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Meaning of $x^2+y^2=0$ (imaginary can have real property?!)
While working for some homework problems for circle to select the radius for circles, I encountered with radius 0 and centre at origin i.e., $$x^2+y^2=0$$...
Apr 15, 2026
Archive: News
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Asymptotics for partitions of $n$ with largest part at most $k$ (or into at most $k$ parts)
Let $\bar p_k(n)$ be the number of partitions of $n$ with largest part at most $k$ (equivalently, into at most $k$ parts). Is there an elementary formula ...
Apr 14, 2026
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Find the mean length of a chord in a unit circle
I stumbled across this problem. I am not sure if I have approached it in a meaningful way. Any advice/help/correction would be much appreciated. The follo...
Apr 14, 2026
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Hard simultaneous equation problem $5x^2y-4xy^2+3y^3-2(x+y)=0$, $xy(x^2+y^2)+2=(x+y)^2$
How to solve this system of equations: $$\begin{align*} 5x^2y-4xy^2+3y^3-2(x+y) &=0 \\ xy(x^2+y^2)+2 &=(x+y)^2 \end{align*} $$
Apr 14, 2026
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Definition of ordinary differential equation
Is a differential equation ordinary if it only contains derivatives with respect to one variable, even if the function has multiple variables? For example...
Apr 14, 2026
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slope of a line in 3D coordinate system
Suppose I have $2$ points in a 3D coordinate space. Say $p_1=(5,5,5)$, $p_2=(1,2,3)$. How do I find the slope of the line joining $p_1$ and $p_2$? After g...
Apr 14, 2026
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When Hyperbolic function is zero?
If we have the determinant of matrix $\sinh x \cosh x=0$ Then $\sinh(x)=0$ or $\cosh(x)=0$ If $\sinh(x)=0$, then $x=0, \pi, 2\pi, 3\pi$ And $\cosh(x)=0$ t...
Apr 14, 2026
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Koch-like fractal of the dodecahedron: Does this object already exist?
Platonic solids are made of squares, triangles and one of them is made of pentagons. If the faces of the cube are taken while preserving its vertices, eac...
Apr 14, 2026
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5-color Theorem proof
I have been studying planar graphs for a while now and found it useful for my learning to formulate a few proofs myself, based on the study material I wor...
Apr 14, 2026
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How to determine the general formula for a summation?
What are some strategies for trying to determine the general formula for a summation? For example, let's say I'm trying to determine the general...
Apr 14, 2026
