Alexey Ivanov

## 1280 Reputation

12 years, 139 days

## Circle of maximum radius inscribed betwe...

Maple

The problem arose while playing with inscribed circles, as in this post. If anyone is interested, try to find a circle of maximum radius inscribed between the curves
x1^2 + 2*x2^2 - 1 = 0 and (x1 - sin(x1))^2 + (x2 - sin(x2))^2 - 1 = 0.

Curve graphs.

## The shortest distance between the green ...

Maple

A little continuation of topics 1 and 2. This is a very similar cube from 2

but with a different equation:

f1 := (x1-sin(x1))^2+(x2-sin(x2))^2+(x3-sin(x3))^2-0.02513144866;
And other point coordinates (-.8283302152, -.8283302152, .8283302152) and (.8283302152, .8283302152, -.8283302152).

## Shortest curve on a surface connecting 2...

Maple

I liked the recent question from user goebeld and especially the answer from Rouben Rostamian.
But what if the red and green  points are on the surface x1^4 + x2^4 + x3^4 -1 = 0
Points coordinates (-0.759835685700000, -0.759835685700000, 0.759835685700000) and
(0.759835685700000, 0.759835685700000, -0.759835685700000).

Where will the shortest distance between these points on a given surface be? Taking into account symmetry, of course.

## Rose and Python...

Maple

It was found on the social networks of the WM group. Written in Python. Perhaps someone would like to adopt it.

## System of nonlinear equations 2x2...

Maple

The question is not at all from me, but, probably, one might say, from the authors of this publication.  interesting_system.pdf

Just for fun.
Find all real solutions to this 2x2 system of nonlinear equations in any given domain.

f1:=x1-x1*sin(x1+5x2)-x2*cos(5x1-x2);
f2:=x2-x2*sin(5x1-3x2)+x1*cos(3x1+5x2);

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