More Bolts with Nuts
By Ralph Abraham
Revised Friday, 13 August 1999
Extended Saturday, 08 August 2010

Here we add some units to 1999b, titles only (N in number) and delete others

Contents

Grade 3: 2,000,000 to 10,000 BCE.Ê(R mentality only)
3.N1. Counting stones, boards, and the abacus (video tutorials)
	this is a thread re subitizing, runs through all grades
3.N2. Notched bones

Grade 4: 10,000 to 3500 BCE. (R mentality only)
4.N1. Frieze patterns of Catal Huyuk
	this is a thread re patterns, runs through all grades

Grade 5: 3500BCE to 1450 BCE. (R and G mentalities)
5.N1. Number symbols, tokens of Mesopotamia (R, Schmandt book)
5.1. The carved balls of Scotland (G, in Bolts book)
5.3. The monochord and the scales of Sumer, musical arithmetic
	this is a thread, all grades (R)
5.4. The rope-stretchers of Egypt and the orientation of temples
5.5. The squareness of the pyramids

Grade 6: 1450 BCE to 350BCE.
6.N1. Canon of Lespugue (and Greek modes, MS#82)
6.N2. Constructions of Euclid (website)
6.N3. Pythagoras and the monochord (R)
6.3. From Pythagoras to Euclid: the root of 2 (R, G)
6.5. Dimensions of the Temple of Solomon (R, G in archives)
6.7. Arithmetic in Phoenician notation (R)

Grade 7: 350 BCE to 800 CE.
7.1. The machines of Archimedes, Heron, and Ctesibius
7.2. Hypatia and the conics of Apollonius
7.3. Tables of chords and astronomy in India (R, G)
7.4. The swath of trig from Ptolemy to Baghdad
7.5. The logic of Aristotle's Isagoge
7.6. Astronomical alignments in Teotihuacan
7.7. The heliacal rising of Venus and the Mayan calendar (R)
7.8. Neoplatonism and Euclid in the Platonic Academy of Byzantium
7.9. Early translations of Euclid in Baghdad, shades of Babylon

Grade 8: 800 CE to 1453 CE. (R. G, and A mentalities)
8.1. The Indian numerals 
8.2. The constructions of Euclid 
8.3. Sacred calligraphy and the birth of Al-jabr
8.4. The 3-sphere in Dante's Divine Comedy
8.5. Algebra of Ibn Tusi
8.6. African divination
8.7. Proportions of Gothic cathedrals, ancient geometry
8.8. Geometry of Giotto
8.9. The Hermetic Corpus in Ficino's academy, astrology and optics

Grade 9: 1453 to 1688.
9.1. Perspectiva from Giotto to Cosimo
9.2. Conics from Apollonius to Durer
9.3. Galileo and the pendulum clock
9.4. Vincenzo and equal temperament, the 12-th root of 2
9.5. Marin Mersenne and musical arithmetic
9.6. Copernicus, Kepler, Newton: will Halley's comet destroy us?
9.7. Cartography, Mercator, etc
9.8. John Dee, Euclid, Shakespeare, the Sidney circle, the Royal Society
9.9. Double entry bookeeping, John Recorde, logarithms
9.10. Cartesian coordinates and the notations of algebra
9.12. Kepler's Mysterium Cosmographicum and the Platonic solids
9.13. Leibniz, historiography, binary arithmetic, the philosophers' war

Grade 10: 1688 to 1851.
10.1. The glass harmonium, Ben Franklin, Mozart, Chladni, Sophie Germain
10.2. The heat equation, Fourier, Sophie Germain
10.3. The wave equation, the hanging chain, more musical arithmetic
10.4. Euclid's fifth postulate, measuring the three angles
10.5. The shape of the earth
10.6. Algebra in India

Grade 11: 1851 to 1945.
11.1. Cantor, his numbers, his fractals
11.2. Hilbert's program, Godel's discovery
11.3. More noneuclidean geometry and logic
11.4. Poincare's Oscar, the rebirth of chaos, Sofia Kovaleskaya
11.5. Fractals of Julia, paintings of Kupka
11.6. The foundations of calculus, Dedekind and the real numbers
11.7. Flatland, differential geometry of curves and surfaces
11.8. German vs French math styles, Hilbert's program, Godel
11.9. Carnap and the Vienna Circle
11.10. Cantor, infinity, the first fractal
11.11. Hertz, radio waves, the field concept, vectors, Maxwell equations
11,12. Hamilton, quaternions, Minkowski, Poincare, Einstein, the ether
11.13. Vibrating strings and quantum mechanics, particles vs waves
11.14. Lewis Frye Richardson, the birth of politicometrics, Gregory Bateson
11.15. Ludwik Fleck, paradigm shifts
11.16. Von Neuman, game theory, the atomic bomb

Grade 12: 1945 to 2010.


END