MSE publications / references 2021

Het is veel gemakkelijker om mensen te belazeren
dan ze ervan te overtuigen dat ze belazerd worden
In die Beschränkung zeigt sich erst der Meister (Goethe).
Questions & Answers @ Mathematics Stack Exchange:

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

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.


MSE publications / references in 2014. Bounty 100 raised for:
Create a number by multi by 2 and divide by 3 (integer part)
& BACKUP

Five attempts have been made:

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

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

Double refinement of Nesbitt's inequality
& BACKUP

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


Stern Brocot tree sequence & BACKUP


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

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

Does there exist a real function with following properties?
& BACKUP (deleted)


Grid coordinates $\Longleftrightarrow$ Triangle numbering
& BACKUP

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 & BACKUP

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 $\sqrt{(x-2)^2+(y-3)^2} + 2\sqrt{(x-3)^2+(y-1)^2} = 4$
& BACKUP

Derivative and inverse & BACKUP

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

The Method Of Frobenius & BACKUP

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where the constant frequency $\omega = \mbox{oo}$ has been replaced by $\omega = 1/x$.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? & BACKUP

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

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

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

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

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

How to approximate a sharply peaked function with deltas? & BACKUP


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

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

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

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

Simplify $N^{N(N-2)}$ with $N=(1\pm i\sqrt{3})/2$ & BACKUP


Is there a closed form for $\sum_{i=1}^n \left(\frac{i}{x + i}\right)^{i y}$? & BACKUP


Where are the Bessel functions in $\int_{0}^{2\pi}\int_{0}^{2\pi}e^{i\alpha[\sin(\theta)-\sin(\varphi)]}d\theta d\varphi$ ?
& BACKUP


Express $\mathrm{Tr}(X)$ in terms of $A$, given that $X=A^TX(I+X)^{-1}A$
& BACKUP


Explicit formula of the solution of $u_{tt}=au_{xx}$ and for which values of a is this a "wave equation"?
& BACKUP


What is a normal at the surface of a hypersphere?
& BACKUP


Problem with normal derivative & BACKUP


When do equations represent the same curve? & BACKUP


Subset as arithmetic mean of geometric means. Not really?
& BACKUP


Conjecture with the CGM of a Circle & BACKUP


Find the area of an isosceles trapezoid $ABCD$ $(AB\parallel CD)$
with height $m$ and perpendicular diagonals $(AC\perp BD)$
& BACKUP


Kernel of Integral Operator of the Newton Equation & BACKUP


Conservation laws in the finite element method for domains with curved boundaries
& BACKUP


Show that the tangent plane of the of the cone intersects the cone in a line
- help in communicating idea correctly
& BACKUP


How to rotate a rectangle inside a rectangle with different scales
& BACKUP


Derivation of bounds of convergence of infinite tower
& BACKUP


Can every continuous function be continuously "transformed" into a differentiable function?
& BACKUP (deleted)


Conjecture with a three-diagonal system of equations & BACKUP


which is the direct and inverse transformation matrix? & BACKUP


Prove or disprove that the function is convex & BACKUP


Prove or disprove that $f_n(x)\gt -1/2$ & BACKUP


Characteristics of equations of the form $u_{xy}=f(u_x,u_y,u)$ & BACKUP