Is the golden ratio or are spirals in general fractals? If not, why?
Mandelbrot wrote: A fractal is a shape whose “Hausdorff dimension” is greater than its “topological dimension.” In simple (and less precise) terms: Fracta...
Apr 14, 2026 1 VIEWS
Topic: General
5104 Articles 
Find a parametrization for a line
We didn't go over how to solve this problem in my class, and I'm trying to piece it together from our textbook and online sources, but I'm ...
Apr 14, 2026 1 VIEWS
Lagrange’s Remainder Theorem
Using only Lagrange’s Remainder Theorem (and no references to Abel’s Theorem) prove $1 − 1/2 +1/3 − 1/4 +1/5 − 1/6 + ··· = \ln(2)$. As I understand, the L...
Apr 14, 2026 2 VIEWS
Minimal generating set
I am having a difficult time wrapping my head around this idea of minimal generating set. The book gives a definition for it and i've tried looking i...
Apr 14, 2026 1 VIEWS
What is the derivative of $y=x^y$
What is the derivative of $y=x^y$ ? I have tried the below. Please correct me if I am wrong on any of the below. $$y=x^y.$$ Taking natural log on both sid...
Apr 14, 2026 1 VIEWS
How do you find the sine of the angle between two vectors?
I do not know what the sine of the angle between two vectors is. I think it may be the vector created by connecting the tips of the two vectors but I am n...
Apr 14, 2026 1 VIEWS
Intersection of Circle and Parabola
Q) Suppose the circle with equation $x^{2} + y^{2} + 2fx + 2gy + c = 0$ cuts the parabola $y^{2} = 4ax,(a> 0)$ at four distinct points. If $d$ denotes ...
Apr 14, 2026 1 VIEWS
How do I know the span of a matrix
I have a marix that is $$R=\pmatrix{1&1&1\\1&1&1+2a\\0&2&2+2b}$$ and the span of R is span=$\left\{\pmatrix{1\\1\\0},\pmatrix{0\\0...
Apr 14, 2026 1 VIEWS
Volume of a spherical balloon question
How would I do this problem I am not sure if I did it correctly. The volume $V$ of a spherical balloon is increasing at a constant rate of 32 cubic feet p...
Apr 14, 2026 1 VIEWS
Why is 1 greater than 0? Show the proof. [closed]
I would like to prove that 1 > 0. And I need to use axioms, could somebody help me? Thanks'
Apr 14, 2026 2 VIEWS
prove Gaussian integral using polar coordinates
The proof method is to equate expression$\mathrm{\iint_{-\infty}^\infty\,e^{-(x^2+y^2)}}$ (Cartesian)with $\mathrm{\int_0^{2\pi}\int_0^{\infty}e^{-r^2}drd...
Apr 14, 2026 2 VIEWS
Given the base and angles of an isosceles triangle, how to find length of the two sides?
I can't seem to find a textbook solution to this. It is always assumed that the length of the sides is know. Isolceles triangle So the base $a$ is kn...
Apr 14, 2026 2 VIEWS