updates
Example of graph with two different MSPs via Prim's Algorithm?
I was discussing Prim's algorithm and Kruskal's algorithm for finding minimum spanning trees the other day and we began to wonder about the cond...
Apr 21, 2026
Archive: Updates
updates
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression?
How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series: $$\sum_{k=0}^{n-1}...
Apr 21, 2026
updates
Permutation vs Variation - To rank 3 people
I am new to permutation and combination and am looking for guidance in the following example: We have 3 people - A, B, C How many ways are there to arrang...
Apr 21, 2026
updates
Translate from english to predicate logic
I'm trying to translate the following $3$ sentences from English to predicate logic. If anyone on the plane is small, then everyone on the plane is n...
Apr 21, 2026
updates
Meaning of simple arc or Jordan arc
I read the definition of simple arc that an arc which do not cross over itself and is one - one function. Parabola is not one to one as $ f(x)=x^2 $ impli...
Apr 21, 2026
updates
Rotating x,y points 45 degrees
I have a two dimensional data set that I would like to rotate 45 degrees such that a 45 degree line from the points (0,0 and 10,10) becomes the x-axis. Fo...
Apr 21, 2026
updates
How is this circle inversion formula calculated?
I know about the inversion of a point inside a circle. But I was reading Peter Sarnak's paper on the Apollonian gasket, and got to the part where he ...
Apr 21, 2026
updates
What are the "roots of unity"?
A question is asking me to "find the sixth roots of unity and represent them on an Argand diagram". I don't need you to do the problem for me, I'...
Apr 21, 2026
updates
Conditional Probability of Y given X (both random variables)
The exercise: A box contains 5 white balls and 5 black balls. 3 balls are drawn randomly, one by one, without replacement. The following random variables ...
Apr 21, 2026
updates
Definition of mathematical expression
According to wikipedia: "In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rule...
Apr 21, 2026
