Find a curve with constraints

asked 2025-01-16 11:03:14 +0200

Hello,

I am trying to find the steepest curve f(x) constrained so that if we consider a segment [AB] with its edges on the curve (A = f(x=a), B = f(x=b)) and with [AB] length = L , the distance between f(x) and the AB segment is < h, with "h" and "L" known.

My maths knowledge faded away - I'm looking for some help on how to approach this - and then to see if it's something where Sage can assist on. Thanks!

edit retag flag offensive close merge delete

Comments

Sounds like a theoretic problem irrelevant to Sage.

Max Alekseyev gravatar imageMax Alekseyev ( 2025-01-18 13:46:34 +0200 )edit

What does it mean "steepest"? For instance, if $A=(0,0)$, $B=(1,0)$, $f:[0,1]\to[0,1]$ with $f(0)=f(1)=0$ and $h=1$, among the many continuous $f$-functions which is the one we want?

dan_fulea gravatar imagedan_fulea ( 2025-02-17 01:19:20 +0200 )edit