Proof in Geometry: With "Mistakes in Geometric Proofs"
This single-volume compilation of two books explores the construction of geometric proofs. In addition to offering useful criteria for determining correctness, it presents examples of faulty proofs that illustrate common errors. High-school geometry is the sole prerequisite.
Proof in Geometry, the first in this two-part compilation, discusses the construction of geometric proofs and presents criteria useful for determining whether a proof is logically correct and whether it actually constitutes proof. It features sample invalid proofs, in which the errors are explained and corrected.
Mistakes in Geometric Proofs, the second book in this compilation, consists chiefly of examples of faulty proofs. Some illustrate mistakes in reasoning students might be likely to make, and others are classic sophisms. Chapters 1 and 3 present the faulty proofs, and chapters 2 and 4 offer comprehensive analyses of the errors.
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Proof in Geometry: With Mistakes in Geometric Proofs
A. I. Fetisov,Ya. S. Dubnov
Limited preview - 2006
AABC altitude assertion axiom of Archimedes Chapter circle rolls circumscribed coincide common measure conclusion congruence of triangles congruent constructed corresponding curved cycloid cylinder deduction diagonals diagram distance drawing equal angles equal to 180 equation example exists exterior fact ﬁnd ﬁrst follows geometry given half-line hence hypotenuse indirect proof inscribed inscribed angles interior angles interior points invalid proof isosceles triangle lateral surface length lies limit line segment means ment method mid-point mistake nested intervals obtain odd number opposite sides pairs parallel postulate perpendicular bisector plane point of intersection polygon polyhedral surface position possible preceding prism Proclus properties proposition Pythagorean theorem radius reader reasoning rectangle regular polygon right angles right triangles rolling circle sequence sides are equal sophism square straight line system of axioms theorem tion trapezoid triangle ABC triangle is equal vertex vertices