Who was Euclid?
After the R/G bifurcation (arithmetic/geometric) around 500 BC, arithmetic, geometry, and geometric algebra were rapidly developed by the Pythagoreans. This rapid development culminated in the Academy of Plato around 350 BC, and the results were collected in logical sequence in texts called stocheia (elements) by various editors. Euclid was one of these, and his text was so successful that it became the 2nd most published book af all time, after the Bible, and the most influential math text of all time, until very recently. As the elements were abandoned and replaced by inferior works, the math crisis and MA (math anxiety) rapidly grew.
What are the EE?
The Elements of Euclid develop in 13 books containing 645 propositions:
Of these 645 propositions, 60 are constructions, the others are used to prove that the constructions work reliably. The catasQI (constructions) may be regarded as the skeleton, the goal, and most ancient part, of the elements, aka sacred geometry, also as ancient geometry, fundamental to the classical cultural ecology in the sense of William Irwin Thompson, and embedded in stone by the master architects and builders of ancient times. The 48 fundamental constructions of plane geometry comprise the heart of the classical math curriculum.
- plane geometry of triangles,
- plane geometry of circles,
- regular polygons in or around a circle,
- proportions (ratios),
- number theory, and
- solid geometry, esp, of the regular solids.
Why has the EE been so successful?
In editing the elements, Euclid was meticulously faithful to the Sheldrake principle, the preservation of historical order. This is the reason that constructions of the golden section appear twice:
as Heath notes in his commentary.
- in book 4, according to the pythags, and
- in book 6, after the theory of proportions,
Why were the EE abandonded?
After the enlightment, ca 1800, the logic of aristotle was blown up into a new paradigm for mathematics, called formalism. The months were renamed (eg, July became Brumaire in French) to avoid the taint of history, and math was reorganised according to logical, as opposed to historical, order. The Elements of Euclid followed the traditional names of the months into the trash bin, and there began a disease of current cultural ecology, of which the math avoidance syndrome and MA are but some of the symptoms.
Why should we return to the EE?
The restoration of Euclid as a basic math text for the middle and high schools would be a giant step toward th elimination of the math disease of our time. It is not the only step required, we would also need to retrain teachers to understand it, and to use the dynapic technique to teach it, as classical teachers used to do.
How could we return to the EE?
The revision of the school math program could be done by:
- creating adequate new texts for a new program, such as new, multimedia editions of Euclid
- retraining teachers understand and to follow the crucial sequence: geometry, geometric algebra, algebra,
- training teachers to use dynapics, and
- abandoning standard tests which misrepresent math.