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1500 questions
1532
votes
86 answers
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 mathematically beautiful at the same time.
Do you know…
RBS
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1205
votes
26 answers
Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?
In Thomas's Calculus (11th edition), it is mentioned (Section 3.8 pg 225) that the derivative $dy/dx$ is not a ratio. Couldn't it be interpreted as a ratio, because according to the formula $dy = f'(x) \, dx$ we are able to plug in values for $dx$…
BBSysDyn
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1067
votes
32 answers
How long will it take Marie to saw another board into 3 pieces?
So this is supposed to be really simple, and it's taken from the following picture:
Text-only:
It took Marie $10$ minutes to saw a board into $2$ pieces. If she works just as fast, how long will it take for her to saw another board into
$3$…
yuritsuki
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921
votes
29 answers
Can I use my powers for good?
I hesitate to ask this question, but I read a lot of the career advice from MathOverflow and math.stackexchange, and I couldn't find anything similar.
Four years after the PhD, I am pretty sure that I am going to leave academia soon. I do enjoy…
Flounderer
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842
votes
23 answers
The staircase paradox, or why $\pi\ne4$
What is wrong with this proof?
Is $\pi=4?$
Pratik Deoghare
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823
votes
27 answers
How to study math to really understand it and have a healthy lifestyle with free time?
Here's my issue I faced;
I worked really hard studying Math, so because of that, I started to realised that I understand things better. However, that comes at a big cost:
In the last few years, I had practically zero physical exercise, I've gained…
Leo
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790
votes
49 answers
Different methods to compute $\sum\limits_{k=1}^\infty \frac{1}{k^2}$ (Basel problem)
As I have heard people did not trust Euler when he first discovered the formula (solution of the Basel problem)
$$\zeta(2)=\sum_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}.$$
However, Euler was Euler and he gave other proofs.
I believe many of you…
AD - Stop Putin -
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789
votes
1 answer
A proof for $\dim(R[T])=\dim(R)+1$ without prime ideals?
If $R$ is a commutative ring, it is easy to prove $\dim(R[T]) \geq \dim(R)+1$, where $\dim$ denotes the Krull dimension. If $R$ is Noetherian, we have equality. Every proof I'm aware of uses quite a bit of commutative algebra and non-trivial…
Martin Brandenburg
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763
votes
17 answers
What's an intuitive way to think about the determinant?
In my linear algebra class, we just talked about determinants. So far I’ve been understanding the material okay, but now I’m very confused. I get that when the determinant is zero, the matrix doesn’t have an inverse. I can find the determinant of a…
Jamie Banks
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728
votes
12 answers
Does $\pi$ contain all possible number combinations?
$\pi$ Pi
Pi is an infinite, nonrepeating $($sic$)$ decimal - meaning that
every possible number combination exists somewhere in pi. Converted
into ASCII text, somewhere in that infinite string of digits is the
name of every person you will ever…
Chani
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679
votes
25 answers
Splitting a sandwich and not feeling deceived
This is a problem that has haunted me for more than a decade. Not all the time - but from time to time, and always on windy or rainy days, it suddenly reappears in my mind, stares at me for half an hour to an hour, and then just grins at me, and…
VividD
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662
votes
164 answers
What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's Lament," and found that I, too, lament the uninspiring…
Liz
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615
votes
8 answers
Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real?
So we all know that the continued fraction containing all $1$s...
$$
x = 1 + \frac{1}{1 + \frac{1}{1 + \ldots}}
$$
yields the golden ratio $x = \phi$, which can easily be proven by rewriting it as $x = 1 + \dfrac{1}{x}$, solving the resulting…
Martin Ender
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609
votes
6 answers
Why can you turn clothing right-side-out?
My nephew was folding laundry, and turning the occasional shirt right-side-out. I showed him a "trick" where I turned it right-side-out by pulling the whole thing through a sleeve instead of the bottom or collar of the shirt. He thought it was…
Chris
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595
votes
40 answers
Examples of patterns that eventually fail
Often, when I try to describe mathematics to the layman, I find myself struggling to convince them of the importance and consequence of "proof". I receive responses like: "surely if Collatz is true up to $20×2^{58}$, then it must always be true?";…
Matt
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