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Category Archives: programming
The wizard’s rational puzzle (solutions, part 2)
At long last, here is the solution I had in mind for the Wizard’s rational puzzle. Recall that the goal is to figure out the numerator and denominator of a secret rational number, if all we are allowed to do … Continue reading
Posted in arithmetic, challenges, logic, programming, puzzles, solutions
Tagged arithmetic, binary, denominator, Euclidean, gcd, logarithm, numerator, puzzle, rational, search, wizard
Comments Off on The wizard’s rational puzzle (solutions, part 2)
The wizard’s rational puzzle (solutions, part 1)
About two and a half months ago I posted a challenge involving a sadistic math wizard, metal cubes containing rational numbers, and a room full of strange machines. I’ve been remiss in following up with some solutions. (Go read the … Continue reading
Posted in arithmetic, challenges, logic, programming, puzzles, solutions
Tagged arithmetic, denominator, Euclidean, gcd, logarithm, numerator, puzzle, rational, wizard
3 Comments
The wizard’s rational puzzle (mind your p’s and q’s!)
You have been abducted by a sadistic math wizard (don’t you hate it when that happens?). He ushers you into a plain but cozylooking room, with a hardwood floor, a few exoticlooking rugs, and wood paneling on the walls. He … Continue reading
Posted in arithmetic, challenges, logic, programming, puzzles
Tagged arithmetic, denominator, numerator, puzzle, rational, wizard
15 Comments
Mystery curve, animated
As a followon to my previous post, here’s an animation (17MB) showing how the “mystery curve” arises as a sum of circular motions: Recall that the equation for the curve is . The big blue circle corresponds to the term—it … Continue reading
Posted in complex numbers, geometry, programming
Tagged animation, circles, complex, curve, graph, parametric, random, symmetry
6 Comments
Random cyclic curves
Princeton Press just sent me a review copy of a new book by Frank Farris called Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. It looks amazing and I’m super excited to read it. Apparently John Cook has been reading … Continue reading
Posted in complex numbers, geometry, programming
Tagged complex, curve, graph, parametric, random, symmetry
24 Comments
Stars of the Mind’s Sky with Diagrams
A few weeks ago, Paul Salomon posted a really beautiful work of mathematical art on his blog, Lost In Recursion: Stars of the Mind’s Sky, by Paul Salomon He included a precise mathematical description of the image, and I naturally … Continue reading
Posted in geometry, group theory, pictures, programming
Tagged art, diagrams, Haskell, polygon, star, visualization
9 Comments
Diagrams!
Over the past few years I’ve written quite a few posts with images generated by a library I (now along with many others) wrote. Most famously, this is how I created those factorization diagrams. But I’ve used it in many … Continue reading
What I Do, Part I: Programming languages (UpGoer 5 edition)
“Splasho” has has created an online text editor which checks to make sure you use only the 1000 most common English words, inspired by this recent XKCD comic. Over the past few weeks, many scientists have taken up the challenge … Continue reading
What I Do, Part 1: Programming languages
[This is the second in an occasional series of posts explaining what I do in my “day job” as a computer science PhD student. The idea is to write a series of posts of increasing specificity, but all aimed at … Continue reading
A computerchecked proof of the odd order theorem
Big news: a proof of the FeitThompson Theorem (also known as the “odd order theorem”) has been completely formalized and verified by a computer, using the Coq proof assistant! Wait, what? Huh? you’re probably thinking. Well, let me unpack that … Continue reading