Ten Lessons in Greek and Arabic Geometry

See Euclid's Elements of Geometry by Richard Fitzpatrick and this talk explaining how محمد بن موسى الخوارزمي solved quadratic equations in the work الجبر. There are six binomial straight-lines in Euclid's Book X and there are six different ways to write a quadratic equation without using zero or negative numbers.

Here's the talk:

At 21:56 note that there are neither zero nor -1 in the group, and that the identity element 1 is generated by the group presentation. See the lazy natural numbers of Girard, Lafont and Taylor in Numberphile - Sophie Maclean on the Catalan Numbers.

See also Charles Gunn and Steven De Keninck - Siggraph2019 Geometric Algebra.

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It's apocalyptic. See Lewis Carroll - Crocodile Story and Another Introduction to Geometric Algebra.

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