updates
Calculating unknowns of nested triangles with common sides
I have 3 triangles joined together with common legs between them. For triangle ABC (the blue one in the diagram below) we know all its angles and the leng...
Apr 16, 2026
Archive: Updates
updates
As many even numbers as natural numbers.
I just read somewhere that there are as many even numbers as natural numbers! Is there an intuitive way of coming to terms with this fact? Because honestl...
Apr 16, 2026
updates
Trying to calculate a flux integral
I'm trying to solve the flux integral of (using big letters for vectors). The vector field is the constant vector ${\bf A} = (1,2,3)$, andthe surface...
Apr 16, 2026
updates
Curl of Cross Product of Two Vectors
I want to prove the following identity $$\text{curl } \left(\textbf{F}\times \textbf{G}\right) = \textbf{F}\text{ div}\textbf{ G}- \textbf{G}\text{ div}\t...
Apr 16, 2026
updates
Help me put these enormous numbers in order: googol, googol-plex-bang, googol-stack and so on
Popular mathematics folklore provides some simple tools enabling us compactly to describe some truly enormous numbers. For example, the number $10^{100}$ ...
Apr 16, 2026
updates
How to calculate interpolating splines in 3D space?
I'm trying to model a smooth path between several control points in three dimensions, the problem is that there doesn't appear to be an explanat...
Apr 16, 2026
updates
Normal unit vector in cylindrical coordinates
Suppose I have a surface in cylindrical coordinates given by $z=f(r,\theta)$. How can I proceed to find the normal unit vector of this surface? My initial...
Apr 16, 2026
updates
Find height of a triangle given length of three sides?
How can I find the height of a triangle given the length of all three sides? The only solution I could find was to use Heron's formula to find area t...
Apr 16, 2026
updates
How do I quickly factorize quadratic equations?
Whenever I have to factorize an equation I usually just look for the common factors and then just work form there. However, I was wondering whether there ...
Apr 16, 2026
updates
Use the fundamental theorem of calculus to evaluate the definite integral
Use the fundamental theorem of calculus to evaluate the definite integral $\displaystyle\int_0^3 \frac{1}{\sqrt{1+x}}dx$ I dont get what they want here is...
Apr 16, 2026
