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Geometric constructions have been a popular part of mathematics throughout history. The ancient Greeks made the subject an art, which was enriched by the medieval Arabs but which required the algebra of the Renaissance for a thorough understanding. Through coordinate geometry, various geometric construction tools can be associated with various fields of real numbers. This book is about these associations. As specified by Plato, the game is played with a ruler and compass. The first chapter is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never seen. The second chapter formalizes Plato's game and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, using only a compass, using toothpicks, using a ruler and dividers, using a marked rule, using a tomahawk, and ending with a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics. He hopes that readers will learn a little geometry and a little algebra while enjoying the effort. This is as much an algebra book as it is a geometry book. Since all the algebra and all the geometry that are needed is developed within the text, very little mathematical background is required to read this book. This text has been class tested for several semesters with a master's level class for secondary teachers.

514.115 --- Geometrical constructions --- Constructions, Geometric --- Constructions, Geometrical --- Geometric constructions --- Geometry --- Theory of geometric constructions --- Geometrical constructions. --- 514.115 Theory of geometric constructions --- Geometry. --- Mathematics --- Euclid's Elements

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Chinese language --- Nominals --- Subordinate constructions

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Swedish language --- -Ruotsi language --- Svenska language --- Scandinavian languages --- Existential constructions --- Existential constructions. --- -Existential constructions --- Ruotsi language

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Time and Modality is a unique work of reference; not only does it unite studies which explore the syntax and semantics of tense or modality but it is the first book of its kind to embrace the interaction of tense and modality within a coherent generative model. Various topics are covered in this volume: among them are the counterfactual uses of conditionals, modals, and past tense; the irrealis use of perfective aspect; a special English subjunctive; the interaction of tense assignment and the definition of an event; the modal verb as a causative verb; the interaction of modality, tense, and aktionsart; the contrast between deontic and epistemic modal with respect to tense interpretation; the syntax of epistemic modals; the long-awaited definition of generic and habitual sentence; and the introduction of intensionality in copular clauses. Although every article deals with English to some degree, two chapters compare the syntax and semantics of tense and modality in Spanish vs English. The authors also investigate Slavic, Germanic, Afro-Asiatic, Oriental, Amerindian Languages and Hungarian.

Grammar, Comparative and general --- Tense. --- Temporal constructions. --- Temporal constructions (Grammar) --- Tense (Grammar) --- Syntax --- Temporal constructions --- Modality --- Linguistics --- Philology

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Romanian language --- Dialectology --- Subordinate constructions --- Daco-Romanian dialect --- Romance languages --- Dialectology. --- Subordinate constructions. --- Romanian language - Dialectology --- Romanian language - Subordinate constructions