Why are the coordinates of origin $(0,0)$
Why are the coordinates of origin $\left(0,0\right)$? I mean why these are not $(1,1)$;$(1,2)$ or anything else? What is special about $(0,0)$? Is this is...
Apr 16, 2026 1 VIEWS
Topic: General
5104 Articles 
Find $6^{1000} \mod 23$ [duplicate]
Find $6^{1000} \mod 23 $ Having just studied Fermat's theorem I've applied $6^{22}\equiv 1 \mod 23 $, but now I am quite clueless on the best wa...
Apr 16, 2026 1 VIEWS
How to calculate the work done to move water into a hemispherical tank from the bottom.
Problem A hemispherical tank of radius 2 feet is positioned so that its base is circular. How much work is required to fill the tank with water through a ...
Apr 16, 2026 1 VIEWS
Does $i^4$ equal $1?$
I can't seem to find a solution to this for the life of me. My mathematics teacher didn't know either. Edit: I asked the teacher that usually te...
Apr 16, 2026 1 VIEWS
Finding the points of a paramertized curve where a tangent line has slope 3?
I have a curve at $c(t) = (-5t^2-3t+4,t^3-9t+5)$ and given a slope for the tangent line of $3$. I would like to find the point $(x,y)$ where this occurs. ...
Apr 16, 2026 1 VIEWS
Logarithm of the determinant of a positive definite matrix
For positive definite $C=LL^T$, where $L$ is the lower triangular Cholesky factor of $C$, why is $\log(\det(C))=2\operatorname{trace}(\log(L))$? I know th...
Apr 16, 2026 1 VIEWS
Proof of the number of edges required to disconnect a graph
Assume that we have a connected graph with $n$ vertices and each vertex with a minimum degree of $\frac{n-1}{2}$. And let $m$ be the minimum degree of the...
Apr 16, 2026 1 VIEWS
Why does Dykstra's projection algorithm work?
Not to be confused with Dijkstra's algorithm! Can anyone help me understand why Dykstra's projection algorithm works, at-least in $\mathbb{R}^d$...
Apr 16, 2026 1 VIEWS
Manifolds and Charts
I have a very silly and basic question about finding charts for a manifold. The point is: I'm self learning differential geometry, however, I didn�...
Apr 16, 2026 1 VIEWS
Equivalence Relations in Discrete Mathematics
Let S be the relation on the set of ordered pairs of positive integers such that ((a,b),(c,d)) ∈ S if and only if ac = bd. Show that S is not an equivalen...
Apr 16, 2026 2 VIEWS
How could a statement be true without proof?
Godel`s incompleteness theorem states that there may exist true statements which have no proofs in a formal system of particular axioms. Here I have two q...
Apr 16, 2026 1 VIEWS
Neumann condition and Dirichlet condition at the same point
I am studying heat equation on a 1-D bar. We now that Neumann conditions at both ends leads to a singular matrix (for finite element methods) in equilibri...
Apr 16, 2026 1 VIEWS