Introduction to Geometry. By H. S. M. Coxeter. Pp. xiv, 443. 1961. (John Wiley)

/pdf/handbook-of-magma-functions-5anhrdxxj3.pdf

Handbook of magma functions

A near-regular texture deviates geometrically and photometrically from a regular congruent tiling. Although near-regular textures are ubiquitous in the man-made and natural world, they present computational challenges for state of the art texture analysis and synthesis algorithms. Using regular tiling as our anchor point, and with user-assisted lattice extraction, we can explicitly model the deformation of a near-regular texture with respect to geometry, lighting and color. We treat a deformation field both as a function that acts on a texture and as a texture that is acted upon, and develop a multi-modal framework where each deformation field is subject to analysis, synthesis and manipulation. Using this formalization, we are able to construct simple parametric models to faithfully synthesize the appearance of a near-regular texture and purposefully control its regularity.

/pdf/near-regular-texture-analysis-and-manipulation-27ca1manv0.pdf

Near-regular texture analysis and manipulation

We present a computational model for periodic pattern perception based on the mathematical theory of crystallographic groups. In each N-dimensional Euclidean space, a finite number of symmetry groups can characterize the structures of an infinite variety of periodic patterns. In 2D space, there are seven frieze groups describing monochrome patterns that repeat along one direction and 17 wallpaper groups for patterns that repeat along two linearly independent directions to tile the plane. We develop a set of computer algorithms that "understand" a given periodic pattern by automatically finding its underlying lattice, identifying its symmetry group, and extracting its representative motifs. We also extend this computational model for near-periodic patterns using geometric AIC. Applications of such a computational model include pattern indexing, texture synthesis, image compression, and gait analysis.

/pdf/a-computational-model-for-periodic-pattern-perception-based-4uj7cxl1yy.pdf

A computational model for periodic pattern perception based on frieze and wallpaper groups

An argument for extending the circulation of knowledge with new publishing technologies considers scholarly, economic, philosophical, and practical issues.

The access principle: The case for open access to research

(1978). The Plane Symmetry Groups: Their Recognition and Notation. The American Mathematical Monthly: Vol. 85, No. 6, pp. 439-450.

The Plane Symmetry Groups: Their Recognition and Notation

Classification-theory of semi-simple algebraic groups

Part I. Personal Reflections On Investigation, Discovery, and Proof: 1. Discovery and dissection of a geometric gem Douglas R. Hofstadter 2. The role and function of proof in dynamic geometry: some personal reflections Michael de Villiers 3. Dynamic geometry renews interest in an old problem Dan Bennett 4. Dynamic geometry as a bridge from Euclidean geometry to analysis Albert A. Cuoco and E. Paul Goldenberg Part II. Dynamic Geometry In The Classroom: 5. Dynamic visualization from middle school through College James Morrow 6. Geometer's sketchpad in the classroom Tim Garry 7. Students discovering geometry using dynamic geometry software Michael Keyton 8. Moving triangles 9. Experiences with geometer's sketchpad in the classroom Kathryn W. Boehm 10. Beyond elementary constructions: selected exercises Arnold Perham and Bernadette H. Perham 11. Interactive generation, manipulation, and application of loci Heinz Schumann 12. Calculus with dynamic geometry Catherine A. Gorini 13. Beginning geometry at college Tony Hampson 14. Identifying transformations by their orbits James M. Parks 15. Dynamic proofs that use similarities James King 16. Visualization of group theory concepts through dynamic geometry Doris Schattschneider 17. Using the geometer's sketchpad with preservice teachers Zhonghong Jian and Edwin McClintock 18. Fish in the pond: inquiry with dynamic geometry Fadia Harik Part III. Dynamic Visualization In History, Perception, Optics and Aerodynamics: 19. Drawing logarithmic curves with geometer's sketchpad: a method inspired by historical sources David Dennis and Jere Confrey 20. Lost in the funhouse: an application of dynamic projective geometry Susan Addington and Stuart Levy 21. The use of dynamic geometry software in teaching and research in optometry and vision science Benjamin T. Backus 22. Creating airfoils from circles: the Joukowski transformation John Olive Part IV. The Worlds Of Dynamic Geometry: Issues In Design And Use: 23. Drawing worlds: scripted exploration environments in the geometer's sketchpad R. Nicholas Jackiw 24. Dynamic geometry and declarative geometric programming Richard J. Allen and Laurent Trilling.

Geometry turned on! : dynamic software in learning, teaching, and research

The importance of recreational mathematics and the involvement of amateur mathematicians has been dramatically demonstrated recently in connection with the prob/ lem of tiling the plane with congruent pentagons. The problem is to describe completely all pentagons whose congruent images will tile the plane (without overlaps or gaps). The problem was thought to have been solved by R. B. Kershner, who announced his results in 1968 [18], [191. In July, 1975, Kershner's article was the main topic of Martin Gardner's column, "Mathematical Games" in Scientific American. Inspired by the challenge of the problem, at least two readers attempted their own tilings of pentagons and each discovered pentagons missing from Kershner's list. New interest in the problem has been aroused and both amateur and professional mathematicians are presently working on its solution.

Tiling the Plane with Congruent Pentagons

(1980). Will It Tile? Try the Conway Criterion! Mathematics Magazine: Vol. 53, No. 4, pp. 224-233.

Doris Schattschneider

Papers

The Plane Symmetry Groups: Their Recognition and Notation

Classification-theory of semi-simple algebraic groups

Geometry turned on! : dynamic software in learning, teaching, and research

Tiling the Plane with Congruent Pentagons

Will It Tile? Try the Conway Criterion!