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Answer by Matteo for Visually stunning math concepts which are easy to explain
An important concept im math is $\infty$: the Bernoulli's lemniscate is very similar to its sign. Here the GIF of its construction from an hyperbole: The equation is very simple:$$\left ( x^2+y^2...
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Answer by Luis Felipe for Visually stunning math concepts which are easy to...
Transpose of a matrix column, this gift shows the easiest proof ever made
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Answer by Pallavi for Visually stunning math concepts which are easy to explain
Riemann integration has always amazed me. Its simple yet extraordinary.
View ArticleAnswer by Tomer Wolberg for Visually stunning math concepts which are easy to...
$$\sum_{i=1}^{\infty}\frac{1}{x^n}=\frac{1}{x-1}$$ In base x this sum equels to 0.1111111.... and if you multiply it by x-1 you get 0.(x-1)(x-1)(x-1).... which equels to 1.
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Answer by user207119 for Visually stunning math concepts which are easy to...
I made this earlier this year in Blender after having spent a few days trying to think of a visual proof of $a^3-b^3 = (a-b)(a^2+ab+b^2)$ so that I could make myself a nice paperweight. I think it's...
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Answer by ArsenBerk for Visually stunning math concepts which are easy to...
In group theory, "visual" explanation of the group $D_4$ (or sometimes called $D_8$, which is dihedral group of order $8$ or degree $4$) was really exciting to me. Even with some elementary knowledge...
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Answer by Arbutus for Visually stunning math concepts which are easy to explain
One of my favourites is from Littlewood's Miscellany, where he amicably mentions that "for the professional the only proof needed" for the one-dimensional fixed point theorem is the following figure....
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Answer by Abhishek for Visually stunning math concepts which are easy to explain
The fact that the graph of inverse of a function is nothing more than its image in line $y=x$ but still finding inverse is so difficult is a math concept I really find amazing. Also inverse of some...
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Answer by The Phenotype for Visually stunning math concepts which are easy to...
The (otherwise also easy to prove) fact that $\sum_\limits{k=1}^n k=\frac{n(n+1)}{2}$ in one picture: Source of the picture
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Answer by Robert Howard for Visually stunning math concepts which are easy to...
The beauty of watching graphs being constructed has always mesmerized me; I love how such simple figures can be used to make such complicated pictures. And it's especially satisfying with polar graphs....
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Answer by totymedli for Visually stunning math concepts which are easy to...
The following animation shows how the surface area of a sphere is calculated.
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Answer by anonymous for Visually stunning math concepts which are easy to...
How to convert a function from Cartesian to Polar coordinates:
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Answer by LCarvalho for Visually stunning math concepts which are easy to...
This site looks very interesting to learn about algebraic surfaces. http://touch-geometry.karazin.ua/list
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Answer by Nicky Hekster for Visually stunning math concepts which are easy to...
A connection between Mathematics and Love: the story goes that a very shy mathematician had fallen in love with a girl but did not dare to tell her. In stead he wrote her a letter with only the...
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Answer by Ken Draco for Visually stunning math concepts which are easy to...
In plane geometry Morley’s theorem is a stunning fact in my opinion: In any triangle, the points of intersections of adjacent trisectors of the angles form an equilateral triangle : In analytical...
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Answer by iadvd for Visually stunning math concepts which are easy to explain
I would like to add some explorations of the concept asked by the OP of my own: Visualization of the set of real roots of quadratic equations $ax^2+bx+c=0$, for the specific values of the intervals $a...
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Answer by MR_BD for Visually stunning math concepts which are easy to explain
I recently find some stunning visualizations. I preferred to share them all: $5)$ Mean inequalities [from Proof without words] $4)$ Streographic projection [by H.Segerman] $3)$ Farey-Ford Tessellation...
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Answer by Simply Beautiful Art for Visually stunning math concepts which are...
The sum of the first $n$ squared numbers: The first 3 triangles are the same, just rotated. Also, notice that $$\begin{align}1^2&=1\\2^2&=2+2\\3^2&=3+3+3\\\vdots\ \ &\quad\ \...
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Answer by mathreadler for Visually stunning math concepts which are easy to...
Polynomials can describe geometric objects In high school we learn that some low order polynomials can describe geometric shapes: Basic shapes we all recognize ( as intro )...
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Answer by user311151 for Visually stunning math concepts which are easy to...
This is @Blue's very nice visual proof from trigonography.com that $$x+\frac{1}{x}\;\geqslant\; 2$$ Two more illustrations from http://www.doubleroot.in We see $(x+(1/x))^2 \geq 4$: We know the...
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Answer by Vim for Visually stunning math concepts which are easy to explain
This one $($via Proof Without Words$)$ is wonderful but not immediately obvious. Ponder on it and you'll find out how fantastic it is when you get it. Explanation: Set the radius to be $1$, then...
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Answer by Markus Scheuer for Visually stunning math concepts which are easy...
Visualisation in ancient times: Sum of squares Let's go back in time for about 2500 years and let's have a look at visually stunning concepts of Pythagorean arithmetic. Here's a visual proof of...
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Answer by user2804123 for Visually stunning math concepts which are easy to...
Simple answer for "what is a radian": Logarithmic spiral and scale:
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Proof that the area of a circle is $\pi r^2$ without words: Proof Without Words: The Circle
View ArticleAnswer by Jenga for Visually stunning math concepts which are easy to explain
A nationwide math contest in Germany recently came up with a task that I found beautiful to explain, because of two points. You can get an idea, what the proof is, without applying mathematically...
View ArticleAnswer by user141101 for Visually stunning math concepts which are easy to...
Just wanted to point out that The Book of Numbers has a lot of the examples above $($ as well as many others $).$
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Answer by Maxim Umansky for Visually stunning math concepts which are easy to...
Here is a very insightful waterproof demonstration of the Pythagorean theorem. Also there is a video about this. It can be explained as follows. We seek a definition of distance from any point in...
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Answer by J.R. for Visually stunning math concepts which are easy to explain
When I look up "area of a rhombus" on Google images, I find plenty of disappointing images like this one: which show the formula, but fail to show why the formula works. That's why I really appreciate...
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Answer by Daniel Geisler for Visually stunning math concepts which are easy...
A visual display that $0^0=1$. The following is a tetration fractal or exponential map with a pseudo-circle shown in orange. The red area is period $1$ and contains $1$. Example is $1^1=1$. The orange...
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Answer by congusbongus for Visually stunning math concepts which are easy to...
I think if you look at this animation and think about it long enough, you'll understand: Why circles and right-angle triangles and angles are all related. Why sine is "opposite over hypotenuse" and so...
View ArticleVisually stunning math concepts which are easy to explain
Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain but are...
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Answer by caffeinemachine for Visually stunning math concepts which are easy...
I have found it intuitively difficult to see that the sequence $(1+\frac{1}{n})^{n}$ is increasing. However the following picture makes it clear.We have drawn the graph of the function $\log(1+x)$. It...
View ArticleAnswer by Ankit Kumar for Visually stunning math concepts which are easy to...
One of my favourite mathematical number is $3$ because $$3=\sqrt{1+2\sqrt{1+3\sqrt{1+4\sqrt{1+5\sqrt{1+\dots}}}}}$$Similary we can...
View ArticleAnswer by SagarM for Visually stunning math concepts which are easy to explain
"Cantor's Diagonal Argument" is something I find amazingly beautiful. It is not geometry, it is not artistically stunning, but it visually captures an implausible mathematical truth. It allows you to...
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Answer by Anindya Prithvi for Visually stunning math concepts which are easy...
A literal meaning of visual math.Almost any line-drawing can be traced on the cartesian plane using the fourier transformations using only one parametric equation.In simple terms tracing multiple...
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Answer by irene dovichi for Visually stunning math concepts which are easy to...
There is a bijection between $\mathbb R$ and $\mathbb R^2$. That is: a line and the space have the same cardinality.You can visualize it with (one of) the Peano curve:P.S. We use the fact that there is...
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I just saw this movie on youtube that gives a visual proof that every prime that is 1 modulo 4 can be written as the sum of two squares. This is a highly non-trivial theorem, and that it can be...
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Answer by Vepir for Visually stunning math concepts which are easy to explain
We can visually encode factorizations of numbers using $2$-digit palindromes!Define $n\times n$ matrices $P_n(k)$ and $N_n$ for $x,y\in[0,n)$ as: (the sum is...
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Answer by michaelmross for Visually stunning math concepts which are easy to...
A number spiral of primes with some prime-dense polynomials noted. Alignment of perfect squares is along the right horizontal axis. (The prime-free gap is accounted for by the squares and the squares...
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Answer by C.F.G for Visually stunning math concepts which are easy to explain
Gluing two Mobius strips along their edges is a Klein bottle.Source
View ArticleAnswer by C.F.G for Visually stunning math concepts which are easy to explain
$\Bbb RP^2\sharp\Bbb RP^2\simeq \text{Klein Bottle}$
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Answer by C.F.G for Visually stunning math concepts which are easy to explain
Why is the Möbius strip not orientable?
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Answer by Some Guy for Visually stunning math concepts which are easy to explain
This is a proof of the Pythagorean by US President J. A Garfield.As you can see, when you line up the triangles like this, it forms a trapezoid. One way to find the area of the trapezoid is by adding...
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Answer by robjohn for Visually stunning math concepts which are easy to explain
The surface obtained by spinning a cube on two diametrically opposite corners:$\hskip{4.5cm}$All the surfaces are ruled surfaces. The top and bottom are simply conical caps. The curved part in the...
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Answer by Timothy for Visually stunning math concepts which are easy to explain
The heptagonal tiling is a tiling of the hyperbolic plane with heptagons with 2 meeting at each vertex. I once found this image in a Google image search.It's amazing. It shows that an order 14...
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Answer by gman for Visually stunning math concepts which are easy to explain
I don't know if this fits "visually stunning" but it stunned me when I saw it in my 40s because I can't believe no teacher ever explained things this way to meTo me this diagram made so many math...
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Answer by asmaier for Visually stunning math concepts which are easy to explain
You might like https://en.wikipedia.org/wiki/Visual_calculus. This was popularised by the beautiful book by Apostol, Mnatsakanian (2013): New horizons in geometrySee also:...
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Answer by Golden_Ratio for Visually stunning math concepts which are easy to...
Nicomachus's theorem:Jensen's inequality:Pizza theorem:
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Answer by pr1268 for Visually stunning math concepts which are easy to explain
$ \displaystyle{\sum_{n=1}^\infty{2^{-2n}}} = \dfrac{1}{4} + \dfrac{1}{16} + \dfrac{1}{64} + ... = \dfrac{1}{3}$Visually:
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