Visual Mathematics

Years ago when I started studying mathematics besides my job in IT I never considered that I would be able to apply mathematics in my day-to-day job. But I do now, because I work on the development of a drawing program ( a specialized drawing program on Android ). Does that make me happy? Just a bit. Because  applied mathematics can get as dirty as computer programming. Once applied, mathematics has lost most if not all of its beauty ( although nothing of its power ). I love pure mathematics, and even more so visual mathematics. The three pictures below are the result of applying a function to respectively the integers 1, 2 and three. The construction ( Mathematica programming, if you like ) of that function however required understanding of calculus, geometry, linear algebra, group theory and tling theory ( they are all parts of the Archimedean tiling of the whole plane with vertex type 4,8,8 ). My point being: this is the mathematics I like so much.

When I really like a picture I made I add it to 'The Gallery'. I am far from being able to create art with mathematics but there is a point where mathematics becomes art or where art becomes ( laying the groundwork for future ) mathematics. M.C. Escher explored mathematics decades before general theories about the subject were formulated.

If you are interested in Mathematics and Art then I can recommend this book: Connections: The geometric bridge between art and science.

The mathematics of beauty.

A mathematics of beauty and art. There is no such thing one would expect. Yet, Owen Jones (1809 - 1874), London architect, wrote the 'General Principles in the Arrangement of Form and Colour, in Architecture and the Decorative Arts ... ' in his book The Grammar of Ornament.

Proposition 4.
True beauty results from that repose which the mind feels when the eye, the intellect and the affections are satisfied from the absence of any want.

from Page PL. I

You'll find the other propositions at the link above in the Digital Copy of the 'The Grammar of Ornament'.

Escher's imaginery workplace

#mathematics #art #Open University #m336 #Escher

The Scream by Edvard Munch was sold for USD 120 million. I didn't like it yesterday and I don't like it now that I know it's perceived value. My favourite artists are Escher, Kandinsky and Dali, their work inspires me, and I am truly impressed by what they have created, art needs beauty. M336 brings group theory and geometry together through visual symmetry, or the symmetry Escher used in a lot of his work. I browse a lot through work of Escher as a result of M336 studies. Recently I came across this sensational video. A must see, really.


( A short movie inspired on Escher's works and a free vision on how it could be his workplace. )

This is another video by Eterea.

( A short movie about numbers and geometry. )

What is Sacred Geometry ?

One of my ( many ) reasons to study mathematics is my fascination for the geometry of crop circles. Appreciating the art in the crop circles does not mean that I have an opinion on how, or by who, the circles are made. I found out that the more you get into the subject the harder it is to answer that question. Only people that know very little about them will say without hesitation that all circles are 'hoaxes'. Hoaxes or not, they are absolutely beautiful.

Bert Janssen, a Dutch crop researcher, looked into the geometry of some circles.

(c) Bert Janssen. Click to enlarge.

See also: crop circle geometry, by Bert Janssen

Another crop circle researcher is Lucy Pringle.

The Godfather of crop circle research is Colin Andrews, he started the crop circle community.

To the point: sacred geometry.

It is rather common to use that word sacred geometry in the crop circle community. But it is also used in the so called ancient aliens theory which explains the sudden appearance of high tech architecture like the Pyramids in Giza by visitations of extra-terrestrials in that period.

The word sacred means:
- devoted or dedicated to a deity or to some religious purpose;
- pertaining to or connected with religion.
The word geometry means:
- a branch of mathematics concerned with questions of shape, size, position of figures, etc.

In mathematics the field of geometry has many branches, i.e. Eucledian, non-Euclidean, algebraic, analytical and so on, but there is no mathematical branch of geometry called sacred geometry. My conclusion is therefore that:

Sacred geometry is the geometry that has been used in the construction of religious artifacts.

By coincidence or not, it turns out that these geometries are often related to the golden ratio which is considered to have special aesthetic qualities.

Dancing in Euclidean Space

I invite you to watch an excerpt of Seventh Sense by the Anarchy Dance Theatre from Taiwan.



There is a somewhat longer excerpt here:


See also previous posts on mathematics and dance:
- Maths and Ballet (2)
- Maths and Ballet (1)
- Music inspired by mathematics ( has item on choreagrapher Crystal Pite )

Music inspired by mathematics

Mathematical songs

I sincerely love this song, Pi. The image is taken from the movie Pi directed by Darren Aronofsky ( Black Swan, Requiem for a Dream ). ( The performer did not take credit for the lyrics. )



More serious, the lyrics on Kraftwerk's, ( visionary ) Computer World album, created in the early 1980s, described a world dominated by computers, like today. Kraftwerk had a major influence on the music of the 80s and 90s. The lyrics of Numbers, one of the songs on Computer World were abstract and mathematical. The video is recent ( 2010 ) and of HD quality. Enjoy!

Crystal Pite

It is not a coincidence that scientists and artists flock together. From the moment they become students they meet and interact. Scientists need to go off the main roads to find new undiscovered territory. In a sense artists guide them because they help them to think differently. Likewise artists are influenced by science. ( Embedding has been disabled but the interview is just one click away ) Crystal Pite talks about Frontier. A ballet choreographer speaks about dark matter, dark energy and the line between what we know and what we don't know.

Symmetry ?

Browsing photo albums on facebook often reveals interesting and beautiful pictures.

(c) Yuliya Keaton

I find patterns like this very interesting because most people would call this a symmetric pattern. Yet, I know of no mathematical symmetry that accurately describes the symmetry we see here. Yet, mathematics claims to have categorized all symmetries of the plane.

Unfolding

Definition: An unfolding is the cutting along edges and flattening out of a polyhedron to form a net.

Somewhat related to unfolding is the pop-up ( as called by the artist ), but what's in a name?



More paper-art here: http://www.l.van.breemen.scarlet.nl/

Art and mathematics: 3D fractals

A 3D fractal from phidelity.com

Rena Jones - Open Me Slowly 3D Fractal Video from Kris Northern on Vimeo.

( Watch it full screen. )

A mathematical clock aka the crypto-clock

I am a great fan of alternative clocks although the clock I like most is the one as can be found at train stations across The Netherlands. To the point.

I have deciphered 9 of the 12 representations so far. And you...?
Update 11/2; deciphered 10 out of 12 of the "crypto-clock".

Time to start debunking Euler ?

Some names are only to be spoken of with respect.

Apple has been around a lot longer than Google. Apple created the i-Tunes software and related store where you can buy songs for only $0.99 and they created the i-Phone gadget. If you are a fan of that gadget I am sure you bought at least four of them in the last three years although the first one is still working it doesn't look that good compared to the i-Phone 4. Besides that Apple created billions of cash for Steve Jobs who has no intention to share it with the poor like Bill Gates from Microsoft does. - Google on the other hand created free software like gmail, google docs and google maps, a free feature we take for granted. Oh, and they created Google Search of course. Since a while, also thanks to Google, we have digital access to the books of Leonhard Euler ( and all the other great mathematicians of course ).

Have a look at the page where Euler defines the number Pi, here at Google Books. ( If you don't read Latin, why not use Google Translate? ) I checked the first 120 decimals of Euler's Pi with those from Mathematica 8 (2010) . They are exactly the same.

When I looked at Pi in 120 decimals I knew immediately that Euler did not make these calculations by himself. He just could not. OK, he was a genius but he did not have more -time- than a mere humanoid like us. How many hours ( if not days, i.e. check double-check ) would it have cost to do that calculation? It's not just -that- calculation. It's about the sheer size and depth of his legacy. Although Euler was still an active mathematician when he died at age 76, it is beyond the capabilities of one human being to create that in one lifetime.

Euler must have used students and computing staff to write his books. We know that he was blind during the last years of his life but even in that period he continued to publish. Perhaps 'Euler' was merely a brand. I don't know. Who was 'Euler'?

Perhaps the comparison of Euler with Ramanujan would be somewhat like a comparison of Rembrandt with van Gogh. We know for sure that everything we read in Ramanujan's notebooks is written by Ramanujan himself. I am not sure that everything in the books of Euler is written by Euler himself, the same is true for Rembrandt and are the cause of the fact that so many Rembrandt's turned out to be work of his students.

Mathematics and ballet

The movie Black Swan ( from the director of Pi ) convinced me that ballet -is- mathematics, even more so than physics. I surfed the Internet on both topics and found an interesting short video on the topic. What would Catherine Asaro say about it?

Find the transcript here. Is she saying -in between the lines- that girls are better suited for mathematics but that the (male) mathematics teachers don't understand how to teach mathematics to girls? An interesting point.

Before Pythagoras

An interesting exhibition in New York - "Before Pythagoras: The Culture of Old Babylonian Mathematics November 12 - December 17, 2010"

Visit the website of Before Pythagoras

Einstein's dice

Einstein once said "God does not play dice". What sort of dice was Einstein thinking of?

Photography with a touch of math: Caleb Charland

This picture somehow reminds me of the movie Pi... the best math movie I have seen to date.

Caleb Charland has a website.

Mathematics as Body Art

Found this picture somewhere on internet. The equation -is- beautiful, no doubt about that, so why not paint it on your body if you are into that stuff anyway?

Math and art

Although I seriously doubt if mathematics and art are even close I added http://math-art.net/ to the 'Cool Sites' list. I do agree that math pics can be beautiful. "... Where Mathematics and Art blends into a zen-like state of peace ...".

The Perfect Beauty

All I know is that there is a Flash program which is generating these images but I haven't got a clue how it's done.

What a difference a day makes [2]

How would our universe look like? It can't be infinite. Can it?

What a difference a day makes