GRADE EIGHT: the required elements

Theory: Medieval Civilizations were hierarchical societies that derived their identity from belief in a universal religion, but based their social structures on land tenure and warrior status and display. As competition and conflict arise among religious civilizations, new ideas are disseminated across boundaries and new religious orders and mystical movements arise that seek to relate the individual in an unmediated way to the source of the sacred. This shift from the temple-formed Geometrical Mentality to the individually experienced Algebraic Mentality is expressed in new forms of literature that reveal an emphasis on the vision-quest and personal romantic love, but it is also expressed in new forms of calligraphy, manuscript illumination, and mathematical understanding that show a shift from the concrete object or worldly state to a spiritual vision of a transcendental ideal expressed in the celestial notation of the empowering script of alchemy and algebra.

Practice: Through an emphasis on art and architecture, we will look at medieval civilizations all around the world.

Integrated Studies Projects (choose one):

• Sacred Architecture: a comparison of the cathedral and the mosque.
• Crusader Songs: Music and Arabic-Sephardic-Christian cultural exchange in song, dance, and musical instruments.

Math Units:

• Topics:
  • Euclid, Book II, selected proofs
  • algebra
• History:
  • Islamic-Christian mathematical and scientific cultural exchange (incl Leo, Fibonacci)
• Suggested Integrative Projects (one required):
  • The geometric algebra constructions of Euclid
  • Sacred calligraphy and the birth of Al-jabr
  • The 3-sphere in Dante's Divine Comedy
  • The algebra of Ibn Tusi
  • African divination
  • Proportions of Gothic cathedrals, ancient geometry
  • The geometry of Giotto
  • The Hermetic Corpus, astrology, and optics