algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety Pierre de Fermat; René Descartes; Leonhard Euler; affine space; barycenter; real affine space; Pasch's theorem; Euclidean space; metric space; Gram-Schmidt process; approximation by the law of least squares; Fourier approximation; Hermitian space; projective space; duality principle; Fano's theorem; projective quadric; Pascal's theorem; Brianchon's theorem; topology of projective real spaces; algebraic plane curves; Bezout's theorem; Hessian curve; Cramer's paradox; group of a cubic; rational algebraic plane curve; Taylor's formula for polynomials in one or more variables; Eisenstein's criterion; Euler's formula; fundamental theorem of algebra; Sylvester's theorem 