Scuola di Atene 1510 1511 RAFFAELLO SANZIO 14831520

아테네 학당 (Scuola di Atene) 1510 -1511 RAFFAELLO SANZIO (1483~1520) 2

아테네 학당 (Scuola di Atene, 1510 -1511) RAFFAELLO SANZIO (1483~1520) 3

4

플라톤 (427 - 347 BCE) Timaeus (of Locri ) Leonardo da Vinci 5

아리스토텔레스 (384 - 322 BCE) Ethics 6

Pythagoras of Samos (569 - c. 475 BCE) 8

Guitar & Recorder 10

Pythagorean Scale 5도 + 4도 = 8도 1 8 9 C 64 3 81 4 8 9 D 243 256 E F 2 3 8 9 16 27 8 9 G 128 1 243 2 8 9 A 243 256 B C 11

Alexander the Great Alexander III of Macedon (356 -323 BCE) 아리스토텔레스의 스승 13

Euclid of Alexandria (325 - 265 BCE) or Archimedes (c. 287 BC – c. 212 14 BC)

Hypatia of Alexandria (ca. 370 - 416 CE) 16

Socrates (469 - 399 BCE) Aeschines (389– 314 BC) 17

Diogenes of Sinope (4 th century BCE) 19

Claudius Ptolemy (ca. 85 - 165) 22

Raffaello Sanzio (1483 -1520 CE) Raphael (left) and Sodoma 23

아테네 학당 (Scuola di Atene, 1510 -1511) RAFFAELLO SANZIO (1483~1520) 24

25

Renaissance 28

사실 (事實, 寫實) M. C. Escher (1898~1972) 29

정 사 각 형 C*O* = CO = QP MQ = M*Q* OMP O*M*P* 38 MQH M*Q*H*

Piero della Francesca, 1412 -1492 1469 42

A. Dürer (1471~1528) 43

Albrecht Dürer, 1525 44

Jan Vredeman de Vries (1527 -1604) 45

47

GIOTTO di Bondone (1 2 6 7 ~ 1 3 3 7) 49

William Hogarth (1697 -1764) • 'Frontispiece: ' Satire on False Prespective (1754) • Whoever makes a Design without the knowledge of perspective will be liable to such Absurdities as are shown in this Frontispiece 52.

Perspective 53

조화평균 1/OH = (1/OA + 1/OB)/2 or h = 2 a b / (a + b) or OA : OB = AH : HB 55

2008. 7. HJK 60

뒤러(A. Dürer, 1528) 67

Morphology 68

천마 天馬 Pegasus 1959 69 M. Escher, 1898~1972

J. H. Conway 주장 71

Majorie Rice (1923 - ) In 1975 I started a journey of investigation into the tiling of the Pentagon sparked by an article by Martin Gardner in my son's Scientific American. http: //tessellations. home. comcast. net/~tessellations/ 72