Mathematics helps develop definitions to compare different means to make something better or more fair. But there are inherent limitations, expressed as mathematical impossibility theorems... Impossible? Joe Malkevitch York College (CUNY) Introduction When you got up from sleeping last night, what were the possibilities that you could achieve in theRead More →
Who might have realized that when the mathematics community studied the properties of cubes, they might be used in error correction technology? Correcting Errors Joe Malkevitch York College (CUNY) Introduction Humans sometimes make errors. Perhaps you have been sloppy with a calculation on a mathematics examination. You made an error.Read More →
If one has a pattern on a band, frieze, or strip (disregarding color if as often happens more than one color appears), regardless of the artistic content of what one sees, there are exactly 7 different patterns that are possible… Remembering Donald W. Crowe Maker of Connections between Symmetry, ArtRead More →
A remarkable theorem involving decompositions is that if one has two plane simple polygons of the same area, it is possible to decompose either of the polygons into polygonal pieces that can be reassembled to form the other polygon… Geometric Decompositions Joe Malkevitch York College (CUNY) Introduction When looking atRead More →
Decomposition Mathematics too has profited from the idea that sometimes things of interest might have a structure which allowed them to be decomposed into simpler parts... Joe Malkevitch York College (CUNY) Introduction One way to get insights into something one is trying to understand better is to break the thingRead More →
In Praise of Collaboration Take a look at an extraordinary collaboration in discrete geometry and related geometrical mathematics, the collaboration of Branko Grünbaum and Geoffrey Colin Shephard. Joe Malkevitch York College (CUNY) Introduction Point and line do many activities together—their collaborations create a rich texture for many mathematicians and geometers,Read More →
Pseudonyms in Mathematics Why would there be pseudonyms for the publication of research papers in mathematics? One possible motive might be… that a group of people collaborated on a piece of work and wanted to simplify the multiple authorship to a single name. Another reason appears to be playfulness orRead More →
Remembering Richard Kenneth Guy: Games and Taking on Mountains This essay is dedicated to the memory of Richard K. Guy (1916-2020) whose life story and accomplishments display a variety of aspects of the complicated landscape of finding fulfilling work on the part of individuals, the concern of society with nourishingRead More →
Points, Lines, and Incidences To honor Mathematics and Statistics Awareness Month, I will treat some remarkable developments concerning a basic intuitive idea in geometry concerning points and lines. … Joseph Malkevitch York College (CUNY Introduction When people think about mathematics they think of numbers and shapes. Numbers covers the interestRead More →