Mathematics Visualization and Recreational Mathematics

- Past Events


29.05.24	Inga Johnson (Willamette University) : Solution Numbers for the Eight Blocks to Madness puzzle. Many puzzles with the 30 MacMahon colored cubes have been studied and solved. The original problem is to create a 2 ×2 ×2 model with eight distinct MacMahon cubes to recreate a larger version a specified target cube, also a MacMahon cube, such that touching interior faces are colored the same color. J.H. Conway is credited with arranging the cubes in a 6 ×6 tableau giving a solution to the puzzle. In fact, there are exactly two ways to arrange the eight cubes used to solve the puzzle. We study a less restrictive puzzle, without the requirement of interior face matching, and look not only for solutions to the 2 × 2 × 2 puzzle but also the number of distinct solutions attained for a collection of eight cubes. We also discuss a related question; given a subset of k ≥ 8 MacMahon colored cubes, how many target cubes can be built with cubes from the subset. We will have colored cubes available for puzzling and play! Joint work with Erika Roldan. Professor Inga Johnson is a topologist, teacher and mentor at Willamette University in Salem, Oregon, USA. She co-wrote the inquiry-based textbook “An Interactive Introduction to Knot Theory” with Allison Henrich. Her research includes articles on knot theory, homotopy theory, topological data analysis and teaching techniques. Inga and co-PI Colin Starr have been awarded two NSF Research Experience for Undergraduates grants that have funded 24 summer projects with undergraduates. Abstract
25.01.24	María García Monera (University of Valencia) : Building real mathematical surfaces At the end of the 19th century, the German teachers Felix Klein (1849-1925) and Alexander Von Brill (1842-1935) designed real surfaces using different materials such as paper, wire or plaster. Inspired by their work, in this talk we present new techniques that allow us to build new cardboard surfaces. The main idea of these techniques consists on finding plane curves contained on surfaces that can be used as a pieces to reproduce a real model of the surface. Biography: María García Monera has a degree in Mathematics by the University of Valencia (Spain) and a Phd in differential geometry by the Polytechnic University of Valencia. She currently works as a teacher in the area of Geometry and Topology at the University of Valencia. Attention: this event is cancelled

29.05.24

Inga Johnson (Willamette University) : Solution Numbers for the Eight Blocks to Madness puzzle.

Many puzzles with the 30 MacMahon colored cubes have been studied and solved. The original problem is to create a 2 ×2 ×2 model with eight distinct MacMahon cubes to recreate a larger version a specified target cube, also a MacMahon cube, such that touching interior faces are colored the same color. J.H. Conway is credited with arranging the cubes in a 6 ×6 tableau giving a solution to the puzzle. In fact, there are exactly two ways to arrange the eight cubes used to solve the puzzle. We study a less restrictive puzzle, without the requirement of interior face matching, and look not only for solutions to the 2 × 2 × 2 puzzle but also the number of distinct solutions attained for a collection of eight cubes. We also discuss a related question; given a subset of k ≥ 8 MacMahon colored cubes, how many target cubes can be built with cubes from the subset. We will have colored cubes available for puzzling and play! Joint work with Erika Roldan. Professor Inga Johnson is a topologist, teacher and mentor at Willamette University in Salem, Oregon, USA. She co-wrote the inquiry-based textbook “An Interactive Introduction to Knot Theory” with Allison Henrich. Her research includes articles on knot theory, homotopy theory, topological data analysis and teaching techniques. Inga and co-PI Colin Starr have been awarded two NSF Research Experience for Undergraduates grants that have funded 24 summer projects with undergraduates.

Abstract

25.01.24

María García Monera (University of Valencia) : Building real mathematical surfaces

At the end of the 19th century, the German teachers Felix Klein (1849-1925) and Alexander Von Brill (1842-1935) designed real surfaces using different materials such as paper, wire or plaster. Inspired by their work, in this talk we present new techniques that allow us to build new cardboard surfaces. The main idea of these techniques consists on finding plane curves contained on surfaces that can be used as a pieces to reproduce a real model of the surface. Biography: María García Monera has a degree in Mathematics by the University of Valencia (Spain) and a Phd in differential geometry by the Polytechnic University of Valencia. She currently works as a teacher in the area of Geometry and Topology at the University of Valencia.

Attention: this event is cancelled


01.11.23	Colm Mulcahy (Spelman College) : Introduction to mathematical card tricks Amaze and amuse your family and friends armed with just a deck of 52 playing cards and a little insider knowledge. Mathematics underpins numerous classic amusements with cards, from forcing to prediction effects, and many such tricks have been written about for general audiences by popularizers such as Martin Gardner. The mathematics involved ranges from simple ''card counting'' (basic arithmetic) to parity principles, to surprising shuffling fundamentals (Gilbreath and Faro) discovered in the second half of the last century. We'll discuss several original and totally different principles discovered since 2000, as well as how to present them as entertainments in ways that leave audiences (even students of mathematics) baffled as to how mathematics could be involved. BioColm Mulcahy taught mathematics at Spelman College in Atlanta from 1988 till 2020. As a teenager growing up in Ireland, he read some early books of Martin Gardner, having no idea that decades later he would meet the great man and get to know him. Colm is currently the Chair of the Gathering 4 Gardner nonprofit Foundation, which stimulates curiosity and the playful exchange of ideas and critical thinking in recreational math, magic, science, literature, and puzzles to preserve and extend the legacy of writer and polymath Gardner. Colm has blogged for the Mathematical Association of America, The Huffington Post, Scientific American, and (aperiodically) for The Aperiodical; and his puzzles and writings have been featured in The New York Times and the Guardian. For 10 years he authored Card Colm, a regular column about mathematics and magic–especially card magic–for the Mathematical Association of America. Much of this work in this arena is collected in his 2013 book Mathematical Card Magic: Fifty-Two New Effects (CRC Press).

01.11.23

Colm Mulcahy (Spelman College) : Introduction to mathematical card tricks

Amaze and amuse your family and friends armed with just a deck of 52 playing cards and a little insider knowledge. Mathematics underpins numerous classic amusements with cards, from forcing to prediction effects, and many such tricks have been written about for general audiences by popularizers such as Martin Gardner. The mathematics involved ranges from simple ''card counting'' (basic arithmetic) to parity principles, to surprising shuffling fundamentals (Gilbreath and Faro) discovered in the second half of the last century. We'll discuss several original and totally different principles discovered since 2000, as well as how to present them as entertainments in ways that leave audiences (even students of mathematics) baffled as to how mathematics could be involved. BioColm Mulcahy taught mathematics at Spelman College in Atlanta from 1988 till 2020. As a teenager growing up in Ireland, he read some early books of Martin Gardner, having no idea that decades later he would meet the great man and get to know him. Colm is currently the Chair of the Gathering 4 Gardner nonprofit Foundation, which stimulates curiosity and the playful exchange of ideas and critical thinking in recreational math, magic, science, literature, and puzzles to preserve and extend the legacy of writer and polymath Gardner. Colm has blogged for the Mathematical Association of America, The Huffington Post, Scientific American, and (aperiodically) for The Aperiodical; and his puzzles and writings have been featured in The New York Times and the Guardian. For 10 years he authored Card Colm, a regular column about mathematics and magic–especially card magic–for the Mathematical Association of America. Much of this work in this arena is collected in his 2013 book Mathematical Card Magic: Fifty-Two New Effects (CRC Press).

Mathematics Visualization and Recreational Mathematics

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