# Tagged Questions

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### What is the Hilbert curve's equation?!

The Hilbert curve has always bugged me because it had no closed equation or function that I could find. What is its equation or function? For example, if I wanted to find the Hilbert's curve point at ...
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### A function to fit a certain S-shaped curve

I am looking for a function to fit a certain type of S-shaped curve. Here are my criteria: The curve always pass three points (0,0), (0.5,0.5) and (1,1). For 0 < x < 0.5, f(x) < x; for ...
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### s-shaped reverse logistic curve

Is there any curve that grows very slow at the beginning then growth picks up exponentially before hitting the wall. I need sort of reverse behavior of the logistic curve ...
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### Real valued function associated with the Diophantine equation $a^2(2^a-a^3)+1=7^b$

The parent question that maybe still remains to be answered at this moment is:Solve the Diophantine equation $a^2(2^a-a^3)+1=7^b$ . As far as the parent question is concerned, when generalizing to ...
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### Functional equations of (S-shape?) curves

I am looking for the way to "quite easily" express particular curves using functional equations. What's important (supposing the chart's size is 1x1 - actually it doesn't matter in the final ...
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### What is the limit distance to the base function if offset curve is a function too?

I asked a question about parallel functions in here . I understood that offset curves that are the parallels of a function may not be functions after J.M.'s answer. I got new questions after that ...
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### Parallel functions.

In 2 dimensions, we can draw 2 parallel lines that have the same distance from a line. I wanted to find parallel functions of a function and their distance is $d$ to the function for all inputs and ...
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### Is there such a function?

Does there exist a continuous function $f:[0,1]\rightarrow\mathbb{R}$ such that for any two points P,Q on the curve, there exists a point R on the curve such that PQR is an equilateral triangle? If ...
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### Non-linear function on $\mathbb{R}^2$ preserving the origin and maps lines onto lines?

Is there an $f:\mathbb{R}^2 \to \mathbb{R}^2$ such that: $(0,0)\mapsto (0,0)$; and for any $a,b,c$ with $a^2 + b^2 >0$, the set $A=\{(x,y):ax+by=c\}$ is mapped onto ...
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### polar graphs and investigation

I am new to polar graphs and I am trying to investigate some certain cases: What happens when you change the $b$ value to different positive integers in polar equations of the forms: ...
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### Continuous curve interpolating a list of points

I need a function (a curve -- preferably a simple one) that, given $n$ points of a 2D space ($R^2$) passes (interpolates) through all points in a smooth/continuous way. Found out that what I need is ...
255 views

### From geometrical figures to function

There's one basilar math thing that keeps bugging me: the fact that a really simple 2D geometrical figure (like a circle) might not be a function. I know what the definition of a function is. A ...