### Mathematics Teacher

#### Geometry Bibliography: Inequalities and Optimization

Hubert Ludwig, Ball State University

 ```Network Neighbors William F. Finzer An experiment in network collaboration using The Geometer's Sketchpad. (88, 1995) 475 - 477 An Isoperimetric Problem Revisited Scott J. Beslin and Laurette L. Simmons Finding a simple closed curve with fixed perimeter which bounds a maximum area. (86, 1993) 207 - 210 Area and Perimeter Connections Jane B. Kennedy Activities for investigating maximum area rectangles with fixed perimeter. (86, 1993) 218 - 221, 231 - 232 The Bug on the Box William Wallace Looking for a shortest path. (85, 1992) 474 - 475 Largest Quadrilaterals J. N. Boyd and P. N. Raychowdhury Given three fixed segments how should a fourth segment be chosen so as to produce a quadrilateral of maximum area? (85, 1992) 750 - 751 Dissecting a Circle by Chords Through n Points A. V. Boyd and M. J. Glencross Finding the maximum number of regions into which a circular region can be divided by chords. (84, 1991) 318 - 319 Make Your Own Problems - and Then Solve Them Robert L. Kimball Activities for solving a maximum problem. (84, 1991) 647 - 655 Geometrical Inequalities via Bisectors Larry Hoehn Alternatives to the usual proofs of inequalities in triangles. (82, 1989) 96 - 99 A Constructive Proof of a Common Inequality Richard C. Ritter Sharing Teaching Ideas. The arithmetic mean - geometric mean inequality. (82, 1989) 531 - 532 A Geometric Solution to a Problem of Minimization Li Changming Rowing and walking to get from a boat to a lighthouse. (81, 1988) 61 - 64 Solving Extreme-Value Problems without Calculus David I. Spanagel and Gerald Wildenberg Some of the examples utilize geometric techniques. (81, 1988) 574 - 576 The Shortest Route J. Andrew Archer Finding the shortest possible route when mowing a rectangular lawn. 80, (1987) 88 - 93, 142. A Matter of Disks William E. Ewbank In what manner should disks be cut from a piece of posterboard in order to minimize wastage? 79, (1986) 96 - 97, 146. Reflective Paths to Minimum-Distance Solutions Joan H. Shyers The uses of reflections in order to find paths of minimum length. 79, (1986) 174 - 177, 203 Problem-solving Techniques with Microcomputers William E. Haigh Finding the dimensions for a rectangle which will yield a sub-rectangle having maximum area. BASIC program included. 79, (1986) 598 - 601, 655 The Spider and the Fly: A Geometric Encounter in Three Dimensions Rick N. Blake Eight problems involving a minimum path. 78, (1985) 98 - 104. A Geometric View of the Geometric Series Steven R. Lay A "sharing teaching idea." Diagrams to illustrate the convergence of the geometric series. 78, (1985) 434 - 435. Geometry For Pie Lovers William Fisher Finding a line through a given point O of a convex region which produces a subregion of maximum area. 75, (1982) 416 - 419. Spherical Geodesics William D. Jamski Find the shortest distance between two points on a globe. 74, (1981) 227 - 228, 236. The Isoperimetric Theorem Ann E. Watkins Activities to aid in the discovery of the fact that for a given perimeter the circle encloses the greatest area. 72, (1979) 118 - 122. An Optimization Problem and Model Deane Arganbright A minimum path problem and a device for exhibiting it. 71, (1978) 769 - 773. Minimal Surfaces Rediscovered Sister Rita M. Ehrmann Soap bubble experiments for Plateau's problem (find the surface of smallest area having a given boundary), soap film experiments for Steiner's problem (minimal linear linkage of points in a plane.) 69, (1976) 146 - 152. Experiments Leading To Figures Of Maximum Area J. Paul Moulton Thirteen results concerning polygons having maximum area under given conditions. 68, (1975) 356 - 363. Maximum Rectangle Inscribed In A Triangle M. T. Bird A characterization. 64, (1971) 759 - 760. Exploring Geometric Maxima and Minima J. Garfunkel Paths, areas, perimeters, chords. 62, (1970) 85 - 90. Maxima and Minima By Elementary Methods Amer Nannina Geometric solutions. 60, (1967) 31 - 32. On Some Geometric Inequalities Murray S. Klamkin Geometric maximum and minimum problems. 60, (1967) 323 - 328. Using Geometry To Prove Algebraic Inequalities J. Garfunkel and B. Plotkin Synthetic and analytic techniques applied to ten problems. 59, (1966) 730 - 734. Geometric Intuition and SQR(ab) < (a + b)/2 E. M. Harais Using surfaces in 3-space. 57, (1964) 84 - 85. Going Somewhere? Oystein Ore Paths of minimum length. 53, (1960) 180 - 182. Out Of The Mouths Of Babes Paul C. Clifford Maximum and minimum problems solved geometrically. 47, (1954) 115. The "Attack" In Propositions On Inequality Of Lines Arthur Haas Teaching propositions on inequalities. 19, (1926) 228 - 234. H.J.L. 07/15/97 email: 00hjludwig@bsu.edu home page: http://www.cs.bsu.edu/~hjludwig/ ```