfrac{1}{3^{7}\cosh\left(\dfrac{3\pi\sqrt{3}}{2}\right)} + …

asked by Paramanand Singh 6 votes

Find the Number of Integral Solutions

Let $k$ be an integer such that $1 \leq k \leq \left(\dfrac{p-1}{2}\right)$ for some odd prime $p$. Let $ a$ be another integer such that $1 \leq a \leq (p-1)$. Then find the number of integral values …

asked by user170039 5 votes
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