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Harkness, Shelly Sheats; Noblitt, Bethany – Contemporary Issues in Technology and Teacher Education (CITE Journal), 2018
A student, Stuart, related perimeter to pixels and the professor, Beth, moved back and forth between "reserved believing" and "reserved doubting" and "doubting" teacher actions (Elbow, 1986; Harkness & Noblitt, 2017) while assessing the merit of his conjecture in the moment. Video allowed the researchers to…
Descriptors: Preservice Teachers, Mathematics Instruction, College Mathematics, Mathematics Teachers
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Frederickson, Greg N. – College Mathematics Journal, 2012
How many rods does it take to brace a square in the plane? Once Martin Gardner's network of readers got their hands on it, it turned out to be fewer than Raphael Robinson, who originally posed the problem, thought. And who could have predicted the stunning solutions found subsequently for various generalizations of the problem?
Descriptors: Geometric Concepts, Plane Geometry, Problem Solving, Generalization
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McCartin, Brian J. – PRIMUS, 2008
This note presents geometric and physical interpretations of the sufficient condition for a critical point to be a strict relative extremum: f[subscript xx]f[subscript yy] - f[superscript 2][subscript xy] greater than 0. The role of the double derivative f[subscript xy] in this inequality will be highlighted in these interpretations. (Contains 14…
Descriptors: Mathematics Instruction, Mathematical Formulas, Geometric Concepts, Mathematical Concepts
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Klee, Victor – Two-Year College Mathematics Journal, 1971
This article presents some easily stated but unsolved geometric problems. The three sections are entitled: Housemoving, Manholes and Fermi Surfaces" (convex figures of constant width), Angels, Pollen Grains and Misanthropes" (packing problems), and The Four-Color Conjecture and Organic Chemistry." (MM)
Descriptors: College Mathematics, Geometric Concepts, Mathematics, Networks
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Patterson, E. M. – Mathematical Spectrum, 1971
The basic ideas of the theory of manifolds is illustrated using elementary geometry. (MM)
Descriptors: College Mathematics, Geometric Concepts, Mathematical Models, Mathematics
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Rogers, Pat – Mathematical Spectrum, 1972
Criteria for a reasonable axiomatic system are discussed. A discussion of the historical attempts to prove the independence of Euclids parallel postulate introduces non-Euclidean geometries. Poincare's model for a non-Euclidean geometry is defined and analyzed. (LS)
Descriptors: College Mathematics, Geometric Concepts, Mathematical Concepts, Mathematical Logic
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Sipser, Kenneth – Mathematics and Computer Education, 1983
Almost-Regular Polygons (ARPs) are viewed as interesting, but hardly ever noticed. The growing availability of computers means that such figures can be examined. A program written in BASIC which was developed to generate and test large blocks of cases is presented and described. (MP)
Descriptors: College Mathematics, Computer Programs, Geometric Concepts, Geometric Constructions
Yates, Robert C. – 1974
This volume, a reprinting of a classic first published in 1952, presents detailed discussions of 26 curves or families of curves, and 17 analytic systems of curves. For each curve the author provides a historical note, a sketch or sketches, a description of the curve, a discussion of pertinent facts, and a bibliography. Depending upon the curve,…
Descriptors: Analytic Geometry, College Mathematics, Geometric Concepts, Geometry
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Love, William P. – Mathematics Teacher, 1989
The theorems and proofs presented are designed to enhance student understanding of the theory of infinity as developed by Cantor and others. Three transfinite numbers are defined to express the cardinality of infinite algebraic sets, infinite sets of geometric points and infinite sets of functions. (DC)
Descriptors: Abstract Reasoning, Algebra, College Mathematics, Geometric Concepts