## Top new questions this week:

### A 1,400 years old approximation to the sine function by Mahabhaskariya of Bhaskara I

The approximation $$\sin(x) \simeq \frac{16 (\pi -x) x}{5 \pi ^2-4 (\pi -x) x}\qquad (0\leq x\leq\pi)$$ was proposed by Mahabhaskariya of Bhaskara I, a seventh-century Indian mathematician. I ...

(trigonometry) (approximation) (math-history)
 asked by Claude Leibovici 78 votes
 answered by Lucian 13 votes

### What did mathematicians study as an undergraduate/graduate before modern mathematics such as modern algebra and analysis?

I am curious as to what mathematicians such as Leibnitz and Gauss and the Bernoulli's studied when they were students in university. I find it fascinating how we are taught calculus and abstract ...

(soft-question) (math-history) (education) (big-list) (mathematicians)
 asked by Johann Franklin 26 votes
 answered by Geremia 5 votes

### Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?

Does $1.0000000000\cdots 1$ (with an infinite number of $0$ in it) exist?

(calculus) (limits) (real-numbers) (decimal-expansion)
 asked by iMath 24 votes
 answered by Asaf Karagila 45 votes

### The Wicked Integral

My brother's friend gave me the following wicked integral with a beautiful result {\Large\int_0^\infty} \frac{dx}{\sqrt{x} \bigg[x^2+\left(1+2\sqrt{2}\right)x+1\bigg] ...

(calculus) (integration) (definite-integrals) (improper-integrals) (closed-form)
 asked by Anastasiya-Romanova 24 votes
 answered by Omran Kouba 25 votes

### What are the odds of hitting exactly 100 rolling a fair die

I roll a fair die and sequentially sum the numbers the die shows. What are the odds the summation will hit exactly 100? More generally, what are the odds of hitting an exact target number t while ...

(probability) (dice)
 asked by Ohad Dan 20 votes
 answered by Did 21 votes

### Can you cancel out a term if equal to zero?

quick question here: In my proofs class we had a problem that after a little work we end up with: $x(x-y)=(x+y)(x-y)$ where $x = y$. Now, I know this is pretty basic, but my teacher said that for ...

(algebra-precalculus)
 asked by Descoladan 19 votes
 answered by Lubin 74 votes

### A function having limit at every point but continuous nowhere

Is there a function $\,f:\mathbb{R}\rightarrow\mathbb{R},\,$ that has a limit at every point but is continuous nowhere?

(calculus) (real-analysis) (analysis) (limits) (continuity)
 asked by Tal Porat 17 votes
 answered by Yiorgos S. Smyrlis 11 votes

## Greatest hits from previous weeks:

### Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain, but are ...

(soft-question) (education) (big-list)
 asked by Nicholas 431 votes
 answered by congusbongus 405 votes

### 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 Oliver Spryn 14 votes
 answered by David Mitra 31 votes

## Can you answer these?

I want to show that if $T$ is a bounded operator between two Hilbert spaces and $T$ is not compact then there exists an orthonormal sequence $y_{n}$ and an $R>0$ such that $\forall n\in ... (functional-analysis)  asked by noether28 4 votes ### Concerning the classical normalized Eisenstein series Earlier I asked this question. As of today, it has not been answered. Yet still, I have a follow-up question: In general, how does one express$E_4(\tau)$and$E_6(\tau)$in closed form for special ... (sequences-and-series) (reference-request) (modular-forms)  asked by glebovg 1 vote ### Proving that an analytic function is$0$We are given an analytic function$f(z)$in the region$\Omega=\{z : b>Re(z)>a\}$. It is also given that the function is continuous and bounded in$\overline\Omega\$. The question is to show that ...

(complex-analysis)
 asked by happymath 1 vote
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