Most Popular
1500 questions
1612
votes
88 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
- 841
1291
votes
27 answers
Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?
In the book Thomas's Calculus (11th edition) it is mentioned (Section 3.8 pg 225) that the derivative $\frac{\textrm{d}y}{\textrm{d}x}$ is not a ratio. Couldn't it be interpreted as a ratio, because according to the formula $\textrm{d}y =…
BBSysDyn
- 16,115
1086
votes
32 answers
If it took 10 minutes to saw a board into 2 pieces, how long will it take to saw another 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
- 10,327
920
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
- 1,322
891
votes
22 answers
The staircase paradox, or why $\pi\ne4$
What is wrong with this proof?
Is $\pi=4?$
Pratik Deoghare
- 13,573
854
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
- 10,672
852
votes
54 answers
Different ways to prove $\sum_{k=1}^\infty \frac{1}{k^2}=\frac{\pi^2}{6}$ (the 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 -
- 10,970
835
votes
0 answers
A proof of $\dim(R[T])=\dim(R)+1$ without prime ideals?
Please read this first before answering. This question is only concerned with a proof of the dimension formula using the Coquand-Lombardi characterization below. If you post something that doesn't mention the characterization, then it's not an…
Martin Brandenburg
- 163,620
819
votes
18 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
- 12,942
787
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
- 7,871
692
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
- 15,966
660
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
- 101
638
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
- 5,980
628
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…
Christopher
- 6,283
621
votes
44 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
- 2,343