![Does Euclid book I proposition 2 have a purpose? [closed]](https://news.conceivablytech.com/uploads/does-euclid-book-i-proposition-2-have-a-purpose-closed_720.jpg)
general
Does Euclid book I proposition 2 have a purpose? [closed]
According to Joyce' commentary, proposition 2 is only used in proposition 3 of Euclid's Elements, book I. As Euclid states himself (I-3, the len...
Apr 10, 2026
Archive: General
general
Green's first identity
Good morning/evening to everybody. I'm interested in proving this proposition from the Green's first identity, which reads that, for any suffici...
Apr 10, 2026
general
I have the four sides of an irregular quadrilateral and none of its angles. How can I calculate its area?
If i have the four sides of an irregular quadrilateral without any angle or diagonal this formula can be use for calculating of area of this triangle $A=s...
Apr 10, 2026
general
How to reverse the $n$ choose $k$ formula?
If I want to find how many possible ways there are to choose k out of n elements I know you can use the simple formula below: $$ \binom{n}{k} = \frac{n! }...
Apr 09, 2026
general
When is $\sin(x) = \cos(x)$?
How do I solve the following equation? $$\cos(x) - \sin(x) = 0$$ I need to find the minimum and maximum of this function: $$f(x) = \frac{\tan(x)}{(1+\tan(...
Apr 09, 2026
general
Easier way of finding out whether a given linear programming problem has optimal solution or not
I have the linear program $$\begin{array}{ll} \text{minimize} & -2x-5y\\ \text{subject to} & 3x + 4y \geq 5\\ & x, y \geq 0\end{array}$$ I can...
Apr 09, 2026
general
How do I remove a number from the numerator of a fraction so that I am left with the variable in the denominator in this equation?
The question is this: $$\frac{1}{R^p} = \frac{1}{4.5\times 10^2} + \frac{1}{9.4\times 10^2}$$ I calculated the equation so that it simplifyed to: $$\frac{...
Apr 09, 2026
![General Solution to $x^2-2y^2=1$ [duplicate]](https://news.conceivablytech.com/uploads/general-solution-to-x-2-2y-2-1-duplicate_720.jpg)
general
General Solution to $x^2-2y^2=1$ [duplicate]
Find a general solution to $x^2-2y^2=1$ I found that (3,2) is a solution. Now what should I do? I can not catch what the question really want. It is about...
Apr 09, 2026
general
Proving resolution inference rule without truth table
I came across resolution inference rule stating: $((p\lor q)\land (\lnot p\lor r))\rightarrow(q\lor r)$ I googled a lot but what I get is either the proof...
Apr 09, 2026
general
recursive mean computation
Wondering if someone can help my feeble mind understand one part of the formula shown below: $$\mu_k = {1\over k}\sum_{j=1}^{k} x_j \tag 1$$ $$ = {1\over ...
Apr 09, 2026
