USAMO $2015/2$ (Doubt in complex numbers solution)
Quadrilateral $APBQ$ is inscribed in circle $\omega$ with $\angle P = \angle Q = 90^{\circ}$ and $AP = AQ < BP$. Let $X$ be a variable point on segment...
22 Apr 2026 1 READS
Archive: News
Real locus of a cone or a double cone
If we take the algebraic set of $X^2+Y^2-Z^2=0$, $V(X^2+Y^2-Z^2)$, why do we obtain a single cone, rather than the real locus of $X^2+Y^2-Z^2$ being a dou...
22 Apr 2026 1 READS
How many passes does a monkey saddle have?
John Stillwell writes in Poincaré's Papers on Topology: The study of "pits, peaks, and passes" on surfaces in $\mathbb R^3$ by Cayley (1859) and Maxw...
22 Apr 2026 1 READS
Example of Partial Order that's not a Total Order and why?
I'm looking for a simple example of a partial order which is not a total order so that I can grasp the concept and the difference between the two. An...
22 Apr 2026 1 READS
Expressing as a single logarithm
I've got the equation: $$\log_{10}(x^2 - 16) - 3\log_{10}(x + 4) + 2\log_{10} x$$ I'm looking to express this as a single logarithm. I came up w...
22 Apr 2026 1 READS
Calculate radical expression without a calculator
How would you calculate any radical expression without a calculator? I know you can do something like long division for square roots, but I mean for big r...
22 Apr 2026 1 READS
how to calculate 2^1.4
So I have got a very basic question but it didn't come up as a google search so I am posting it here. I want to know how to easy calculate 2^1.4 = 2....
22 Apr 2026 1 READS
$N^2$ leaves a remainder of $1$ when divided by $24$. What are the possible remainders we can get if we divide $N$ by $12$?
My solution approach is as below :- $Rem[\frac{N^2}{24}] = 1$ $\Rightarrow Rem[\frac{N \times N}{24}] = 1$ $\Rightarrow Rem[\frac{N}{24}] \times Rem[\frac...
22 Apr 2026 1 READS
Linear equation with 3 equal signs
Here is my linear equation: Solve for p: $\frac{5}{6} = \frac{n}{72} = \frac{m+n}{84} = \frac{p-m}{120}$ How am I supposed to solve for this 1 variable wh...
22 Apr 2026 1 READS
Relation between fan and toric variety
I understand what a fan is, but I don't really know how it associated to a toric variety. Could a non-toric variety has a fan?
22 Apr 2026 1 READS
