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Tetris is a computer game which has obsessed many computer users and attracted much attention, despite the simplicity of its rules. This paper addresses the question: ‘can you “win” the game Tetris?’Designed by Soviet mathematician Alexey Pazhitnov in the late eighties and imported to the United States by Spectrum Holobyte, Tetris won a record number of software awards in 1989. Versions of Tetris are sold for most personal computers. There are Tetris arcade games, Tetris Nintendo cartridges, and hand-held Tetris games; Tetris has been played on machines ranging from mainframes to calculators. The game's success has prompted the invention of several similar games, including Hextris, Welltris, and Wordtris.

M.C. Escher's use of dilation symmetry in Path of Life III gives rise to a pattern of logarithmic spirals and an oddly ambiguous sense of depth.

This paper classifies and gives methods for computing the irreducible realizations of the abstract polyhedra corresponding to regular maps of type {3, 6} and {6, 3}. A complete list of irreducible realizations is given for polyhedra of type {3, 6}.

The number of computer science (CS) courses has been dramatically expanding in U.S. high schools (HS). In comparison with well-established courses in mathematics and science, little is known about how the decisions made by HS CS teachers regarding how and what to teach impact student performance later in introductory college CS courses. Drawing on a large sample of 2,871 introductory college CS students at 115 U.S. institutions who had taken a CS course in HS, we examined the topic coverage and prevailing instructional methods in the HS course and investigated how these experiences influenced student performance in college CS. Controlling for differences in student background, we find two predictors of higher grades in college CS: greater frequency of coding-related activities in HS (programming, debugging, studying algorithms) and lower frequency of “non-coding” computer use (e.g., data analysis, computer security). Interaction models revealed a more complex story. Coding-related activity more heavily benefited students who did not have coding help available at home. In the 28% of college CS courses in which instructors employed innovative pedagogies, students with higher ACT or SAT mathematics scores had a greater advantage than in traditionally taught courses. Finally, in the innovative college courses, students whose HS CS exams had typically included testing on vocabulary did worse than students whose exams had not included such tests.