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A quiz concerning algebraic geometry is presented.

The article provides information on the inequalities of lattice polygons in relation to Scott's inequality and the equation 2i + 7. It states that algebraic geometry is used to study lattice equivalent polygons, since toric geometry is a powerful link that connects discrete and algebraic geometry. Moreover, the proposition b ⩽ 2i + 7 is proven using Pick's Theorem with three equivalent inequalities. Furthermore, Scott's proof indicates that (x,y) = (3,3) is the only point where both upper bounds reach zero and the only case where equality can hold in Onion-Skin Theorem.

This article presents a study regarding multivariate calculus, focusing on saddle points and inflection points. It discusses the similarities between saddle points on surfaces and inflection points on curves. It explores the direct connection between saddle points on surfaces and inflection points on curves. It presents the theorem which provides a simple constructive method to obtain continuous functions to connect the saddle points of functions of two variables with the inflection points of functions of one variable.

The article discusses the mathematical principles and applications concerning the families of plane algebraic curves that contain a special set of points. The case of curves in cages is associated with the elementary methods that presume the familiarity with algebraic geometry and geometrical applications. These applications can be considered as natural generalizations of classical theorems in projective geometry and are associated with familiarity with Pascal's theorem and its comparison with the classical Pascal diagram.

Discusses various mathematical analysis. Concept of the superposition problem presented by Hilbert; Feasibility of representing any function on a tree in Euclidean space; Evaluations of topological complexity in real algebraic geometry.

The article traces the contributions of Pierre Hérigone in making mathematics algebraic rather than geometric. It discusses the algebraic concepts and notation of Hérigone which can be found in his volume on algebra. It introduces his universal symbolic language applicable to all branches of mathematics. It presents his algebraic procedures and subsections on identities, equations, geometric constructions and ambiguous equations. His influence on later mathematicians including Isaac Barrow and Gottfried Wilhelm von Leibniz is also discussed.

The article reviews several articles, including "The Hidden Math behind Alice in Wonderland," by Keith Devlin in the March 2010 issue of MAA Online, "Alice's Secrets in Wonderland," by Melanie Bayley in the December 2009 issue of "New Scientist," and "Algebra in Wonderland," by Melanie Bayley in the March 7, 2010 issue of "New York Times."