0
votes
0answers
13 views

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 ...
0
votes
0answers
26 views

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 ...
1
vote
1answer
34 views

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 ...
1
vote
1answer
56 views

Express parametric curve as graph of a function

I have a parametric curve in $\mathbb{R}^2$ given by $$ t\mapsto f(t)\left(\begin{array}{c}1\\1\end{array}\right)+\sqrt{-f'(t)}\left(\begin{array}{c}1\\-1\end{array}\right),\quad ...
-2
votes
2answers
394 views

Change parabolic equation to canonical form

I have equation $y = -x^2 + 2x + 7$. How can I change it to canonical form, which looks like $y^2 = 2px$ ? ($p$ will be parameter) What i ve tried so far: $$\begin{align} y &= -x^2 + 2x + 7\\ y ...
1
vote
2answers
3k views

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 ...
2
votes
2answers
108 views

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 ...
2
votes
2answers
621 views

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 ...
4
votes
4answers
601 views

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 ...
2
votes
3answers
98 views

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 ...
1
vote
1answer
195 views

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: ...
1
vote
1answer
151 views

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 ...
0
votes
1answer
231 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 ...