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1500 questions
304
votes
15 answers
Math without pencil and paper
For someone who is physically unable to use a pencil and paper, what would be the best way to do math?
In my case, I have only a little movement in my fingers. I can move a computer mouse and press the left button. Currently I do very little math…
Jeroen
- 2,599
302
votes
27 answers
Why do mathematicians use single-letter variables?
I have much more experience programming than I do with advanced mathematics, so perhaps this is just a comfort thing with me, but I often get frustrated when I try to follow mathematical notation. Specifically, I get frustrated trying to keep track…
eater
- 3,153
300
votes
18 answers
Why does this innovative method of subtraction from a third grader always work?
My daughter is in year $3$ and she is now working on subtraction up to $1000.$ She came up with a way of solving her simple sums that we (her parents) and her teachers can't understand.
Here is an example: $61-17$
Instead of borrowing, making it…
user535429
- 2,167
299
votes
48 answers
Can't argue with success? Looking for "bad math" that "gets away with it"
I'm looking for cases of invalid math operations producing (in spite of it all) correct results (aka "every math teacher's nightmare").
One example would be "cancelling" the 6s in
$$\frac{64}{16}$$
Another one would be something like
$$\frac{9}{2} -…
kjo
- 14,904
298
votes
63 answers
Funny identities
Here is a funny exercise
$$\sin(x - y) \sin(x + y) = (\sin x - \sin y)(\sin x + \sin y).$$
(If you prove it don't publish it here please).
Do you have similar examples?
AD - Stop Putin -
- 11,200
294
votes
11 answers
Is '$10$' a magical number or I am missing something?
It's a hilarious witty joke that points out how every base is '$10$' in its base. Like,
\begin{align}
2 &= 10\ \text{(base 2)} \\
8 &= 10\ \text{(base 8)}
\end{align}
My question is if whoever invented the decimal system had chosen $9$…
Shubham
- 2,533
293
votes
24 answers
Is mathematics one big tautology?
Is mathematics one big tautology? Let me put the question in clearer terms:
Mathematics is a deductive system; it works by starting with arbitrary axioms, and deriving therefrom "new" properties through the process of deduction. As such, it would…
Coffee_Table
- 2,945
290
votes
14 answers
Help with a prime number spiral which turns 90 degrees at each prime
I awoke with the following puzzle that I would like to investigate, but the answer may require some programming (it may not either). I have asked on the meta site and believe the question to be suitable and hopefully interesting for the…
Karl
- 4,763
289
votes
5 answers
Is $7$ the only prime followed by a cube?
I discovered this site which claims that "$7$ is the only prime followed by a cube". I find this statement rather surprising. Is this true? Where might I find a proof that shows this?
In my searching, I found this question, which is similar but…
David Starkey
- 2,393
287
votes
6 answers
In (relatively) simple words: What is an inverse limit?
I am a set theorist in my orientation, and while I did take a few courses that brushed upon categorical and algebraic constructions, one has always eluded me.
The inverse limit. I tried to ask one of the guys in my office, and despite a very shady…
Asaf Karagila
- 405,794
285
votes
3 answers
How does one prove the determinant inequality $\det\left(6(A^3+B^3+C^3)+I_{n}\right)\ge 5^n\det(A^2+B^2+C^2)$?
Reposted on MathOverflow
Let $\,A,B,C\in M_{n}(\mathbb C)\,$ be Hermitian and positive definite matrices such that $A+B+C=I_{n}$, where $I_{n}$ is the identity matrix. Show that $$\det\left(6(A^3+B^3+C^3)+I_{n}\right)\ge 5^n \det…
math110
- 94,932
- 17
- 148
- 519
284
votes
5 answers
Evaluate $\int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\,\Bbb dx$
Evaluate the following integral
$$
\tag1\int_{0}^{\frac{\pi}{2}}\frac1{(1+x^2)(1+\tan x)}\,\Bbb dx
$$
My Attempt:
Letting $x=\frac{\pi}{2}-x$ and using the property that
$$
\int_{0}^{a}f(x)\,\Bbb dx = \int_{0}^{a}f(a-x)\,\Bbb dx
$$
we…
juantheron
- 56,203
283
votes
6 answers
A 1400 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 wondered how much this could be improved using our…
Claude Leibovici
- 289,558
283
votes
5 answers
The Mathematics of Tetris
I am a big fan of the old-school games and I once noticed that there is a sort of parity associated to one and only one Tetris piece, the $\color{purple}{\text{T}}$ piece. This parity is found with no other piece in the game.
Background: The Tetris…
Eric Naslund
- 73,551
279
votes
6 answers
What is the practical difference between a differential and a derivative?
I ask because, as a first-year calculus student, I am running into the fact that I didn't quite get this down when understanding the derivative:
So, a derivative is the rate of change of a function with respect to changes in its variable, this much…
Faqa
- 2,791