Is there a way to project the infinite Complex plane to either the Poincare disk or the unit disk – for all values of x + iy ?

I’m trying to think of a 3D analogue to the ellipse, but not the ellipsoid. A circle is constructed with a piece of string anchored at the radius. So the distance from center to the curve is always the same. An ellipse is constructed with a piece of string ending at two foci. The sum […]

$ABCD$ is a square and there is a point $E$ such that $\angle EAB = 15^{\circ}$ and $\angle EBA = 15^{\circ}$. Show that $\triangle EDC$ is an equilateral triangle. Now there is a proof by contradiction to this problem. I was wondering if there is a pure geometric solution too (no trigonometry)?

If the plane is partitioned into convex regions each of area $A$ and each containing a single vertex of a unit square lattice, is $A\in (0,\frac{1}{2})$ possible? If each each vertex is in the interior of its region is $A \neq 1$ possible? More generally if $\rm{ I\!R}^n$ ($n\ge 1$) is partitioned into convex regions, […]

I came up with the following question while playing around with Geogebra, and rather than do it myself I figured I’d offer it here. For a given ellipse, the director circle is defined to be the set of all points where two perpendicular tangents to the ellipse cross each other. Suppose we instead consider the […]

I am trying to find the vertices of a regular polygon using just the number of sides and 2 vertices. After the second vertex, I will make left turns to find each subsequent vertex that follows. For example, If I have 4 sides, and 2 points, (0,0) & (0,10), how would I go about find […]

If there are two “nice” shapes in $R^2$, such as circles or polygons, whose intersection has area 0, then they must be interior-disjoint, as their intersection can only contain pieces of their boundary. My question is: what is a simple term for those “nice” subsets of $R^2$ for which intersection of area 0 implies interior-disjointness? […]

The Pythagorean theorem written as $$ a^2 + b^2 = c^2 $$ has the simply geometric meaning that the sum of the areas of the two squares on the legs ($a$ and $b$) equals the area of the square on the hypotenuse $c$ But algebraically the Pythagorean theorem can also be written using complex numbers […]

I am writing a game and need to figure out some math. If I have a circle with the equation $r^2 = (x-d)^2+(y-e)^2$, where $r$, $d$, and $e$ are constants, and a point $A(a,b)$, how do I find the point(s) on the circumference of the circle that are a given straight-line distance $D$ from $A$? […]

$AB$ is a chord of a circle $C$. (a) Find a point $P$ on the circumference of $C$ such that $PA.PB$ is the maximum. (b) Find a point $P$ on the circumference of $C$ which maximizes $PA+PB$. My work: (a)I draw a chord $AB$ on the cirlce $C$, and choose any random point $P$ to […]

Intereting Posts

Measure theory and topology books that have solution manuals
Every infinite Hausdorff space has an infinite discrete subspace
Wielandt's proof of Sylow's theorem.
Intuition for the Cauchy-Schwarz inequality
How do I solve a linear Diophantine equation with three unknowns?
Partial fractions to integrate$\int \frac{4x^2 -20}{(2x+5)^3}dx$
For complex $z$, $|z| = 1 \implies \text{Re}\left(\frac{1-z}{1+z}\right) = 0$
Floating point arithmetic operations when row reducing matrices
Compactly supported continuous function is uniformly continuous
Showing $H$ is a normal subgroup of $G$
A question about $\prod_{x\in \mathbb{R}^{*}}{x}$
What is a simple example of an unprovable statement?
Set of All Groups
Extension of partial derivatives and the definition of $C^k(\overline{\Omega})$
Scheme: Countable union of affine lines