The Geometry Aspect of M. C. Escher’s Circle Limit III by Thuan Huynh
Jan 03, 2016
About M. C. Escher Maurits Cornelius Escher was born on
17th June, 1898 in Leeuwarden, Netherlands.
He studied at the School of Architecture and Decorative Arts in Haarlem. However, he gave up architecture in favor of graphic arts .
At first, his works depicted landscapes using impossible perspectives.
After 1937, he discovered the “open gate” of mathematics and made a few attempts in his early works to satisfy his urge for filling the plane.
His fame slowly spread, and during the 1950s, articles on his work appeared. His works began to be displayed in science museums rather than art galleries.
He died in 27th March, 1972 at the age of 73.
According to Escher’s measurement, the angle between the bounding circle and the white circle is precisely
My goal is to calculate mathematically.
080
Fig. 3. Fig. 4.
2
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ly,respective BO and AO sides toopposite 4
and
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22
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4
1)+32)(-6(-) 2)+61)(-3( =
4
)CO-(BO=cos =>
2-) )(BO(4cos-) (BO =2-) )(CO(4cos+) (CO
:let we(6) From
(8) 1)+32)(-6( =) (CO
2)+61)(-3(=) (BO
: thatfollowsIt
2=) )(CO(BO
:have we(7) From
2)BO-6(=) BO-2(AO=1)CO-3(
:have we(3) From
12
22
212
1
21
22
1 2
2221
woodcut. theof
tsmeasuremen actual get the to20.5cmby result hesemultiply t
weso41cm, ofdiameter has circle bounding sEscher' Since
.66059750 AB
.33940250BO
.69662140BO
2.2104024AO
1.3572189AO
1.8047860 BO
1.1081646CO
:find alsocan wehere From
79.97=(0.17416)cos= =>
3
1
2
1
2
1
0(-1)
ReferencesDunham, Douglas. “Some Math Behind M. C. Escher’s
Circle Limit
Patters”. d.umn.edu.14 April. 2013.
http://www.d.umn.edu/~ddunham/umdmath09.pdf
Schattschneider, Doris. M. C. Escher: Visions of Symmetry. New
York: Harry N. Abram, Inc., 2004. Print.
Schattschneider, Doris, and Michele Emmer. M. C. Escher’s
Legacy. New York: Springer, 2003. Print.