Calculating Solid angle for a sphere in space
How can I calculate the solid angle that a sphere of radius R subtends at a point P? I would expect the result to be a function of the radius and the dist...
18 Apr 2026 1 READS
Archive: News
Generalizing values which Euler's-totient function does not take
I was reading about Euler's totient function on wikipedia, and it eventually led me to this book on google: Page 74 of the book, Prime numbers: the m...
18 Apr 2026 1 READS
Quadratic Equations - One rational solution?
I have a question that I am working on: Which of the following will give one rational solution? 4x^2 = 9 4x^2 - 12x = -9 x^2 = 5 x^2 - 2x + 14 = 0 2x^2 = ...
18 Apr 2026 1 READS
Orthogonality of major and minor axes of an ellipse
How would one go about proving that the major and minor axes of an ellipse are perpendicular bisectors of each other? I've read several proofs of exp...
18 Apr 2026 1 READS
What's the motivation for Runge-Kutta methods?
Recently, I have been taking a course on ODEs and learning Runge-Kutta methods. To be specific, the 4th order Runge-Kutta method on solving initial value ...
18 Apr 2026 1 READS
Each regional of a maximal planar graph is a triangle
Show that every region of a maximal planar graph is a triangle. A planar graph G is called maximal planar if the addition of any edge to G creates a nonpl...
18 Apr 2026 1 READS
How to find the smallest square possible, out of Tetris pieces?
I need to arrange an uncertain number of Tetris pieces, into the smallest possible square. The pieces I get are static, so I am not allowed to turn them a...
18 Apr 2026 0 READS
Basis for the range of the matrix
I did the first part properly and showed that the rank is 2, but putting this matrix into a reduced row echleon form. For the second part, I get the wrong...
18 Apr 2026 1 READS
How can I prove using the definition of limits that $\lim _{(x,y)\rightarrow (2,3)} y\sin(xy-6)= 0$?
I want to prove that $\lim_{(x,y)\rightarrow (2,3)} y\sin(xy-6)= 0$ using the definition of limit. However I am unable to make the step of transforming $|...
18 Apr 2026 1 READS
Increasing/Decreasing intervals of a parabola
I am being told to find the intervals on which the function is increasing or decreasing. It is a normal positive parabola with the vertex at $(3,0).$ The ...
18 Apr 2026 1 READS
