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a couple of math & gaming articles
Feb. 4th, 2019 10:17 pmRecently, I came across a couple of fun articles about math and computer games in MAA (Mathematical Association of America) publications.
( Here's a disclaimer on reading math articles. )
Aaron M. Broussard, Martin E. Malandro, and Abagayle Serreyn, Optimizing the Video Game Multi-Jump (American Mathematical Monthly).
This article is about platformer video games where a character can jump, then magically start another jump in mid-air. The question is how to time the jumps so the character lands at a specific point (on a floating platform, for example). There are explicit solutions if the path of each jump is part of a parabola, as well as a discussion for more general, perhaps-fantastic jump shapes. I enjoyed the comments in this article about the way AI-controlled characters in specific games fail to make optimal decisions.
Tom Edgar and Jessica Sklar, A Confused Electrician Uses Smith Normal Form (Mathematics Magazine).
This article is about the type of puzzle where flipping a switch or pressing a button can turn multiple lights on or off, or rotate them through different colors. The goal is to find the right combination of button-presses that will turn all the lights on or off simultaneously. The analysis starts with graph theory, converts it to a problem involving matrices of integers, invokes the SageMath computer algebra system and a little bit of number theory, and ends with Smith normal form. Smith normal form is a beautiful way to factor matrices, but if you never restrict yourself to integer matrices, you probably haven't heard of it. It was the solution to a problem I ran into when I was writing my dissertation, and I've had a soft spot for it ever since.
( Here's a disclaimer on reading math articles. )
Aaron M. Broussard, Martin E. Malandro, and Abagayle Serreyn, Optimizing the Video Game Multi-Jump (American Mathematical Monthly).
This article is about platformer video games where a character can jump, then magically start another jump in mid-air. The question is how to time the jumps so the character lands at a specific point (on a floating platform, for example). There are explicit solutions if the path of each jump is part of a parabola, as well as a discussion for more general, perhaps-fantastic jump shapes. I enjoyed the comments in this article about the way AI-controlled characters in specific games fail to make optimal decisions.
Tom Edgar and Jessica Sklar, A Confused Electrician Uses Smith Normal Form (Mathematics Magazine).
This article is about the type of puzzle where flipping a switch or pressing a button can turn multiple lights on or off, or rotate them through different colors. The goal is to find the right combination of button-presses that will turn all the lights on or off simultaneously. The analysis starts with graph theory, converts it to a problem involving matrices of integers, invokes the SageMath computer algebra system and a little bit of number theory, and ends with Smith normal form. Smith normal form is a beautiful way to factor matrices, but if you never restrict yourself to integer matrices, you probably haven't heard of it. It was the solution to a problem I ran into when I was writing my dissertation, and I've had a soft spot for it ever since.