Maurits Cornelis Escher, usually referred to as M. C. Escher, was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, tessellations and mezzotints. Escher (pictured left) was a great master of tessellation (the regular division of the plane, or tiling). He created symmetrical designs and planar tesselations, which he described as congruent, convex polygons joined together."
In 1922 Escher visited the Alhambra palace in Granada, Spain and saw the wall tilings of the Moors, a people who originated from Northern Africa (pictured right). He was excited to find other artists who had been captivated by tilings, but also made this revealing comment: "What a pity their religion forbade them to make graven images." Escher's notebooks soon became full of repeating patterns inspired by the Moors. Imagery gave his patterns a different psychological character from the serene designs of Islam.
Tessellations also known as tilings are a collection of polygons that fill the plane with no overlaps or gaps. There are regular tessellations that tessellates with just one polygon and semi-regular tessellations that use two or more regular polygons. Tessellations are a good way to introduce students to the beauty of mathematics which can be very artistic and
While, Escher's work includes representation, it is still involved with the language of visual symmetry and order. Symmetry is integral to the medium of printmaking and graphic arts. The impression of a woodblock is a reflection or mirror image of the design carved into the block. Multiplicity and repetition are functions of printing as well. Thus, Escher chose a medium that naturally expressed two motions of symmetry: reflection and translation. These elements of symmetry also showed Escher's strong love of order. The technical difficulty of woodcutting suited Escher's fastidious nature too they symbolize the idea of boundlessness in a manner that is not obtainable."
Escher was also fascinated by the concept of infinity, which led him into explorations of space beyond the two dimensional plane. He carved the surface of this six inch ball with twelve identical fishes to show that a "fragmentary" plane could be filled endlessly. "When you turn this ball in your hands, fish after fish appears in endless succession. Though their number is restricted, they symbolize the idea of boundlessness in a manner that is not obtainable."
Escher pursued themes of transformation in works he called "Image Stories" which involved images transforming from one state into another. In another version of "Pessimist and Optimist", he explains, "... on a gray wall, these human figures increase their mutual contrast toward the center ... each kind detaches themselves from the wall surface and walks into space ... Thus going round they can't help meeting in the
This lesson involves using polygonal relationships to form tessellations. Our goals are to understand and create tessellations and tillings, to learn concepts and notations important for understanding and discussing polyhedra. Also which types of polygons can we use in order to make a regular tessellation and what are the conditions are needed for irregular tessellations. The lesson involves the use of scissors, construction paper, lizard stencils, and glue which should be fun and hands- on for the students. The main objectives for the students to take away from this lesson are to:
• Recognize and explore the properties of tessellations. • Identify and examine symmetry in geometric figures.
- Describe, and classify polygons, examine the role of mathematics in society and nature.
1. The aim is to get Pacesetters working together in groups using a discovery method for Pacesetters to learn the ideas of polygons angles and construction using the Zome System. For Pacesetters who are new to art tools introductory about the Zome System may be helpful to get Pacesetters comfortable with using the tools. 5-10 mins
2. Once the introduction is over, Pacesetters will be broken up into groups of four or five Pacesetters and handed out the worksheet for this activity. The first few questions are to get Pacesetters thinking or recalling properties about tessellations such as vertex conditions, types of tilings and different types of symmetries tilings can have. Pacesetters will also have time to get familiar with the Zome tools by making simple constructions 10-15 min
3. Then each group will be giving a challenging construction that they will have to work together on to complete. These can be assigned arbitrarily by just assigning one of the challenge questions to each group.
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