3D rotation about z-axis
I am struggling to understand the 3D rotation. I have one picture from internet which is drawn by me. The initial object position is $A(x_1, y_1, z_1).$ W...
Apr 21, 2026 2 VIEWS
Topic: General
5104 Articles 
Area of Triangle inside a Circle in terms of angle and radius
A circle $O$ is circumscribed around a triangle $ABC$, and its radius is $r$. The angles of the triangle are $\angle CAB = a, \angle ABC = b$ and $\angle ...
Apr 21, 2026 1 VIEWS
Find gcd and lcm of two polynomials
Let $f(x)=x^3+x^2+x+1$ and $g(x)=x^3+1$. Then in $\mathbb{Q}[x]$ $\gcd (f(x),g(x))=x+1$ $ \gcd(f(x),g(x))=x^3-1$ $\operatorname{lcm}(f(x),g(x))=x^5+x^3+x^...
Apr 21, 2026 2 VIEWS
The sum of any four consecutive integers is never divisible by 4
I want to prove this statement: S : The sum of any four consecutive integers is never divisible by 4. Proof: The sum of four consecutive integers $n,n+1,n...
Apr 21, 2026 1 VIEWS
how many semantically different boolean functions are there for n boolean variables?
In short, this is an assignment question for a course I am taking - the exact wording is this: "Given n Boolean variables, how many 'semantically...
Apr 21, 2026 1 VIEWS
prove equilateral triangle
Recently I have encountered such a proving problem. As shown below, given a $\triangle ABC$, $AD$ intersects $BC$ at $D$ so that $AD$ is perpendicular to ...
Apr 21, 2026 1 VIEWS
Why isn't $\frac{1}{x}$ a polynomial?
Why isn't $\frac{1}{x}$ a polynomial? Does it directly follow from definition? As far as I know, polynomials in $F$ are expressions of the form $\sum...
Apr 21, 2026 1 VIEWS
Monte Hall Problem - Question on Decision Tree Construction (Conditional Probability)
(The Monte Hall Problem, also known as the 3 door problem): On the game show Let's Make a Deal, there are 3 doors hiding 3 prizes. Two of the prizes ...
Apr 21, 2026 1 VIEWS
How do i solve $e^{ax}-e^{bx}=c$ for $x$?
How do i solve $e^{ax}-e^{bx}=c$ for $x$? The constants $a$, $b$ and $c$ are real numbers. It is the final form of a longer equation that I simplyfied. Ed...
Apr 21, 2026 2 VIEWS
Determine whether the given vectors are orthogonal
Determine whether the given set of vectors are orthogonal? $$S=\{ (1,0,-1),(0,3,-6),(0,2,-4) \}.$$ I just know that orthogonality of vectors in a vector s...
Apr 21, 2026 1 VIEWS
Find the formula for the sequence $\frac{5}{1},\frac{8}{2},\frac{11}{6},\frac{14}{24},\frac{17}{120}$
I'm supposed to find the formula for the sequence: $$\frac{5}{1},\frac{8}{2},\frac{11}{6},\frac{14}{24},\frac{17}{120}$$ I started by writing this: $...
Apr 21, 2026 1 VIEWS
What does actually probability mean?
I am a beginner in quantum information. Reading about it has made me question the definition of probability. If the probability of an outcome $m$ in an ex...
Apr 21, 2026 1 VIEWS