Linked Questions

50
votes
18answers
7k views

Intuitive Understanding of the constant “$e$”

Potentially related-questions, shown before posting, didn't have anything like this, so I apologize in advance if this is a duplicate. I know there are many ways of calculating (or should I say "...
119
votes
7answers
13k views

$\pi$ in arbitrary metric spaces

Whoever finds a norm for which $\pi=42$ is crowned nerd of the day! Can the principle of $\pi$ in euclidean space be generalized to 2-dimensional metric/normed spaces in a reasonable way? For ...
61
votes
10answers
5k views

Symbol for “probably equal to” (barring pathology)?

I am writing lecture notes for an applied statistical mechanics course and often need to express the notion that something is very probably true for functional forms found in the wild, without ...
27
votes
20answers
3k views

Interesting Math for 3-graders

I'm supposed to give a 30 minutes math lecture tomorrow at my 3-grade daughter's class. Can you give me some ideas of mathemathical puzzles, riddles, facts etc. that would interest kids at this age? ...
35
votes
1answer
2k views

Are $\pi$ and $e$ algebraically independent?

Update Edit : Title of this question formerly was "Is there a polynomial relation between $e$ and $\pi$?" Is there a polynomial relation (with algebraic numbers as coefficients) between $e$ or $\pi$ ?...
7
votes
4answers
814 views

Why are all circles similar? (Why is $\pi$ a constant?) [duplicate]

I just know that I'm going to look like a crackpot, but here goes. The number $\pi$ is defined as the ratio of the circumference of a circle to its diameter. So there is an assumption here that all ...
2
votes
5answers
414 views

The origin of $\pi$

How was $\pi$ originally found? Was it originally found using the ratio of the circumference to diameter of a circle of was it found using trigonometric functions? I am trying to find a way to find ...
2
votes
4answers
285 views

Philosophical question about Pi and connections in maths

Pi is the ratio of circumference of a circle to its diameter. Okay. Got that, easy enough. Now, why does the following equality hold true? $$ \frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} - \frac{1}{...
2
votes
2answers
307 views

Is the value of $\pi$ in 2d the same in 3d? [closed]

I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!) Given my first question: What is ...
5
votes
6answers
282 views

Not $\pi$ - What if I used $3$? Teaching $\pi$ discovery to K-6th grade

So, in ancient Mesopotamia they knew that they didn't really have the correct number ($\pi$) to determine attributes of a circle. They rounded to $3$. If you acted as though $\pi=3$, what shape would ...
0
votes
1answer
745 views

Why is treating $i$ as a constant in integration, valid?

Why do we, when doing integrals like $\int i\cos xdx$, treat $i$ to be a constant? Is there any proof? Wolfram gives the answer simply as $i\sin x+\text{[constant]}$. I have a confusion, because ...