Linked Questions

If we take the definition of π in the form: π is the ratio of a circle's circumference to its diameter. There implicitly assumed that the norm is Euclidian: \begin{equation} \|\boldsymbol{x}\|_{...

Does any one know of a concept analogous to $\pi$ in metric spaces. Namely, taking the all the points $1$ away from a point, and measuring the distance as some sort of limit? This was prompted when I ...

Wait before you dismiss this as a crank question :) A friend of mine teaches school kids, and the book she uses states something to the following effect: If you divide the circumference of any ...

I have never seen a formal definition of the Hilbert curve, much less a careful analysis of why it fills the whole square. The Wikipedia and Mathworld articles are typically handwavy. I suppose the ...

How/why does $\pi$ vary with different metrics in p-norms? Full question is below. Background Long ago I did an investigation on Taxicab Geometry using basic geometry. One think I recall is that a ...

This is a silly question that came to mind after watching numberphile video on How Pi was nearly changed to 3.2. For which $p\in(1,+\infty)$ is the ratio of the perimeter of the $L^p$ disc in $\Bbb R^...

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 ...

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 ...

So this is straight from my homework so please don't all out answer it but maybe point me in the right direction. We are learning about dimensionality and clustering algorithms and this is one ...

Suppose I have a normed vectorspace $(X,\|.\|)$ and a (differential) path $\gamma:[0,1]\rightarrow X$. Can the Length of the curve be defined as $$L(\gamma)=\int_0^1\|\gamma'(t)\|\text{d}t$$ Or do ...

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 ...

More precisely, can we build a norm $N$ on $\mathbb{R}^2$, such that the ratio circumference / diameter (computed with norm $N$) of a standard circle is $42$? (By standard circle, I mean a circle ...

$\pi$ is dependent on properties of geometry, assuming that we define it as $C/d$. Could there be a geometry where $\pi$ is a rational number or an integer?

In which $L^p$ metric is $\pi = 3.5$? I am interested because it's well known that $\pi$ can range from $3.14...$ to $4$ in $L^{\infty}$

For a metric space, $(X,d)$, define the following: for every $x \in X$, the local similitude group, $Sim(X, x)$, is the set of all surjective similitudes $X \to X$ which fix $x$. for every $x \in X$,...