Mathematics Teacher

Geometry Bibliography: Transformational Geometry

Hubert Ludwig, Ball State University

 ```Geometry, Iteration, and Finance A. Landy Godbold, Jr. Relation of calculation of balances to transformations on the number line. (889, 1996) 646 - 651 Guidelines for Teaching Plane Isometries In Secondary School Adela Jaime and Angel Gutiérrez Connecting Research to Teaching. Isometries as a link for different branches of mathematics or for mathematics and other sciences. (88, 1995) 591 - 597 Geometric Transformations - Part 1 Susan K. Eddins, Evelyn O. Maxwell, and Floramma Stanislaus Activities. Opportunities to become familiar with translations, rotations, and reflections. (87, 1994) 177 - 181, 187 - 189 Geometric Transformations - Part 2 Susan K. Eddins, Evelyn O. Maxwell, and Floramma Stanislaus Activities. Coordinate approaches to transformations utilizing matrices. (87, 1994) 258 - 261, 268 - 270 Reflections on Miniature Golf Nancy N. Powell, Mark Anderson, and Stanley Winterroth A transformational geometry project involving the designing of holes for miniature golf courses. (87, 1994) 490 - 495 Integrating Transformation Geometry into Traditional High School Geometry Steve Okolica and Georgette Macrina Moving transformation geometry ahead of deductive geometry. (85, 1992) 716 - 719 Line and Rotational Symmetry Nancy Whitman Activities for introducing the concepts of line and rotational symmetry. Includes some investigations of quilt patterns. (84, 1991) 296 - 302 An Application of Affine Geometry Thomas W. Shilgalis A discussion of affine properties and the use of affine concepts in obtaining geometric results. (82, 1989) 28 - 32 Which Method Is Best? Edward J. Barbeau Synthetic, transformational, analytic, vector, and complex number proofs that an angle inscribed in a semicircle is a right angle. (81, 1988) 87 - 90 Elementary Affine Transformation Models James B. Barksdale, Jr. An analytic approach to some algebraic problems. (81, 1988) 127 - 130 Reflection Patterns for Patchwork Quilts Duane DeTemple Forming patchwork quilt patterns by reflecting a single square back and forth between inner and outer rectangles. Investigating the periodic patterns formed. BASIC program included. 79, (1986) 138 - 143. 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 The Bank Shot Dan Byrne Geometry of similar triangles and reflections applied to pool. 79, (1986) 429 - 430, 487. Where Is the Ball Going? Jack A. Ott and Anthony Contento Examination of ball paths on a pool table. BASIC routine included. 79, (1986) 456 - 460. Reflections on Miniature Golf Beverly A. May Using reflections to determine bank shots. 78, (1985) 351 - 353. A Piagetian Approach to Transformation Geometry via Microworlds Patrick W. Thompson The use of a computerized microworld called Motions to allow students to work with transformation geometry. 78, (1985) 465 - 471. Transformation Geometry: An Application of Physics Ken A. Dunn An analytic approach to transformations in the Euclidean plane and in the Minkowski plane. 77, (1984) 129 - 134. General Equations for a Reflection in a Line J. Taylor Hollist An analytic development. 77, (1984) 352 - 353. Visual Thinking with Translations, Half-Turns, and Dilations Tom Brieske Visual imagery applied to composition of functions. 77, (1984) 466 - 469. Geometric Transformations On A Microcomputer Thomas W. Shilgalis Microcomputer programs to demonstrate motions and similarities. 75, (1982) 16 - 19. Pythagorean Theorem and Transformational Geometry Medhat H. Rahim A proof utilizing translations and rotations. 72, (1979) 512 - 515. Geometric Transformations and Music Composition Thomas O'Shea Relations between musical procedures (transposition, inversion, etc.) and transformations of the plane. 72, (1979) 523 - 528. Line Reflections In The Plane, - A Billiard Player's Delight Gary L. Musser Applications, complex numbers, reflections and aiming a cue ball. 71, (1978) 60 - 64. A Strip Of Wallpaper Joseph A. Troccolo Symmetries and transformations involving wallpaper patterns. 70, (1977) 55 - 58. Mathematical Reflections and Reflections On Other Isometries Thomas D. Bishop and Judy K. Fetters Transformation geometry activities using mirrors. 69, (1976) 404 - 407. Exploring Skewsquares Alton T. Olson A transformational consideration of properties of quadrilaterals having congruent, mutually perpendicular diagonals. 69, (1976) 570 - 573. Transformation Geometry and The Artwork Of M.C. Escher Sheila Haak Analyzing the symmetries and transformations in Escher's drawings. Techniques for producing such drawings. 69, (1976) 647 - 652. Real Transformations From Complex Numbers Robert D. Alexander Complex numbers and transformation geometry. 69, (1976) 700 - 709. Application Of Groups and Isomorphic Groups To Topics In The Standard Curriculum, Grades 9 - 11 Zalman Usiskin Relations of some groups and geometry. Part I. 68, (1975) 99 - 106. Part II. 68, (1975) 235 - 246. A Finite Field As A Facilitator In Algebra and Geometry Classes Marc Swadener Some uses of a finite field to exemplify geometric concepts. 68, (1975) 271 - 275. Elementary Linear Algebra and Geometry via Linear Equations Thomas J. Brieski Relations of the set of solutions of a homogeneous linear equation, the coordinate plane and the set of translations of the plane. 68, (1975) 378 - 383. Applications Of Transformations To Topics In Elementary Geometry, Stanley B. Jackson Introduces some simple transformations which are intuitively appealing and explores ways in which they can be used to work with geometric concepts. Part I. Half-turns and reflections. 69, (1975) 554 - 562. Part II. Homothety and rotation. 69, (1975) 630 - 635. Do Similar Figures Always Have The Same Shape Paul G. Kumpel, Jr. Transformational geometry applied to conics with a hint about cubics. 68, (1975) 626 - 628. The Logarithmic Spiral Eli Maor Analytic geometry of the spiral, some work with transformations. 67, (1974) 321 - 327. Transformations In High School Geometry Before 1970 Z. Usiskin A discussion of early appearances of transformational approaches in secondary texts. 67, (1974) 353 - 360. A Key Theorem In Transformational Geometry Daniel Pedoe Product of rotations. 67, (1974) 716 - 718. Fixed Point Theorems In Euclidean Geometry Stanley R. Clemens Theorems about dilations and their applications to the theorems of Menelaus, Ceva and Desargues. 66, (1973) 324 - 330. Recreation: Hexiamonds Raymond E. Spaulding Developing the concepts of symmetry and rigid motion. 66, (1973) 709 - 711. A Transformation Approach To Tenth-Grade Geometry Z.P. Usiskin and A.F. Coxford Uses of reflections, symmetry, congruence and similarity. 65, (1972) 21 - 29. A Theorem On Lines Of Symmetry Thomas W. Shilgalis If a figure has exactly two lines of symmetry, must they be perpendicular? 65, (1972) 69 - 72. Transformations In High School Geometry Frank M. Eccles Some suggestions for introducing geometry through the use of transformations. 65, (1972) 103, 165 - 169. A Transformation Proof Of The Collinearity Of The Circumcenter, Orthocenter and Centroid Of A Triangle Thomas W. Shilgalis Using a dilation and a half-turn. 65, (1972) 635 - 636. The High-School Geometry Controversy: Is Transformation Geometry The Answer? Richard H. Gart Discusses several proposals which favor the inclusion of transformational geometry and answers them. 64, (1971) 37 - 40. The Use Of Elastic For Illustrating Homothetic Figures Alexander Arcache A model for demonstrating homotheties. 61, (1968) 54. Rotations, Angles and Trigonometry Robert Troyer Transformation geometry, vectors, and trigonometry. 61, (1968) 123 - 129. Congruence Geometry For Junior High School J. Sanders and J. Richard Dennis Development of transformations and some applications to theory. 61, (1968) 354 - 369. On Similarity Transformations James Hardesty Images and curvature. 61, (1968) 278 - 283. Reflections and Rotations Burton W, Jones Any plane motion is the product of at most three reflections. 54, (1961) 406 - 410. The Geometry Of Space and Time Edward Teller Some discussion of invariants. 54, (1961) 505 - 514. Illustrating Simple Transformations William Koenen A device for demonstrating rotations. 49, (1956) 467 - 468. H.J.L. 07/15/97 email: 00hjludwig@bsu.edu home page: http://www.cs.bsu.edu/~hjludwig/ ```