Hubert Ludwig, Ball State University

Back to Geometry Bibliography: Contents

Making Connections: Spatial Skills and Engineering Drawings Beverly G. Baartmans and Sheryl A. Sorby Orthographic drawings and isometric drawings. (889, 1996) 348 - 357 The Volume of a Sphere: A Chinese Derivation Frank J. Swetz A history of the development of the formula. (88, 1995) 142 - 145 Exploring Three- and Four-Dimensional Space Charlotte Williams Mack Activities. Building a model for a cube and representations of a hypercube. (88, 1995) 572 - 578, 587 - 590 Nested Platonic Solids: A Class Project in Solid Geometry Ronald B. Hopley Using solid models and nets. Calculating edge lengths. (87, 1994) 312 - 318 Practical Geometry Problems: The Case of the Ritzville Pyramids Donald Nowlin Volumes and surface areas of cones. (86, 1993) 198 - 200 The Method of Archimedes John del Grande Finding the volumes of various geometrical objects. (86, 1993) 240 - 243 The Excitement of Learning with Our Students -- an Escalator of Mathematical Knowledge Alan H. Hoffer Some of the discussion involves nets for the construction of polyhedra. (86, 1993) 315 - 319 The Volume of a Cone Boris Lavric Sharing Teaching Ideas. A method for demonstrating a development of the formula for the volume of a cone. (86, 1993) 384 - 385 Cube Challenge Judy Bippert Activities for promoting logical thinking skills in a spatial context. (86, 1993) 386 - 390, 395 - 398 Looking at Sum k and Sum k*k Geometrically Eric Hegblom Using squares and determining area, using cubes and determining volume. (86, 1993) 584 - 587 Illustrating Mathematical Connections: Two Proofs That Only Five Regular Polyhedra Exist Peter L. Glidden and Erin K. Fry A geometric proof and a graph-theoretic proof. (86, 1993) 657 - 661 Graphing a Solid: A Classroom Activity George Marino Sharing Teaching Ideas. Using three-dimensional coordinates and a distance formula to generate models of solids which students can build. (86, 1993) 734 - 737 Making Connections: Beyond the Surface Dan Brutlag and Carole Maples Dealing with scaling-surface area-volume relationships. (85, 1992) 230 - 235 Problem Solving with Cubes Christine A. Browning and Dwayne E. Channell Activities for developing spatial-reasoning skills. (85, 1992) 447 - 450, 458 - 460 Playing with Blocks: Visualizing Functions Miriam A. Leiva, Joan Ferrini-Mundy, and Loren P. Johnson Activities which could be used to develop spatial visualization. (85, 1992) 641 - 646, 652 - 654 A Fractal Excursion Dane R. Camp Area and perimeter results for the Koch curve and surface area and volume results for three-dimensional analogs. (84, 1991) 265 - 275 Calculating Surface Area Ray A. Krenek Sharing Teaching Ideas. Calculating the area of a rectangular solid and a cylinder. (84, 1991) 367 - 369 Estimating the Volumes of Solid Figures with Curved Surfaces Donald Cohen Gives examples of solid figures that students can use to develop estimating skills. (84, 1991) 392 - 395 The Circle and Sphere as Great Equalizers Steven Schwartzman Relations between parts of figures and inscribed figures. (84, 1991) 666 - 672 Some Discoveries with Right-Rectangular Prisms Robert E. Reys Activities for problem-solving experiences with area and volume. (82, 1989) 118 - 123 Interdimensional Relationships Joseph V. Roberti. A look at relationships suggested by the fact that the derivative of the area of a circle yields the circumference and the derivative of the volume of a sphere yields the surface area. (81, 1988) 96 - 100 Pyramids, Prisms, Antiprisms, and Deltahedra Donovan R. Lichtenberg A description of, and patterns for, some polyhedra which have faces that are regular polygons. (81, 1988) 261 - 265 Discovery With Cubes Robert E. Reys Activities for pattern investigation with cubes. (81, 1988) 377 - 381 Puzzles That Section Regular Solids William A. Miller Activities for developing a recognition of the surface formed when a solid is cut by a plane. (81, 1988) 463 - 468 Dodecagon of Fortune Dane R. Camp Sharing Teaching Ideas. A game for use during reviews. (81, 1988) 734 - 735 Discoveries with Rectangles and Rectangular Solids Lyle R. Smith Differentiating between area and perimeter for rectangles and between volume and surface area for rectangular solids. 80, (1987) 274 - 276. Crystals: Through the Looking Glass with Planes, Points, and Rotational Symmetries Carole J. Reesink Three-dimensional symmetry related to crystallographic analysis. Nets for constructing eight three-dimensional models are provided. 80, (1987) 377 - 389. A Geometric Figure Relating the Golden Ratio and Pi Donald T. Seitz The ratio of a golden cuboid to that of the sphere which circumscribes it. 79, (1986) 340 - 341. An Interesting Solid Louis Shahin Can the sum of the edges, the surface, and the volume of a three-dimensional object be numerically equal? 79, (1986) 378 - 379. The Spider and the Fly: A Geometric Encounter in Three Dimensions Rick N. Blake Eight problems involving a minimum path. 78, (1985) 98 - 104. Making Boxes Steve Gill Activities for measurement skills. Developing spatial relationships from two-dimensional patterns. 77, (1984) 526 - 530. Spatial Visualization Glenda Lappus, Elizabeth A. Phillips, and Mary Jean Winter Activities involving three-dimensional figures. Building shapes from cubes. 77, (1984) 618 - 625. Generating Solids Evan J. Maletsky Activities involving solids of revolution generated by polygons. 76, (1983) 499 - 500, 504 - 507. An Easy Dodecahedron Jean M. Shaw Construction of a model. 75, (1982) 380 - 382. Semiregular Polyhedra Rick N. Blake and Charles Verhille Activities for use in searching for patterns involved in the structure of polyhedra. 75, (1982) 577 - 581. Visualization, Estimation, Computation Evan M. Maletsky Activities for investigating the manner in which the dimensions of a cone change as the shape changes. BASIC program provided. 75, (1982) 759 - 764. A New Look Pythagoras Carol A. Thornton A 3-space extension of the theorem. 74, (1981) 98 - 100. Some Circular Reasoning Scott G. Smith Formulas for lateral areas. 74, (1981) 191 - 194. Spherical Geodesics William D. Jamski Finding the shortest distance between two points on a sphere. 74, (1981) 227 - 228, 236. A Model Of Three Space Jane Keller and Robert Anderson Description of a student developed model. 74, (1981) 350 - 353. Pythagoras On Pyramids Aggie Azzolino Activities involving the use of the theorem of Pythagoras to find the altitudes of pyramids. 74, (1981) 537 - 541. The Second National Assessment In Mathematics: Area and Volume James J. Hirstein A discussion of student results on these concepts. 74, (1981) 704 - 708. Sectioning A Regular Tetrahedron Edward J. Davis and Don Thompson Activities for the development of generalizations about sections of a tetrahedron. 73, (1980) 121 - 125. Applying The Technique Of Archimedes To The "Birdcage" Problem W. A. Stannard Finding the volume common to two intersecting cylinders. 72, (1979) 58 - 60. Facts Of A Cube Ruth Butler and Robert W. Clark Activities for the development of spatial visualization. 72, (1979) 199 - 202. Rectangular Solids With Integral Sides Robert W. Prielipp, John A. Aman and Norbert J. Kuenzi What happens geometrically if all side lengths are relatively prime? 72, (1979) 368 - 370. On Archimedean Solids Tom Boag, Charles Boberg and Lyn Hughes Junior high explorations using vertex sequences. 72, (1979) 371 - 376. Polyhedra Planar Projection Geraldine Daunis Activities for developing geometric perception. 72, (1979) 438 - 443. Painting Polyhedra Christian R. Hirsch Activities involving polyhedra. Euler's formula. 71, (1978) 119 - 122. A Recursive Approach To The Construction Of The Deltahedra William E. McGowan A guide for constructing polyhedra. 71, (1978) 204 - 210. An Easy-To-Paste Model Of The Rhombic Dodecahedron M. Stroessel Wahl Instructions for construction. 71, (1978) 589 - 593. Polycubes William J. Masalski Activities involving cubes. 70, (1977) 46 - 50. Polyhedra From Cardboard and Elastics John Woolaver Activities for construction. 70, (1977) 335 - 338. Hypercubes, Hyperwindows and Hyperstars Dean B. Priest Some n-dimensional geometry. 70, (1977) 606 - 609. Three Dimensional Geometry Gordon D. Pritchett Polyhedra construction. Platonic solids. Euler's formula. 69, (1976) 5 - 10. The Algebra and Geometry Of Polyhedra Joseph A. Troccolo Algebraic and geometric approaches to the building of polyhedra. 69, (1976) 220 - 224. A General Intersection Formula For Subspaces Of n-Dimension J. Taylor Hollist Generalizing to higher dimensions. 68, (1975) 153. Discovery With Cubes Robert E. Reys Activities for visualizing three dimensional figures. Looking for patterns. 67, (1974) 47 - 50. An Application Of Volume and Surface Area Robert W. Mercaldi A game for dealing with the concepts. 67, (1974) 71 - 73. The Fourth Dimension and Beyond ... With A Surprise Ending! Boyd Henry Patterns for familiar figures are extended to higher dimensions. 67, (1974) 274 - 279. Tetrahedral Frameworks Charles W. Trigg A model for the analysis of tetrahedral frameworks. 67, (1974) 415 - 418. The Volume Of The Regular Octahedron Charles W. Trigg Five methods of computation. 67, (1974) 644 - 646. Collapsible Models Of Isosceles Tetrahedrons Charles W. Trigg How to build them from envelopes and strips of triangles. 66, (1973) 109 - 112. Some Investigations Of N-dimensional Geometries Sallie W. Abbas Bounds and cross sections of n-dimensional figures. 66, (1973) 126 - 130. Soma Cubes George S. Carson Possible and impossible configurations. How to show that a design is impossible. 66, (1973) 583 - 592. Patterns and Positions Evan M. Maletsky Activities for visualizing a cube using two-dimensional patterns. 66, (1973) 723 - 726. The Total Angular Deficiency Of Polyhedra William L. Lepowsky Investigates the angles at the vertices of a polyhedron. 66, (1973) 748 - 752. Collapsible Models Of The Regular Octahedron Charles W. Trigg How to make them. 65, (1972) 530 - 533. Total Surface Area Of Boxes L. Carey Bolster Activities for investigation. 65, (1972) 535 - 538. A Look At Regular and Semiregular Polyhedra Carol E. Stengel History, interrelationships and properties. 65, (1972) 713 - 719. Viewing Diagrams In Four Dimensions Adrien L. Hess Representations of results in four-dimensional geometry. 64, (1971) 247 - 248. On Skewed Regular Polygons Ernest R. Ranucci Polygons whose elements are not coplanar. 64, (1971) 219 - 222. A Geometry Capsule Concerning The Five Platonic Solids Howard Eves History and occurrence in nature. 62, (1969) 42 - 44. What Points Are Equidistant From Two Skew Lines? Alexandra Forsythe Analytic approach. 62, (1969) 97 - 101. A Study Of The Ability Of Secondary School Pupils To Perceive The Plane Sections Of Selected Solid Figures Barbara L. Roe The title explains the content. 61, (1968) 415 - 421. Can Space Be Overtwisted? Douglas A. Engel Twisting chains of links of geometric figures. 61, (1968) 571 - 574. The World Of Polyhedra Rev. Magnus Wenninger History and theory. 58, (1965) 244 - 248. The History Of The Dodecahedron J. P. Phillips Applications also. 58, (1965) 248 - 250. The Mathematics Of The Honeycomb David F. Siemans, Jr. An explanation of the shapes in which bees build. 58, (1965) 334 - 337. Remarks On Some Elementary Volume Relations Between Familiar Solids A. L. Loeb The relation of volume to diagonal length. 58, (1965) 417 - 419. The Volume Of A Truncated Pyramid In Ancient Egyptian Papyri R. J. Gillings History and formulae. 57, (1964) 552 - 555. Stellated Rhombic Dodecahedron Puzzle Rev. M. Wenninger, O.S.B. Cardboard model. 56, (1963) 148 - 150. Interest In The Tetrahedron John J. Keough Some properties. 56, (1963) 446 - 448. The Construction Of Skeletal Polyhedra John McClellan Models and topological properties. 55, (1962) 106 - 111. Stalking Solid Geometry With Knife and Clay Jack Price Constructing clay models. 54, (1961) 47. The Wiequahic Configuration E. R. Ranucci Visualization in three space. 53, (1960) 124 - 126. A Historical Puzzle N. A. Court The altitudes of a tetrahedron. 52, (1959) 31 - 32. On Teaching Dihedral Angle and Steradian Howard Fehr Extension of the definition of angle in a plane. 51, (1958) 272 - 275. On Teaching Trihedral Angle and Solid Angle Howard Fehr Solid geometry methods suggestions. 51, (1958) 358 - 361. The "Steinmetz Problem" and School Arithmetic Richard M. Sutton The volume contained by the intersection of two cylinders. 50, (1957) 434 - 435. A Paper Model For Solid Geometry Ethel Saupe Prisms. 49, (1956) 185 - 186. Three Folding Models Of Polyhedra Adrian Struyk How to make them. 49, (1956) 286 - 288. Casting Geometric Models In Plaster-of-Paris Wallace L. Hainlin Model constructions. 48, (1955) 329. Fishline and Sinker Emil J. Berger A model for a polyhedral angle. 48, (1955) 408. A Model For Giving Meaning To Superposition In Solid Geometry Emil J. Berger Construction of teaching aids. 47, (1954) 33 - 35. Eureka Emil J. Berger The ratio of the surface area of a sphere to the lateral area of a circumscribed cylinder. 47, (1954) 105. A Tetrahedron With Planes Bisecting Three Dihedral Angles Emil J. Berger Construction of a model. 47, (1954) 186 - 188. Parallelogram and Parallelepiped Victor Thebault Theorems about diagonals. 47, (1954) 266 - 267. A Problem From Solid Geometry Emil J. Berger A sphere and a trihedral angle. 46, (1953) 505 - 506. Some Notes On The Prismoidal Formula B.E. Meserve and R.E. Pingry Volume formulas. 45, (1952) 257 - 263. Leonardo da Vinci and The Center Of Gravity Of A Tetrahedron John Satterly History and a proof. 45, (1952) 576 - 577. Models For Certain Pyramids Joseph A Nyberg Construction. 39, (1946) 84 - 85. Continuous Transformations Of Regular Solids H. v. Baravalle Relations between cube and tetrahedron, etc. 39, (1946) 147 - 154. Demonstration Of Conic Sections and Skew Curves With String Models H. v. Baravalle Construction and uses of models. 39, (1946) 284 - 287. Models Of The Regular Polyhedrons R. F. Graesser Construction. 38, (1945) 368 - 369. Teaching Solid Geometry Nancy C. Wylie Suggestions. 36, (1943) 126 - 127. Models In Solid Geometry Miles C. Hartley Models and theorems which they can be used to illustrate. 35, (1942) 5 - 7. Looking At Solid Geometry Through Perspective Ethel Spearman Using perspective drawings to deal with solid geometric concepts. 34, (1941) 147 - 150. A Helpful Technique In Teaching Solid Geometry James V. Bernardo Use of models. 33, (1940) 39 - 40. The Efficiency Of Certain Shapes In Nature and Technology May Hickey A suggested unit of instruction in intuitive solid geometry. 32, (1939) 129 - 133. The Dandelin Spheres Lee Emerson Boyer History and comments. 31, (1938) 124 - 125. The Teaching Of Solid Geometry At The University of Vermont G. H. Nicholson Approaches, objectives, techniques. 30, (1937) 326 - 330. The Tetrahedron and Its Circumscribed Parallelepiped N.A. Court Construction of the parallelepiped, some of its geometry and some geometry of the tetrahedron. 26, (1933) 46 - 52. Drawing For Teachers Of Solid Geometry John W. Bradshaw Part Four. Drawing solids bounded by the right circular cylinder and the sphere. 26, (1933) 140 - 145. Part Three. Techniques for drawing prisms. 19, (1926) 401 - 407. Part Two. Representing positions of points in space. 18, (1925) 37 - 45. Part One. Some beginning techniques. 17, (1924) 475 - 481. The Fourth Dimension Anice Seybold General discussion. 24, (1931) 41 - 45. The Fourth Dimension and Hyperspace Theresa Tremp A discussion of their nature. 19, (1926) 140 - 146. A Course In Solid Geometry William A. Austin Description, methods and content. 19, (1926) 349 - 361. Some Applications Of Algebra To Theorems In Solid Geometry Joseph B. Reynolds Volumes of solids. 18, (1925) 1 - 9. Reflections On Fourth Dimension A. N. Altieri A 1920's student view. 18, (1925) 490 - 495. The Extension Of Concepts In Mathematics Aubrey W. Kempner Infinite elements in geometry, non-Euclidean geometry, four-dimensional geometry. 16, (1923) 1 - 23. A Study Of The Cultivation Of Space Imagery In Solid Geometry Through The Use Of Models Edwin W. Schreiber Construction and use of models. 16, (1923) 103 - 111. The Volume Of A Sphere Proof of the formula. 15, (1922) 90 - 93. A Simple Method Of Constructing A Hyperbolic Paraboloid E.J. Guy A model. 12, (1919-1920) 28 - 29. A Geometric Representation E. D. Roe, Jr. The surface on which a family of spirals lies. Analytic approach. 11, (1918-1919) 9 - 25. A Geometric Representation E. D. Roe, Jr. Analytic geometry in space. 10, (1917-1918) 205 - 210. Geometric Stereograms - A Device For Making Solid Geometry Tangible To The Average Student Walter Francis Shenton The use of colored glasses and special drawings to produce 3-D effects. 8, (1915-1916) 124 - 131. Geometry Of Four Dimensions Henry P. Manning Results which are presented in more detail in the author's book which has the same title. 7, (1914-1915) 49 - 58. The Five Platonic Solids James H. Weaver Some of their properties. 7, (1914-1915) 86 - 88. The Way To Begin Solid Geometry Howard F. Hart Teaching methods. 4, (1911-1912) 54 - 57. Solid Geometry Howard F. Hart Some geometry on a sphere. 3, (1910-1911) 24 - 26. H.J.L. 07/15/97 email: 00hjludwig@bsu.edu home page: http://www.cs.bsu.edu/~hjludwig/ |

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