I'm a middle-school student. As some sort of challenge, my maths teacher gave us the problem that follows:
$\triangle ABC$ is a triangle such that $AB=84$ and $AC=28$. Let $D$ be a point on the line ...
Antonio Asis
Antonio Asis (1932 - 2019) was an Argentine artist and one of the main exponents of kinetic art and op art. Asis was born in Buenos Aires. At the age of 14 he enrolled at the National ...
If a parabola is of the form $\frac{1}{8}$ ${(42x-15x^2)}$, what would be the optimised area a rectangle can have inside it if the bottom (width) of the rectangle is aligned on the X axis i.e the y ...
This question is a reference request.
Let $(M,g)$ be a Riemannian manifold of dimension $n$, and $b_i(M) = \dim H_i(M,\mathbb{R})$. Gromov proved it that there are constants $C(n)$ such that, if the ...
I don't know if this is a good question to ask but I need some advice, anything is appreciated.
(Contruction here, doesn't imply geometric construction tools one)
Q1:In solving problems in geometry, ...
Consider a 16x16 square subdivided by grid lines into unit squares. It is easy to completely tile (no overlaps, no gaps) this square with 64 1x4 rectangles. Each 1x4 rectangle in the tiling (no ...
The recent discovery of a molecule that mimics the Sierpinski gasket has spurred headlines identifying it as the first fractal scientists have found in nature. I find these claims highly dubious ...
Bridget Riley
Bridget Riley (born 1931 in London) is an English painter known for her op art paintings. Alongside Victor Vasarely and Vera Molnรกr, she is one of the best-known representatives of this ...
For $n\geq 1$, endow $\mathbb{R}^n$ with the usual scalar product. Let $u=(1,1,\dots,1)\in\mathbb{R}^n$, $v\in {]0,+\infty[^n}$ and denote by $p_{u^\perp}$ and $p_{v^\perp}$ the orthographic ...
Can you tile a $25 \times 25$ square (no overlaps, no gaps) with a mixture of $2 \times 2$ squares and $3 \times 3$ squares?
This puzzle is by David A. Klarner.
Clarification: The number of $2 \times ...
inspired by : Make a square table top with six (or fewer) pieces
A carpenter has three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square, respectively. They want to use ...
$\newcommand\R{\Bbb R}$Let $Q(x_1,\dots,x_n)\in\R[x_1,\dots,x_n]$ be an irreducible polynomial such that the dimension of the set $Z:=\{(x_1,\dots,x_n)\in\R^n\colon Q(x_1,\dots,x_n)=0\}$ (defined, ...
I tried to substitute side lengths with variables and use the area to get somewhere, but that failed. I also found that in an acute triangle, all of the heights intersect at the orthocenter, but am ...
I am a highschool student and i was studying kineamtics about position of a body so one thing i do not understand in this diagram is the position of woman initally at t=0 this women was at x=1.5m ...
According to taxicab geometry, there are 1226 possible paths from A(2,5) to B(7,9), all with a distance of 9 units, |2-7|+|9-5|=9. I wanted to write a code where I could be obtaining the plots of some ...
Suppose we have a vector bundle $E$ with connection $\nabla$ over a smooth manifold $M$. Letโs also say we have a sequence of smooth paths $\gamma_n\in C^\infty([0,1],M)$ starting at the same point ...