Day-knights and night-knights
Mathrecreation
by dan.mackinnon
5y ago
In his book To Mock a Mockingbird, Raymond Smullyan provides another variation on his classic 'knights and knave' puzzles, in which he imagines the puzzle solver not visiting an island, but exploring a bizarre underground city. Illustration from The Child of the Cavern:Or, Strange Doings Underground (sometimes published as The Underground City) by Jules Vern In the strange community of Subterranea, visitors cannot tell day from night, but the residents can. The residents are of two types: day-knights or night-knights. Day-knights tell the truth during the day and lie at night, while night-k ..read more
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Star polygon fun
Mathrecreation
by dan.mackinnon
5y ago
Star and compound polygons are pretty mathematical objects that are fun to draw or create in code. star and compound polygons on 2 to 9 vertices You might draw ten pointed polygons while exploring the multiplication table, for example. In the picture below, skip counting by 6 while drawing a line between the last digits of consecutive numbers gives us a pentagon: counting 0, 6, 12, 18, 24, 30 we draw lines connecting 0, 6, 2, 8, 4, and 0. skip counting by 6 draws {5/2} When drawing star and compound polygons by hand, you start with n points spaced evenly around a circle, and then from each po ..read more
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Desmos Chladni
Mathrecreation
by dan.mackinnon
5y ago
Like Lissajous figures, Chladni figures provide a surprising and aesthetically engaging example of wave interaction. Named for Ernst Chladni, these figures represent nodal patterns formed by vibrating surfaces. Traditionally, these are formed placing fine particles on a surface, like a sheet of metal that is set vibrating (a violin bow against an edge of the metal plate is one popular method). The particles settle in the areas of the surface that have the least motion - the nodes. When you achieve a resonant frequency, a characteristic pattern emerges. In past posts I've pointed to code that ..read more
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Why horizontal transformations are tricky
Mathrecreation
by dan.mackinnon
5y ago
Both the Common Core and Ontario curricula ask students to look at families of functions that are connected to each other through simple transformations, and to build new functions from existing functions. In Ontario as with the Common Core, students get an understanding of function families "by playing around with the effect on the graph of simple algebraic transformations of the input and output variables." In the Ontario curriculum (MCR3U), students spend a significant amount of time graphing complicated examples from a function family by relating them to transformed graphs of a simple bas ..read more
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LaTeX for high school math teachers
Mathrecreation
by dan.mackinnon
5y ago
TLDR: Please check out the online workshop I am developing for high school math teachers who want to learn about LaTeX. That this community needs  something like LaTeX raises questions about teaching and learning math in online situations.I have been using LaTeX a lot recently, but not in the way I first used it a long time ago when writing my master's thesis. (Not sure what LaTeX is? Check out the first module of the online workshop here.) Now I am using it daily to provide feedback to students in the LMS that I teach an online course in (Brightspace), include bits of math on webpages, and a ..read more
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