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Greek & Roman art and Mathematics

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Ruth Dapkus
Ruth Dapkus

The Parthenon, built in Greece between 447-438 BC, and the Pantheon, built in Rome in 126 AD, are both ancient temples with architectural features related to mathematics. The Parthenon precisely fits a golden rectangle shape and its proportions follow the golden ratio, including a 1.618 ratio between its base and height. Elements of the Parthenon and Greek sculptures like proportions between body parts also reflect the golden ratio. The Pantheon's dome construction also demonstrates sophisticated use of mathematical concepts in architecture. Both structures exemplify how ancient Greek and Roman builders incorporated mathematical principles into their temple designs.

Education
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GREEK & ROMAN ART AND MATHEMATICS MATH 213 /SPRING 2015 RUTH ANN DAPKUS http://goldenratio.wikidot.com/greek-and-roman-art
The Pantheon and the Parthenon are both ancient temples. While the Pantheon was built in Rome to celebrate all the Roman gods, the Parthenon was built in Ancient Greece for the goddess Athena. The Parthenon pre-dates the Pantheon by about six centuries; it was built around 447-438 BCE, while the Pantheon was built in 126 CE. http://www.diffen.com/difference/Pantheon_vs_Parthenon
Pantheon Parthenon Location Rome, Italy Athenian Acropolis, Greece Built in 126 AD 447-438 BC Original purpose Temple to all the gods of Ancient Rome Temple to goddess Athena Built by Publius Aelius Hadrianus Iktinos, Kalikrates Current use Roman Catholic church Museum Architectural system Arch Technology Post and Lintel System http://www.diffen.com/difference/Image:Pantheon-dome.jpg
THE GOLDEN RATIO A Mathematics Inspiration ~ Probably more than any other
• History • The Pantheon was originally built by Marcus Agrippa in 27 BC, and the inscription on the front reads “M Agrippa L F Cos Terium Fecit,” or “Marcus Agrippa built this when he was consul for the third time.” However, the entire Pantheon was destroyed except for this façade, and the Emperor Hadrian rebuilt it on the same site in 126 AD. The building was given to Pope Poniface IV in 609 AD and was converted to a Christian church, saving it from destruction or looting. It was used as a tomb in the Renaissance and is the location of some royal tombs. https://www.google.com/search?q=pantheon+pictures&es_sm=122&tbm=isch&imgil=EvxtqUOMkQKs2M %253A%253BXvzsk- yUNFhroM%253Bhttp%25253A%25252F%25252Fen.parismuseumpass.com%25252Fmusee-pantheon- 38.htm&source=iu&pf=m&fir=EvxtqUOMkQKs2M%253A%252CXvzsk- yUNFhroM%252C_&usg=__M95mrimaC_SIhZVgdzu- QesDyKU%3D&biw=1600&bih=731&ved=0CDIQyjdqFQoTCPaw3sX1hsYCFUeaiAodoCcAdQ&ei=6h15VfaTD 8e0ogSgz4CoBw#imgrc=EvxtqUOMkQKs2M%253A%3BXvzsk- yUNFhroM%3Bhttp%253A%252F%252Fwww.parismuseumpass.com%252Fdatas%252Fmusees%252Fp%2 52Fa%252Fpanthon%252Fxl%252Fpantheon- 50c07d2be57f8.jpg%3Bhttp%253A%252F%252Fen.parismuseumpass.com%252Fmusee-pantheon-
https://www.youtube.com/watch?t=297&v=ANWz9a09KAg Pantheon
The Parthenon was built between 447 and 438 BC by Iktinos and Kallikrates as a temple to Athens’ patron goddess, Athena. https://www.youtube.com/watch?t=264&v=9wO0VglnxK4 Greek Classic the Parthenon
• The Parthenon has been subscribed in the golden rectangle, because it gives a pleasant vision to whom looks at it, it is a sort of divine ownership. • The golden ratio is a characteristic that you can find in a lot of circles (from the zoology, to the botany, to the art…)
THE PARTHENON CAN BE INSERTED IN A GOLDEN RECTANGLE BECAUSE THE RELATIONSHIP BETWEEN ITS BASE AND THE HEIGHT IS 1,618: THE GOLDEN NUMBER. THIS RELATIONSHIP IS ALSO VISIBLE IN OTHER ELEMENTS AND DECORATIONS OF THE PEDIMENT.
*If from it we remove a square of side of it equal to the height, the remaining part it is still a golden rectangle. http://goldenratio.wikidot.com/greek-and-roman-art
SCULPTURE In some Greek sculptures the navel (belly button) represents the mean of the golden ratio: The navel is positioned such that the ratio of the short half to the long half is equal to the ratio of the long half to the whole. Aphrodite of Cnidos by Prassitele From feet to head= 1,606 (in this photo) From feet to navel= 1 From feet to head= 1,618 http://goldenratio.wikidot.com/greek-and-roman-art
The width of height ratio of 9:4 governs the vertical and horizontal proportions of the temple as other relationships of the building, for example the spacing between the columns.
Greek Columns
Doric columns are the simplest. They have a capital (the top, or crown) made of a circle topped by a square. The shaft (the tall part of the column) is plain and has 20 sides.
Ionic shafts were taller than Doric ones. This makes the columns look slender. They also had flutes, which are lines carved into them from top to bottom.
Entasis is the application of a convex curve to a surface for aesthetic purposes. Its best-known use is in certain orders of Classical columns that curve slightly as their diameter is decreased from the bottom upwards. en·ta·sis ˈen(t)əsəs/ Noun ARCHITECTURE a slight convex curve in the shaft of a column, introduced to correct the visual illusion of concavity produced by a straight shaft.http://www.cmhpf.org/kids/dictionary/classicalorders.html
References: http://www.cmhpf.org/kids/dictionary/classicalorders.html http://www.diffen.com/difference/Image:Pantheon-dome.jpg https://www.youtube.com/watch?t=264&v=9wO0VglnxK4 http://goldenratio.wikidot.com/greek-and-roman-art Musser, G. L., Burger, W. F., & Peterson, B. E. (2005). Mathematics for Elementary Teachers: A Contemporary Approach United States: John Wiley & Sons.

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Greek & Roman art and Mathematics

  • 1. GREEK & ROMAN ART AND MATHEMATICS MATH 213 /SPRING 2015 RUTH ANN DAPKUS http://goldenratio.wikidot.com/greek-and-roman-art
  • 2. The Pantheon and the Parthenon are both ancient temples. While the Pantheon was built in Rome to celebrate all the Roman gods, the Parthenon was built in Ancient Greece for the goddess Athena. The Parthenon pre-dates the Pantheon by about six centuries; it was built around 447-438 BCE, while the Pantheon was built in 126 CE. http://www.diffen.com/difference/Pantheon_vs_Parthenon
  • 3. Pantheon Parthenon Location Rome, Italy Athenian Acropolis, Greece Built in 126 AD 447-438 BC Original purpose Temple to all the gods of Ancient Rome Temple to goddess Athena Built by Publius Aelius Hadrianus Iktinos, Kalikrates Current use Roman Catholic church Museum Architectural system Arch Technology Post and Lintel System http://www.diffen.com/difference/Image:Pantheon-dome.jpg
  • 4. THE GOLDEN RATIO A Mathematics Inspiration ~ Probably more than any other
  • 5. • History • The Pantheon was originally built by Marcus Agrippa in 27 BC, and the inscription on the front reads “M Agrippa L F Cos Terium Fecit,” or “Marcus Agrippa built this when he was consul for the third time.” However, the entire Pantheon was destroyed except for this façade, and the Emperor Hadrian rebuilt it on the same site in 126 AD. The building was given to Pope Poniface IV in 609 AD and was converted to a Christian church, saving it from destruction or looting. It was used as a tomb in the Renaissance and is the location of some royal tombs. https://www.google.com/search?q=pantheon+pictures&es_sm=122&tbm=isch&imgil=EvxtqUOMkQKs2M %253A%253BXvzsk- yUNFhroM%253Bhttp%25253A%25252F%25252Fen.parismuseumpass.com%25252Fmusee-pantheon- 38.htm&source=iu&pf=m&fir=EvxtqUOMkQKs2M%253A%252CXvzsk- yUNFhroM%252C_&usg=__M95mrimaC_SIhZVgdzu- QesDyKU%3D&biw=1600&bih=731&ved=0CDIQyjdqFQoTCPaw3sX1hsYCFUeaiAodoCcAdQ&ei=6h15VfaTD 8e0ogSgz4CoBw#imgrc=EvxtqUOMkQKs2M%253A%3BXvzsk- yUNFhroM%3Bhttp%253A%252F%252Fwww.parismuseumpass.com%252Fdatas%252Fmusees%252Fp%2 52Fa%252Fpanthon%252Fxl%252Fpantheon- 50c07d2be57f8.jpg%3Bhttp%253A%252F%252Fen.parismuseumpass.com%252Fmusee-pantheon-
  • 7. The Parthenon was built between 447 and 438 BC by Iktinos and Kallikrates as a temple to Athens’ patron goddess, Athena. https://www.youtube.com/watch?t=264&v=9wO0VglnxK4 Greek Classic the Parthenon
  • 8. • The Parthenon has been subscribed in the golden rectangle, because it gives a pleasant vision to whom looks at it, it is a sort of divine ownership. • The golden ratio is a characteristic that you can find in a lot of circles (from the zoology, to the botany, to the art…)
  • 9. THE PARTHENON CAN BE INSERTED IN A GOLDEN RECTANGLE BECAUSE THE RELATIONSHIP BETWEEN ITS BASE AND THE HEIGHT IS 1,618: THE GOLDEN NUMBER. THIS RELATIONSHIP IS ALSO VISIBLE IN OTHER ELEMENTS AND DECORATIONS OF THE PEDIMENT.
  • 10.
  • 11. *If from it we remove a square of side of it equal to the height, the remaining part it is still a golden rectangle. http://goldenratio.wikidot.com/greek-and-roman-art
  • 12. SCULPTURE In some Greek sculptures the navel (belly button) represents the mean of the golden ratio: The navel is positioned such that the ratio of the short half to the long half is equal to the ratio of the long half to the whole. Aphrodite of Cnidos by Prassitele From feet to head= 1,606 (in this photo) From feet to navel= 1 From feet to head= 1,618 http://goldenratio.wikidot.com/greek-and-roman-art
  • 13.
  • 14.
  • 15. The width of height ratio of 9:4 governs the vertical and horizontal proportions of the temple as other relationships of the building, for example the spacing between the columns.
  • 17. Doric columns are the simplest. They have a capital (the top, or crown) made of a circle topped by a square. The shaft (the tall part of the column) is plain and has 20 sides.
  • 18. Ionic shafts were taller than Doric ones. This makes the columns look slender. They also had flutes, which are lines carved into them from top to bottom.
  • 19. Entasis is the application of a convex curve to a surface for aesthetic purposes. Its best-known use is in certain orders of Classical columns that curve slightly as their diameter is decreased from the bottom upwards. en·ta·sis ˈen(t)əsəs/ Noun ARCHITECTURE a slight convex curve in the shaft of a column, introduced to correct the visual illusion of concavity produced by a straight shaft.http://www.cmhpf.org/kids/dictionary/classicalorders.html