Euclid's Elements

Geometers and broader mathematicians

>>8505384
Axiomatic geometry is only needed for pure mathematicians. Everyone else will be fine with watered down analytic geometry.

>>8505384

People who study the history of math and science since everything pre-18th century is based heavily on it.

Is this book an adequate replacement for High School geometry? I heard there were some errors of logic in it.

>>8505418
>errors of logic
>in Elements

who the fuck do you think you are you hyperbolic little shit did you just try to imply that euclid was not literally perfect in every fucking way you stupid brainlet don't ever ever ever talk about euclid like that again get the fuck out of my board

>>8505418
>High School geometry?
Isn't high school geometry just coordinate garbage? Because there's none of that in The Elements.

>>8505423
https://en.m.wikipedia.org/wiki/Pasch's_axiom

>>8505423
When we studied Euclidean geometry for my first and second semester and pure math the professor was always pointing out how he did not agree with certain definitions and how he was not convinced by some proofs, sometimes telling us to "believe the book if you want" and sometimes going as far as to define the terms himself and prove theorems his own way.

So Euclid is not perfect but who am I to tell. I didn't read the book, I had an old guy read it to me.

>>8505427

High school geometry done right introduces the concept of a proof as an argument; a sequence of steps, with each step having a perfectly clear justification, terminating with what was to be demonstrated.

Other concepts include ways of causing plane figures to coincide/be shown to be congruent, being those used regularly by M.C. Escher in his plane-tiling art: translation, rotation, and mirroring/glide reflexion. Dilation can be added to this. Cases of triangle congruence can be taught as primitives, which are then used as the vaild justifications for proofs of triangle congruence, as a case of the above. The special situations of the 30-60-90 triagle and the right isosceles triangle anticipate trigonometry, which may be rolled into geometry itself depending on the locale.