Taking a Look at Tessellations

The line work used in this sculpture is not composed of physical markings but it is visible through the component of light in the large mountain. The shadows brought on by light create the lines from which the shape of the central mountain takes form. This shape is comprised of rough intersecting “lines” that look unplanned giving the shape a veristic sense. This “unplanned” shapes come together to create a realistic landscape that mirrors the uncalculated plan of structure of the natural world. The reason why these mountains appeal to the senses is because of Laramée’s extreme use of texture. The surface quality brings the landscapes to life by adding a hyper realistic feel, an accomplishment so impressive to pull of considering the medium in which the artist sculpted “The Web”, extremely thin paper of a Webster dictionary. The artwork is in a three-dimensional plane since it is sculpted but the small additions of windows in the small temple-like structure at the corner of the piece and the deep precipices between mountains add to the illusion of space. These details enhances the sense of depth throughout the art piece by adding small spaces that look as if they are infinite. The star maps on either side of the book covers add to the illusion of space by integrating a galactic background that makes it

Van Gogh (March 30, 1853-July 29, 1890) is a well-known Dutch artist for his authentic post-impressionist paintings and sketches (Wikipedia, 2017a). His vivid art has laid the main foundation for the emergence of modern art movement (1860-1970s), which is characterized by the deconstruction and transgression of the traditional art forms, symbols, structures, and meanings (Wikipedia, 2017b). Many scholars and art critiques describe Van Gogh as a transformational leader of our world (Ballou, 2012; Blatt, 1994; Colman, 2014) because he was a visionary dreamer, who could paint his dreams. Moreover, his art is often considered as an important contribution to mathematical studies and physics (Blatt, 1994; Colman, 2014). For example, Colman found that a painting entitled Starry Night accurately depicts the concept of turbulence with “a degree of sophistication and accuracy that rivals the way physicists and mathematicians have best explained turbulence in their own scientific papers” (2014, para. 2). In this context, I would like to analyze his painting Road With Cypress and Star (1890) with a focus on the geometry of lines, planes, and shapes.

Juane Quick-To-See Smith uses geometric motifs many times in Eclipse. She uses patterns of geometric shapes, using triangles, squares, and circles all over the canvas. Smith also uses lines to create patterns in the artwork. Her use of geometric shapes and lines shows us that those were important to her and her Native American people. Natives Americans must have used these on an everyday basis showing how important it is for them. Even though they were not the ones to create them, we still use it today on an everyday basis.

The first article that I read had to do with the history of a tessellation and it also explains what a tessellation is. “Tessellations of a plane can be found in the regular patterns of tiles in a bathroom floor, or flagstones in a patio.” (Mackenzie) Which is what I explained in the previous paragraph. “ A tessellation of a plane is any subdivision of a plane into regions or “cells” that border each other exactly, with no gaps in between.” (Mackenzie) Some patterns you see you may think they are tessellations they are actually not. You know why? Because you may not think that there was a skip and or gap of the pattern. That just makes a regular pattern. What did I learn? Well I knew that their was a more professional name for a pattern which is a tessellation. For example of a

Pentangles began as crude drawings as diagrams that were found scratched into the walls of caves. From this point onward the assumption is, they began to have a belief encompassing some realm of spiritual significance but, the real meaning of the star-shape is a mystery. With the cultivation of civilizations that had followed, the pentangle has held various references, most notably though with religion. Serving also as a way to mark directions in

There are all different factors that go in with tessellations. There are regular tessellations, semi-regular tessellations, monohedral tessellations, duals, M.C. Escher and modified monohedral tessellation and aperiodic tessellations. A regular tessellation has “...three regular shapes…: the equilateral triangle, the square and the regular hexagon.” The “[s]emi- regular tessellations are made of more than one kind of regular tessellations.” There are more tessellations and different rules that come into play when making them, but they all

Maurits Cornelis (M.C.) Escher (1898-1972) was a Dutch graphics artist who specialized in many printmaking techniques, mainly lithographs as well as mezzotints. Like many famous artists such as Michelangelo, Leonardo da Vinci, Albrecht Dürer, and Holbein, M.C. Escher was left-handed. His trade was not limited to printmaking / graphics artist, he was also known for his book illustrations, tapestries, postage stamps as well as murals. What makes Escher’s works so intriguing is the mathematical nature that leaves the viewers in awe, looking for reason and ways that the pieces “work”. His work can be described as “meticulous realism with enigmatic optical illusions” (Encyclopædia Britannica However, a lot of his works focus on physical impossibility,

Have you ever looked into the concepts behind what makes a tessellation? Tessellations are made using a combination of artistic and mathematical abilities. M.C. Escher was a talented man from the Netherlands who made tessellations. He made such interesting art pieces of various types by using mathematical concepts and artistic details. M.C. Escher’s techniques on his tessellations made them stand out to viewers.

Tesselations can be found in paintings, project and kids items. Tesselations can be grouped into two things “real things” like people, housepets, and pencils. He earliest tessellations were stone floors, walls, and brick walls. In Roman times Tessellatios often made pictures, The pictures were usually grouped of simple colored square tiles. The group of pictures were very large. It was viewed as like a battlefield. Screens such as tv’s and computers are the same, they are large screens made of pixels. The first kind of tessellation is called Escher-Style or Representational art. In that kind of tesselation each tile likes real and each tile has a repeating shape. Escher invented it and made it popular in Western Culture.

Tessellations have occurred in nature since the dawn of time. Tessellations can be found in large patterns such as skin cells or scales on a fish or in small tight patterns such as rectangular plant cells. Tessellations were introduced into artistic creations during the late 19th and early 20th century by acclaimed artist M.C. Escher. After they were introduced artistically they were introduced into production and manufacturing

“I could fill an entire second life with working on my prints.”(M.C. Escher) That quote, said by Maurits Cornelius Escher (M.C. Escher), is the basis of his unique creations and projects. M.C. Escher is known today as the world’s most famous Dutch graphic artist. His art is enjoyed by millions of people all over the world as his work included impossible constructions such as ascending and descending, relativity, and transformation prints. He also made some realistic work such as Castrovalva, a lithograph print of a place he visited in Italy. However, his most fascinating works he has made have been his wonderful creations of Tessellations. A Tessellation, also known as a tiling, is created when a shape is being repeated over and over again

M.C Escher, also known as Mauk, lived from 1898-1972 and is one of the world’s most famous graphic artists. He was born in Leeuwarden, Holland and studied at the School for Architecture and Decorative Arts in Haarlem. He played with architecture, perspective and impossible spaces. His art continues to amaze and wonder millions of people all over the world. He used only simple drawing tools and the naked eye, but was able to create remarkable mathematical pieces that beautifully combines art with math. His drawings caught the eyes and looked possible by perception, but are mathematically impossible. Some of his more famous or well-known works are Ascending and Descending,

The use of geometric shapes in this painting allows the subject to be viewed in both a recognizable and unrecognizable state at the same time. Overall, geometric shapes and patterns play an essential role in what the viewer sees, which is further supported by a powerful color palate.

One of the non-Euclidean geometries used in modern architecture is elliptic geometry. It is also known as spherical geometry, a special case of the Riemann geometry for a constant and positive curvature. (Gawell 35) In elliptic geometry, all the straight lines are closed lines with a finite length and two different points may be connected by two segments. Historically this nothing new in architecture. Elliptic geometric elements have been

The most ancient and familiar shapes of mathematics are smooth and regular such as the circle, Platonic solids or undulating manifolds that humans strive to perfect in the form of cuboidal glass skyscrapers and sleek cars, but which are so alien to the natural world. Mandelbrot is much quoted for pointing out in The Fractal Geometry of Nature 1 ” clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line”. In fact, if you look closely, the shapes of these objects seem to be constant at all levels of magnification. A new form of geometry – fractal geometry,