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1500 questions
63
votes
12 answers
Is there an equation to describe regular polygons?
For example, the square can be described with the equation $|x| + |y| = 1$. So is there a general equation that can describe a regular polygon (in the 2D Cartesian plane?), given the number of sides required?
Using the Wolfram Alpha site, this input…
Vincent Tan
- 733
63
votes
3 answers
$5^n+n$ is never prime?
In the comments to the question: If $(a^{n}+n ) \mid (b^{n}+n)$ for all $n$, then $ a=b$, there was a claim that $5^n+n$ is never prime (for integer $n>0$).
It does not look obvious to prove, nor have I found a counterexample.
Is this really…
Aryabhata
- 82,206
63
votes
1 answer
When are nonintersecting finite degree field extensions linearly disjoint?
Let $F$ be a field, and let $K,L$ be finite degree field extensions of $F$ inside a common algebraic closure. Consider the following two properties:
(i) $K$ and $L$ are linearly disjoint over $F$: the natural map $K \otimes_F L \hookrightarrow KL$…
Pete L. Clark
- 97,892
63
votes
8 answers
Example of Partial Order that's not a Total Order and why?
I'm looking for a simple example of a partial order which is not a total order so that I can grasp the concept and the difference between the two.
An explanation of why the example is a partial order but not a total order would also be greatly…
eZanmoto
- 749
63
votes
8 answers
Graphs for which a calculus student can reasonably compute the arclength
Given a differentiable real-valued function $f$, the arclength of its graph on $[a,b]$ is given by
$$\int_a^b\sqrt{1+\left(f'(x)\right)^2}\,\mathrm{d}x$$
For many choices of $f$ this can be a tricky integral to evaluate, especially for calculus…
Mike Pierce
- 18,938
63
votes
8 answers
Is there a third dimension of numbers?
Is there a third dimension of numbers like real numbers, imaginary numbers, [blank] numbers?
awesomeguy
- 749
63
votes
2 answers
Is there a step by step checklist to check if a multivariable limit exists and find its value?
Do we rely on certain intuition or is there an unofficial general crude checklist I should follow?
I had a friend telling me that if the sum of the powers on the numerator is smaller then the denominator, there is a higher chance that it may not…
Yellow Skies
- 1,710
63
votes
14 answers
Is there a math expression equivalent to the conditional ternary operator?
Is there a math equivalent of the ternary conditional operator as used in programming?
a = b + (c > 0 ? 1 : 2)
The above means that if $c$ is greater than $0$ then $a = b + 1$, otherwise $a = b + 2$.
dataphile
- 812
63
votes
1 answer
Which Algebraic Properties Distinguish Lie Groups from Abstract Groups?
This question is motivated by a previous one: Conditions for a smooth manifold to admit the structure of a Lie group, and wants to be a sort of "converse".
Here I am taking an abstract group $G$ and looking for necessary conditions for it to admit…
Lor
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63
votes
6 answers
What is the difference between homotopy and homeomorphism?
What is the difference between homotopy and homeomorphism? Let X and Y be two spaces, Supposed X and Y are homotopy equivalent and have the same dimension, can it be proved that they are homeomorphic? Otherwise, is there any counterexample?…
liufu
- 691
63
votes
5 answers
In how many different ways can a 9-panel comic grid be used?
While writing my answer to Why does “Watchmen” use the 9-panel grid? I used this picture to indicate the many ways it can be divided into groups (which may be used for the panels of a comic, as was the case in “Watchmen”):
Image source…
Gallifreyan
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63
votes
2 answers
The most effective windshield-wiper setup. (Packing a square with sectors)
I was on the bus on the way to uni this morning and it was raining quite heavily. I was sitting right up near the front where I could see the window wipers doing their thing. It made me think "what is the best configuration of window wipers for…
Harambe
- 8,230
63
votes
7 answers
Why is the Continuum Hypothesis (not) true?
I'm making my way through Thomas W Hungerfords's seminal text "Abstract Algebra 2nd Edition w/ Sets, Logics and Categories" where he makes the statement that the Continuum Hypothesis (There does not exist a set with a cardinality less than the reals…
zetavolt
- 863
63
votes
10 answers
Big List of Erdős' elementary proofs
Paul Erdős was one of the greatest mathematicians of all time and he was famous for his elegant proofs from The Book. I posted a question about one of his theorem and got a reference, and I have other questions I want to know the answer to too. But,…
Saikat
- 2,461
63
votes
7 answers
How do we know the ratio between circumference and diameter is the same for all circles?
The number $\pi$ is defined as the ratio between the circumeference and diameter of a circle. How do we know the value $\pi$ is correct for every circle? How do we truly know the value is the same for every circle?
How do we know that $\pi =…
Happy
- 1,363