This question was posed to me by a friend (formulated as creating a peg to fit perfectly into holes of these shapes), and after an experiment in OpenSCAD it seems it is not possible – either one profile has to be an isosceles triangle rather than equilateral, rectangular rather than square, or elliptical rather than […]

I want to find a Möbius transformation that takes the two circles $C(i,3), C(-i,1)$ to the parallel lines $Re(z)=0, Re(z)=1$. I know that they intersect at -2i, which means I have to map $2i \mapsto \infty$. I’m not sure how to ensure that both get mapped to the appropriate line. I’ve tried using 2 other […]

When working in the complex plane, often times I would like to scale a disk $|z-z_0|<R$ to the unit disk. I would first translate $z_0$ to the origin, but after that, what can we multiply by to scale the radius down from $R$ to $1$? I’m curious because in reading a proof of Schwarz’ lemma, […]

Given $n$ points on the plane, no three of which are collinear, what is the maximum number of acute triangles formed by them? [Source: Based on Hungarian competition problem]

HI: I have the following question: Definition: A Lie group $T$ is called a torus if $T\cong \prod_{1\leq i\leq k} \mathbb{R}/\mathbb{Z}$ for some $k\in \mathbb{N}$. ${\bf Question}$: Is it true that a torus is an injective object in the category of abelian Lie groups? Thanks very much!

I have this problem: On space $ (Oxyz)$ given point $M(1,2,3)$. Plane ($\alpha$) contain point $M$ and ($\alpha$) cross $Ox$ at $A(a,0,0)$; $Oy$ at $B(0,b,0)$; $C(0,0,c)$. Where a,b,c>0 Write the equation of plane ($\alpha$) such that It makes $V_{OABC}$ reach minimum. I don’t know which inequality should use in here to find out $\min_{V_{OAB}}$ . […]

Let $S\subset \mathbb{R}^3$ be a connected smooth surface. Suppose that every point of $S$ is an umbilic point. Prove that $S$ is a subset of either a plane or a sphere in $\mathbb{R}^3$. Here’s a HW problem. I wonder how to prove it.

I know the coordinates of the 4 rhombus’ vertices. I also have the coordinates of another arbitrary point (the result of a click on the screen). How do I determine if that point is within the rhombus?

I have a plane which is represented as a 3d point $\vec{p}$ with a normal $\hat{n}$. I also have a line segment specified by two points $\vec{v_1},\vec{v_2}$ . I want to get the intersection point (if any). Here’s what I have: $${\rm dist}_{v_1} = \hat{n} \cdot (\vec{v_1} – \vec{p})$$ $${\rm dist}_{v_2} = \hat{n} \cdot (\vec{v_2} […]

How can I obtain the distance between two points $\mathbf{x}=(x_1,x_2,x_3,x_4)$ and $\mathbf{y}=(y_1,y_2,y_3,y_4)$ that belong to the $2$-torus $\mathbb{S}^1\times \mathbb{S}^1$? This is, I want to measure the distance (I do not require the geodesic) of $\mathbf{x}$ to $\mathbf{y}$ along the manifold $$\mathbb{S}^1\times\mathbb{S}^1=\big\{(x_1,x_2,x_3,x_4)\in\mathbb{R}^4:x_1^2+x_2^2=1,x_3^2+x_4^2=1\big\}.$$ I guess that there should be a way of doing this considering an isomorphism(?) […]

Intereting Posts

Is there any difference between a math invention and a math discovery?
Polynomial fitting where polynomial must be monotonically increasing
Is $x^3-9$ irreducible over the integers mod 31?
How many ways a composite number can be resolved into two factors which are prime to each other?
Find the conectives of a composed proposition given a a true table
“A Function Can't Be Odd&Even” They said, Right?
Proof that the power set of $\mathbb{N}$ is uncountable, and that the composition of two bijections is a bijection
Is there any non-abelian group with the property $AB=BA$?
Let $a$ be a quadratic residue modulo $p$. Prove that the number $b\equiv a^\frac{p+1}{4} \mod p$ has the property that $b^2\equiv a \mod p$.
Why is $n$ divided by $n$ equal to $1$?
Connected But Not Path-Connected?
If all of the integers from $1$ to $99999$ are written down in a list, how many zeros will have been used?
The inegral $\int_1^2 2x \sqrt{x^2 + 1}\; dx$ using differential forms
Mathematical problem induction: $\frac12\cdot \frac34\cdots\frac{2n-1}{2n}<\frac1{\sqrt{2n}}$
How do I simplify and evaluate the limit of $(\sqrt x – 1)/(\sqrt x – 1)$ as $x\to 1$?