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Escher on Escher Ribbons

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Page 1: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

Escher on EscherRibbons

Page 2: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

Ribbons

“Curved ribbons or strips are suited to suggest a three dimensionality”

Page 3: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

Rind

• “… a spiraling ribbon, like an orange peel,portrays a fragmentary head of a woman.

• It floats through space as a hollowsculpture.

• The illusion of depth is accentuated bymeans of a cloud cover receding towardan invisible horizon.”

Page 4: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

• Rind• 1955

• Wood engraving

• Brown-red,gray-green,dark-brown

• 3 Blocks

Page 5: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

Bond of Union

“Here, two spirals, portraying a woman’s and aman’s head, are united in one endless strip.

With their foreheads even hooked to eachother, they form together an indissolublebond of union.

Spheres, floating in front, between, and behindthe folds of the empty heads, should suggestinfinite space and time.

Page 6: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

• Bond of Union• 1956 Lithograph

Page 7: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

Ribbons - afternote

• Escher explained that the initial impetus camefrom H.G. Well’s novel the Invisible Man.

• “… the invisibility being rather inconvenient,he wants to get visible again and swathes hisface with a bandage”

Page 8: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

• Sphere Spirals, 1958, Printed from 4 Blocks• Woodcut, Grey, Black, Yellow, Pink

Page 9: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

Quote on Sphere Spirals

• “… a system of four theoretically never-ending ribbons, running over thesurface of a sphere, link up its twopoles. Both poles are visible, oneexternally and the other internally,through the open interspace betweenthe two ribbons”

Page 10: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

Math remark on Sphere Spirals

• The Sphere is meant to be invertible.That is if it were turned over, it would‘show the same path’.

• A spherical spiral is a curve a shipwould travel from the south pole to thenorth pole. Theoretically, the pathwould become infinite at the poles.

Page 11: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

• Sphere Surface with fish, 1958

Escher applied the sameMathematical curve tothis

Page 12: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

Moebius Strips

• A Moebius strip - is a “one-sided pieceof paper”

• Escher considered the following two aspart of his “ribbon” themed work.

Page 13: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

Moebius Strip I 1961

Wood Engraving and Woodcut

Red, green gold, black

Printed from 4 blocks.

“… folded three times and presented as if it were in cut in two parts with a pair of scissors over the whole length.

Page 14: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

• Moebius Strip II 1963

Woodcut in red, blackand grey-green

Printed from 3 blocks

“…red ants walking ina continuous file…”

Page 15: Escher on Escher - 1 Four Hobbies Ribbonsmathserver.neu.edu/~eigen/1220DIR/EscherArticles/Escher on Escher... · Escher applied the same Mathematical curve to this. Moebius Strips

…quote…

• “I think I have never yet done any workwith the aim of symbolizing a particularidea, but the fact that a symbol issometimes discovered is remarkedupon is valuable for me because itmakes it easier to accept theinceplicable nature of my hobbies,which constantly preoccupy me.”