Russian Constructivism

I found this website showcasing one of my favorite design movements, Russian Constructivism (correct me if it is actually another -ism, they aren't labeled but I'm pretty sure). Design 1- Design 8 shows a bunch of examples. Constructivist design is based very heavily on geometric shapes, as well as the use of angled figures and typography to create movement in the composition. This was a huge breakthrough in design at the time, because static text and realistic images were replaced with flat and very expressive geometric-based compositions.

The Divine Proportion and DESIGN!

This is continuation from my last comment about the Divine Proportion. I found out that the design process should also follow this "natural language". The Golden Section, or the Divine Proportion is a visual representation of a number called Phi. Phi is a number produced by bisecting a line at a particular point (see above.) Phi is 1.618033988749895, or by the numerical sequence called the Fibonacci sequence. If you use the Divine Proportions in creating your compositions it will improve the communication of the design. I think an example would be paper. Anyone want to figure that one out?

New Technology! touch screen and intuitive keyboards.

Baman vs. Piderman

This video doesn't have much to do with Math but it is full of epic artness check it out!

paper folding architecture

I stumbled upon this website about using geometry to fold paper into architectural forms. Here is a quote from the page about how they were created:
The original form was generated by radiating the hexagonal grid of a geodesic sphere and trimming the resultant surfaces with an inner and outer cube. The resulting network of cells gives the impression of a sphere caught within a cube.

http://roryhyde.com/pavilion.htm

tessellations

http://www.mathpuzzle.com/Tessel.htm
this website classifies different types of tessellations. it also gives examples of translation, rotation and reflection.

Math can even make things absurd.

http://www.alaska.net/~clund/e_djublonskopf/Flatearthsociety.htm

Contraptions

This game lets you create contraptions to move shapes to their goals. You learn a lot about the structure and strength of different shapes. It also allows users to save and show off their contraptions and the way they chose to solve puzzles. You don't need an account to play though either. Enjoy, it's fun!

http://fantasticcontraption.com/

Geometry and Symmetry at its Best

The Symmetry of Man by Leonardo Da Vinci is distinctively geometry and symmetry. This type of symmetry is called relfectional symmetry. There are five points (looks like a pentagon) which is said to be "the five points of living things." Da Vinci illustrates the form with two positions of both arm and legs. This depicitingg symmetry and proportion of the human figure.

http://www.ted.com/index.php/talks/robert_lang_folds_way_new_origami.html

Applied math to make crazy origami figures, relating origami to every different type of math such as quantum mechanics in simplicity, where simple laws govern the entire subject. Break down into the simplest form and move from there, shape related to square is equal to origami. The movement in origami is related to science and moving large objects into space by folding them, and finally to saving lives. Very Very interesting.

Math Magic

http://www.ted.com/index.php/talks/arthur_benjamin_does_mathemagic.html

Arthur Benjamin is a truly amazing mathematician who does HUGE math equations in his head, it is almost a performance. Enjoy his math magic.

article on rosette patterns

so i found this article online on rosette patterns and thought it was pretty interesting and thought you guys should have a look http://www.jstor.org/pss/1576515

                                

So I wikipedia-ed mathematics and art, and found something kind of interesting about platonic solids and polyhedrons being used frequently in western art.  "In geometry, a platonic solid is a regular convex polyhedron.  These are the three-dimensional analogs of the convex regular polygons...They are unique in that the faces, edges and angles are all congruent" (wikipedia).

These shapes appear in, to name a few,  Dali's "The Last Supper", da Vinci's book The Divine Proportion, and Albrecht Durer's "Melancholia".

Rosette Patterns- -Spider Web

While i was playing with some rosette patterns on Kali, i was reminded of this spider web i once saw.
(the setting- we were in the jungle and my friend was nursing a crazy infection that prevented him from walking...)
I walked in to my friends room to check on him and when i looked in the corner, I was kind of shocked, mostly in awe of this beautiful spider web. When i commented on the intricate and unique pattern, my friend smiled and said "yeah... i watched him make it"
The pattern is amazing to me as is the thought of Joe sitting there all day watching the spider move back and forth through space to weave this web...
Just like we criss cross and set points with the mouse in the Rosette program on Kali, this spider built his web building thread upon thread in this pattern he knew to create...

pattern game

i came across this game that reminds me of the patterns you can make with kali.
it's fun and it's based on symmetry and patterns.
patchworkz!

We talked about Robert Smithson in my critical theory class...a lot of his work is mathematically based.  The drawing of his, "A Heap of Language", which was made in 1966, is widely talked about in art historical circles.  It uses a traditional grid format that was typical in the 50s and 60s.  He also does some cool geometrical earthworks.

Here's a link to his website:  Robert Smithson

Fractal Calender!

So i was looking in my room for something i could math blog about and i saw my calender. apparently all the images are drawn using some kind of math equation. I just thought it was pretty, but apparently its smart too! I've attached a picture of next years calender so you can see it.

Notre Dame's Rosette Stained Glass Window

When I visited Paris this past semester, I went inside Notre Dame and right away noticed the most beautiful stained glass rosette pattern on its wall. The colors coming through from the sunlight illuminated it so magically. This was the photography that I had taken myself. It was so amazing.

The 3 rosette patterns in the church were constructed in the 13th Century. Each element of the design represents the flowers of Heaven, which resemble roses with multi-coloured glass petals. Each coloured petal sets off the others, but the design is not only used for its visual impact, it is a reminder that everyone is unique, but the children of God are even more beautiful when they come together!

Stonehenge Math

Stonehenge is a great early example of the math involved in design. The monument in Wiltshire, England shows how mathematics was used in the design process long ago. The creators of Stonehenge needed to not only use mathematics to determine the exact size and placement for the stones, but the long process of getting the stones to the location. Up to 43 of the 4-ton stones were transported from 250 kilometers away, which must have involved a great deal of mathematics to move across the country, which is believed to have been a series of logs to which the stones were rolled across. It is a standing monument to the use of mathematics involved in design.

Napoleon's Theorem

So I was complaining to a friend about having to blog about math, and he pulled out a notebook and explained a surprisingly interesting phenomenon called Napoleon's Theorem. He drew 3 different triangles connected at the corners and found the centers of each. The triangle made from these 3 points was an equilateral triangle. Apparently this works with any 3 triangles, which is very cool.

link to Wikipedia page

Origami

I just thought this might be interesting to some people. My brothers friends has this origami website he made where he displays some of the projects he has created. It's neat stuff. Enjoy

http://www.corigami.com/

Kenetic

Kinetic sculptures...math and art.

http://video.google.com/videoplay?docid=-2073061059547146995&ei=ZurPSP7pDoqYrALqueTJAg&q=kenetic+energy+sculpture&vt=lf&hl=en

Deep Oceans

This doesn't have alot to do with math and art but its super interesting and math did get us there.

http://www.ted.com/index.php/talks/david_gallo_on_life_in_the_deep_oceans.html

Damien Hurst

There are a lot of artists in the world that I would love to share, but I think Damien Hurst is a great one to talk about on this blog.  The work I love the most is made up of colored dots placed in geometric patterns.  The perfect blend of math and art!

Mash-Up Makers

I was reading the news online this afternoon when I came upon this article about mash-up makers.  I had not heard this term before and now realize 'mash-ups' are "the end result of bringing together two or more different creations or applications that were not originally intended to work together, and the concept is a firm part of the Web 2.0 world."  Music and art are also incorporated into these 'mash-ups'.  Read this if you are interested!

i really see you upside down

while reading the article for homework this weekend i found it fascinating that our brains can recognize symmetry almost immediately especially when it is a vertical line running down the image which then got me to thinking about the brain and how it works. and if really our eyes see everything upside down and our brain processes what our eyes are seeing and turns it right side up to give the "correct" image then is that why we see vertical symmetry better than any other kind of symmetry, because i brain is working to rotate an image to begin with so technically we are seeing it rotated, although our mind does not let us realize that, so our mind is seeing the dimensions of an objects and somewhat studying the object while it's rotating it so we can recognize it. so my point is; is there a connection for realizing vertical symmetry rather than horizontal or cyclic or dihedral symmetry to the way our brain works and the way it sees an object and does an extensive amount of work on it to then let us realize what we are seeing. and if we did not have the ability to do this and our eyes worked as they should and saw everything right side up would our perceptions change?

create a perfectly symmetrical face

I came across this strange website where you can upload a photograph of yourself and it will warp the photo to make your face perfectly symmetrical....they have examples of familiar faces to us all that for the most part just look creepy, but anyways try it out yourself and you will find you will be very happy that all of our faces are a little uneven and not perfectly symmetrical!....here's the link http://www.symmeter.com/symfacer.htm

symmetry in architecture

This particular piece of architecture is based on symmetry. If you were to cut through the center, both sides would be identical (minus the furniture). I think the symmetry provides the room with more interest and it gives it a more contemporary look.

Funny Math Videos

After going through my favorites list on Youtube  found these two videos. The first is a cover of New Math by Tom Lehrer which got a few awards on Youtube. The second is a series of math jokes that has another Lehrer song in the background.

golden rectangle

so i saw a girl at the train station with this tattoo on her arm and i thought about this class and how this math is everywhere.

Chand Baori Well

This is the Chand Baori Well in India. It was built in the 10th century as a practical solution to the water problem in the area. It is 30 meters deep, it has 13 floors and 3,500 steps. And legends say that ghosts build it in one night and that it has so many steps to make it impossible for someone to retrieve a coin once it’s been dropped in the well.

Symmetric Figure Exploration

When reading the Introduction to Symmetry article today, I tried the Symmetric Figure Exploration and I really enjoyed making the wallpapers. One example I made is to the left. If you need some interactive visuals, this a great exercise.

games are usually fun

so i just found this website with fraction games on it. it's pretty easy and completing things is rewarding (a pop up to congratulate you on your completion of the fun fraction game? aw, thanks internet)
games!

also you can play ninja angle games. it's a kind of fun way to practice what we've been doing in class.

Wire Design

When I'm bored, I use a site called Stumble Upon.com that gives me a list of interests and then it shuffles websites based on my interests. This came up the other day and I was really interested in its formation of shapes but simply looking at it almost as if it was a flat image. Just being created by wire supports for this tower and light structure, I like its probably accidental making of a cool image.

I enjoy the music of Chopin, one of most well-known Romantic composers. He tended to use the golden ratio in many of his works. He based many of his musical studies off of this mathematical theory of repetition and focus. I suggest listening to his music and hearing it for yourself.


http://en.wikipedia.org/wiki/Golden_ratio
This is where you can find a quick synopsis of the golden ratio.

I've heard people talk about how they think Jackson Pollock's work is based on math or that each painting may even be an entire math equation.  I don't think I agree with this, but it is interesting to read about.  Here are a couple of articles:

Jackson Pollock's Fractals  

Discover Magazine

infinity

The work by the designer Karim Rashid reminds me of M.C Escher's tessellations. Rashid represents infinity very similarly to the way Escher does...(change in scale & repetition of the same shape). I think that Rashid does an excellent job of creating a type of optical illusion, just as Escher did in his pieces.

Gaudi

In class we spoke of the ways in which an artist can find a solution to a "mathematical" problem in a piece of art by using calculation or through trial and error - an often correct and faster method. I spent my fall semester in Barcelona, Spain last year living down the street from Gaudi's La Sagrada Familia. We spoke of him in all of my courses, with particular emphasis on his precision of detail and innovative architectural techniques. I guess I had just assumed he was a mathematician of sorts to make such brave choices in his designs, but as it turns out, he used little math. This discovery fascinates me. I have copied a bit about one of his techniques below:

"Gaudí spent ten years working on studies for the design, and developing a new method of structural calculation based on a stereostatic model built with cords and small sacks of pellets. The outline of the church was traced on a wooden board (1:10 scale), which was then placed on the ceiling of a small house next to the work site. Cords were hung from the points where columns were to be placed. Small sacks filled with pellets, weighing one ten-thousandth part of the weight the arches would have to support, were hung from each catenaric arch formed by the cords. Photographs were taken of the resulting model from various angles, and the exact shape of the church's structure was obtained by turning them upside-down obtaining therefore the form, absolutely precise and exact, of the structure of the building, without having to have conducted an operation of calculation and without possibility of error. The forms of cords corresponded to the lines of tension of the prim structure and when inverting the photo, the lines of pressure of the compressed structure were obtained. An absolutely exact and simple method, giving an example of the intuitive and elementary methods that Gaudí applied in its architecture and that allowed him to obtain balanced forms very similar to which nature offers."

Inspiration for our patterns

(Micro landscape - nano-scale titanium crystals on the surface of an orthopaedic implant magnified 70,000 times... cool!)

http://www.bbc.co.uk/northyorkshire/content/image_galleries/paul_gunning_microsope_images_gallery.shtml?3

there are some really nice images of patterns here, the photographs are being presented as visual art, but could also be looked at from a very scientific or mathematic eye. or all three simultaneously which probably offers a deeper undertsanding of what is going on.
it is interseting beacuse these really beautiful patterns exist everywhere and what this photographer has done is focus our eyes on some very tiny ones...

A good term refresher course

I found this very helpful when trying to describe the shapes we found and created in class and in our homework.

As I was reading about Escher's life and work in the textbook, one pattern in particular caught my attention (pg. 9). I have used Moroccan patterns in my art before, and enjoy filling spaces with geometric pattern as a way to catch the eye. Here are some additional Moroccan patterns that I found very interesting.

Ok so i was listening to this new song "swagger like us", and i was thinking about math art and design. i was wracking my head for an interesting post, something with substance, and then it came to me the song that i was listening to has the properties that we are learning about. Although i know this may not be the ideal concept of this course i still feel it works. Everyone knows music is defiantly an aspect of art i.e. Mozart, Beethoven etc, it has never been questioned, but listening to this song i realized the composer Kanye West took another song "Paper Planes" extracted a single line "swagger like us" looped it and shortened it and elongated it a bunch of times added base drums trumpets and an abundance of others sounds and he made this the beat. And what i love about this idea is the abstraction of this one song. He is known to take songs and take a line and make it apart of the beat, however normally it is only apart of the beat it is never the beat itself, the abstraction of these words by Kanye is amazing. and the way i think this is a good blog for the site is because the artistic aspect of the beat is great. He designed it through abstraction which is what Escher did; repition through abstraction with a lot of his pieces. and although this is something you hear rather than see it is still in the same context the math is in the numbers of the beats and the precision of the melody. It is an amazing idea that Kanye created.

Photosynth

Last semester, my friend shared this video with me.

http://www.youtube.com/watch?v=lkuGrCB85H8

Photosynth is a program that almost completely is over my head as far as understanding is concerned. However, this link will help better explain how it works.

http://en.wikipedia.org/wiki/Microsoft_Live_Labs_Photosynth

Essentially, the relevance and similarities I found between this program and MC Escher's paintings is the ability to make things that are actually 1 dimensional and make them into 3 dimensional. For instance, MC Escher took a 1 dimensional canvas and turned it into this 3 dimensional drawing using shading.

http://aaronbaird.net/pictures/Escher/Hand_with_reflecting_globe.jpg

The video I linked you all to explains how Photosynth does the same thing with 1 dimensional photographs by collectively turning them all into one 3 dimensional image. I think it's really neat.

Architecture is Geometric

I was looking through my brothers architectural books and came across some interesting information....
When most people think of symmetry they think of basic line symmetry. In architecture, symmetry is a way to describe shapes and design and to organize geometry. One architectural feature where symmetry is evident is a frieze design. A frieze design consists of repeated copies, along a line, of a single figure or block. Frieze patterns can be seen on walls, railings, verandas, etc. These patterns can be seen in art and architecture around the world.

The Dot and the Line

http://www.youtube.com/watch?v=OmSbdvzbOzY

This is a cute and really well-made animation called The Dot and the Line: A Romance in Lower Mathematics that some of you have probably seen before. The story is in reference to the book Flatland: A Romance of Many Dimensions, which we actually have to read for this class. The author of the story is Norton Juster, and it was animated in 1965 and won an academy award.

Tyography and Math: A tutorial for good typography

I know Angela said she was interested in Math and how it is involved with typography. Especially modernist typography!

http://typophile.com/node/47265#comment-291071

http://www.ted.com/index.php/talks/benjamin_zander_on_music_and_passion.html

Click link above to watch video.
Benjamin Zander is a Composer/Teacher, in this talk he characterizes classical music as a medium to which everyone likes but they just don't know it yet. This inspirational talk led me to thinking of how math is a universal language between all people just as music is. I urge you to watch the entire video, I've watched it seven or eight times since my first encounter with it.

Repeated forms from two different sources

I Found this image very interesting because of the use of two different sources to create a geometrically pleasing and symmetrical piece. The combination of the tiling which is always present added with the sunlight and shadows at the perfect time of the day works very well...This was taken in one of the many Yukatan Haciendas one of which I had the chance to visit.

Quadrilaterals in Science Fiction

During class on Wednesday, I couldn't help but notice something familiar about some of the quadrilaterals being displayed on the board.  It was then that I realized just exactly where I had seen some of these shapes before...Star Wars space crafts!  I went back to my apartment on my day off and decided to do a little research, just to make sure I wasn't crazy.  This is what I found.

Parallelogram?



Or Jawa Sand Crawler?



Kite?



Or a Star Destroyer?



You be the judge.