Square Limit by M.C. Escher How are the fish in the middle of the design and the surrounding fish...
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Transcript of Square Limit by M.C. Escher How are the fish in the middle of the design and the surrounding fish...
![Page 1: Square Limit by M.C. Escher How are the fish in the middle of the design and the surrounding fish alike? How are they different?](https://reader035.fdocuments.net/reader035/viewer/2022081520/5697bfdc1a28abf838cb11b7/html5/thumbnails/1.jpg)
Square Limit by M.C. Escher
• How are the fish in the middle of the design and the surrounding fish alike?
• How are they different?
![Page 2: Square Limit by M.C. Escher How are the fish in the middle of the design and the surrounding fish alike? How are they different?](https://reader035.fdocuments.net/reader035/viewer/2022081520/5697bfdc1a28abf838cb11b7/html5/thumbnails/2.jpg)
Square Limit by M.C. Escher
• Escher used a pattern of squares and triangles to create Square Limit.
These two triangles are similar.
Similar figures have the same shape but not necessarily the same size.
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One way to create artwork with a smaller and smaller framework is to base it on an isosceles triangle with an apex angle whose measure divides 360º evenly.
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We have elected to base our artwork on an isosceles triangle with an apex angle of measure 45º where 360º/45º = 8. An octagonal configuration will result.
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Select the midpoint of the base of the triangle.
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Add a row of five similar smaller triangles by drawing line segments parallel to the slant sides of the triangle.
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The result is the basis of the shrinking repeating fundamental unit.
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Add a continuous curve from vertex to vertex of one of the sides of the original triangle.
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Rotate this curve about the apex of the original triangle to its congruent side.
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Draw reductions of this curve from vertex to vertex of each of the four reduced line segments
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This is the shrinking tessellating unit.
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Add interpreting interior features.
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Continue the reduction algorithm indefinitely …
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Continue the reduction algorithm indefinitely …
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Continue the reduction algorithm indefinitely …
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Continue the reduction algorithm indefinitely …
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Continue the reduction algorithm indefinitely …
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Continue the reduction algorithm indefinitely …
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… then add the tessellating unit with its interpreting features and reductions thereof as required.
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… then add the tessellating unit with its interpreting features and reductions thereof as required.
![Page 22: Square Limit by M.C. Escher How are the fish in the middle of the design and the surrounding fish alike? How are they different?](https://reader035.fdocuments.net/reader035/viewer/2022081520/5697bfdc1a28abf838cb11b7/html5/thumbnails/22.jpg)
… then add the tessellating unit with its interpreting features and reductions thereof as required.
![Page 23: Square Limit by M.C. Escher How are the fish in the middle of the design and the surrounding fish alike? How are they different?](https://reader035.fdocuments.net/reader035/viewer/2022081520/5697bfdc1a28abf838cb11b7/html5/thumbnails/23.jpg)
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