## MSE publications / references 2021

In die Beschränkung zeigt sich erst der Meister (Goethe).
Questions & Answers @ Mathematics Stack Exchange:

### Find the area enclosed by $\sqrt{(x-2)^2+(y-3)^2} + 2\sqrt{(x-3)^2+(y-1)^2} = 4$& MIRROR

Free accompanying (Delphi Pascal essentials) source code available:
Version with Isoline refinement:
The software is also available with binary instead of ternary refinement, according to
  Syntax: [program] [number base] [refinement depth]

Also available: a generalization to three dimensions, with the volume of a sphere as an example.

### Can any positive real be approximated as $2^m/3^n$ with $(m,n)$ large enough?& MIRROR

Free accompanying (Delphi Pascal) source code available for this problem:

### Double refinement of Nesbitt's inequality& MIRROR

Free accompanying (Delphi Pascal) source code available for this problem:
Output of Project7:

### Can the Stern-Brocot tree be employed for better convergence of $2^m/3^n$?& MIRROR

Free accompanying (Delphi Pascal essentials) source code available for this problem:

### Grid coordinates $\Longleftrightarrow$ Triangle numbering& MIRROR

Free accompanying (Delphi Pascal essentials) source code available for this question:
Free accompanying (Delphi Pascal) source code available with the answer:

### Length of a line inside a rectangle & MIRROR

Free accompanying (Delphi Pascal essentials) source code available with the answer:
It is noticed that this problem is very much related to the isolines refinement in:
Find the area enclosed by $\sqrt{(x-2)^2+(y-3)^2} + 2\sqrt{(x-3)^2+(y-1)^2} = 4$
& MIRROR

### Derivative and inverse & MIRROR

Free accompanying (Delphi Pascal essentials) source code available with the answer:

### The Method Of Frobenius & MIRROR

Free accompanying (Delphi Pascal essentials) source code available with the answer:
The numerical method in the software is based upon an old sci.math article,
where the constant frequency $\omega = \mbox{oo}$ has been replaced by $\omega = 1/x$.

### How wide can a unit-length planar curve be? & MIMIC

Free accompanying (Delphi Pascal essentials) source code available with the answer:

### Why does ${x}^{x^{x^{x^{\,.^{\,.^{\,.}}}}}}$ bifurcate below $\sim0.065$? & MIRROR

Free accompanying (Delphi Pascal essentials) source code available with the question:

### How to find the slope of certain lines matching random points & MIRROR

Free accompanying (Delphi Pascal essentials) source code available with the answer:

### Is this Laplace BVP well posed? If not, why? & MIRROR

Free accompanying (Delphi Pascal essentials) source code available with the answer:

### How about Cantor's Theory in a Finite context? & MIRROR

Free accompanying (Delphi Pascal essentials) source code available with the answer: