updates

Finding Measuring Points in three-point perspective drawing

In his Complete Guide to Perspective Drawing (page 39), Craig Attebery places Measuring Points of two-point perspective in a line perperdicular to that cr...

Published: Aug 10, 2026

general

Difference in the definitions of glb and lub in real analysis and abstract algebra

The following text is from the book Abstract Algebra by T. W. Judson : Let $X = {\{1,2,3,4,6,8,12,24}\}$ be the set of divisors of $24$ with the partial o...

Published: Aug 10, 2026

updates

In a parallelogram, does the diagonal bisect the angles that they meet?

I understand the following properties of the parallelogram: Opposite sides are parallel and equal in length. Opposite angles are equal. Adjacent angles ad...

Published: Aug 10, 2026

news

Two circles with a common external tangent problem. [closed]

Two circles are tangent externally at A, and a common external tangent touches them at B and C. The line segment BA is extended, meeting the second circle...

Published: Aug 10, 2026

general

Find normal vector of a 3d vector

I need to find the normal vector for the following 3d vector presented in the vectorial equation because I need to find a plane that is orthogonal to the ...

Published: Aug 10, 2026

updates

Rank theorem on manifolds

Rank theorem on manifolds says that : Suppose $M$ and $N$ are two smooth manifolds of dimensions $m$ and $n$, respectively, and $F:M\rightarrow N$ be a sm...

Published: Aug 10, 2026

updates

Prove: $\operatorname{rank} A \leq 1$ iff $A=xy^T$ for some $x,y \in \mathbb{R}^{n \times 1}$. [duplicate]

Let $A \in \mathbb{R}^{n \times n}$. Then $\operatorname{rank} A \leq 1$ if and only if $A = xy^T$ for some $x, y \in \mathbb{R}^{n \times 1}$. Need help....

Published: Aug 10, 2026

updates

Is a function that is one-to-one necessarily onto?

I'd would like to know that, because I don't want to prove a function is onto if I don't have to. If the answer is no, is there any particu...

Published: Aug 10, 2026

news

Orientation(geometry) [closed]

A xy-plane is rotated about x and y-axis. But when it is rotated along z-axis, it doesn't change the orientation of xy-plane, why? I've tried to...

Published: Aug 10, 2026

general

Complex variable limit at infinity

Is $\lim\limits_{z\to\infty} \frac{4z^2}{(z-1)^2}$, $z\in\mathbb{C}$, evaluated the same way as a real variable function limit? Or does one need to show s...

Published: Aug 10, 2026