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February 9, 2023

Another orbit around the sun and here we are again: back where we started but spinning – changed, perhaps insane.

Henry Segerman, a British-American mathematician and math artist at Oklahoma State University, has just created a puzzle for the bewildering annual event: Continental Drift, a 3D sliding puzzle that was presented this year debuted earlier. The basic geometric concept is the law of completeness: when you go around a surface and return to the starting point, you arrive at a bit of a U-turn, rotated, maybe 180 degrees.

“Think of a mathematical idea, can you bring it to life?” – Dr. Segerman says this question inspired his invention.

He is passionate about visualizing mathematics, whether it is 3D printing (he wrote a book on topic) or via Non-Euclidean Virtual Reality ExperienceBut Dr. Segman suffers from hallucinations, an inability to construct mental pictures, or, as he puts it, “optical hallucinations at will.” This might explain his passion for producing concrete images, especially the impressive series he produced in 2022.

The Continental Drift is a microcosm of the Earth, mapped onto a truncated icosahedron—a football—made up of a regular patchwork of 12 pentagonal and 20 hexagonal faces.

Concept inspired by a Victorian craze: the classic 15 Puzzle, in which squares numbered 1 to 15 are shuffled on a 4×4 grid with one square left empty; you solve the puzzle by sliding the squares in numerical order .

In Continental Drift (the spherical version of the 15-puzzle), the hexagonal puzzle is shuffled. (The pentagons sunk and remained stationary.) “One of the hexagons, this one in the South Pacific, came out,” said Dr. Segerman explained on his youtube channel“Then we can activate the San Andreas fault and slide California south into the ocean. We can go ahead and mix all the continents.”

Full circles occur when a tile travels a full circle along the puzzle’s curved surface: slide the tile with Greenland along the perimeter of a single pentagonal tile—perhaps the tile with the North Atlantic Ocean. After one full circle, the Greenlander rotates 60 degrees back to the starting position. If the loop contains two adjacent pentagons, the tile will return to the starting point rotated 120 degrees. wait.

Dr. Segerman’s more formal research is topology, the study of geometric objects without regard to length or angle. “You’re left with how things are connected together—how many holes a thing has, and so on,” he said.as an old topological joke Cloud: “A topologist is someone who can’t tell the difference between a coffee cup and a donut.”

“Henry is a mathematician, and he likes to make,” said his brother Will Segerman, a former collaborator. Mr. Segerman, who lives in Manchester, UK, is a maker who loves mathematical shapes; he studied fine arts and now designs and makes escape room games. The brothers’ creative process was to ask everything together, “But what if…?” Whenever Dr. Segman mentions a new project, it’s always “very, very smart,” Mr. Segman said, though, he Still hoping to find bugs.

Several years ago, Dr. Segerman demonstrated that extensor: A construction kit for making extension mechanisms from scissor-like hinge parts. “Not stupid enough,” said his brother, who wanted to be even more stupid. They added an activator handle on one end and a four-prong prong on the other.The results, which debuted in April, are grabbing mechanism – this patent Waiting.

Sabetta Matsumoto, an applied mathematician at Georgia Tech and a collaborator with Dr. Segerman, was involved in the development of the device and came up with the name Extensor. Mathematics was “a very common topic” between them, Dr. Matsumoto said.

In a variation on the scissors theme, Dr. Segerman and former student Kyle VanDeventer demonstrate Power Cycle Scissors this summer.

The present invention is an answer to the question: Given a tile pattern of “self-similar” quadrilaterals—same shape but rotated, translated, scaled—can the tiles be replaced by a scissor linkage (such as a scissor lift), the structure Can it then be forced to move?

Two types of shapes come into play, they confirmed: “boring parallelogram” and “surprising cyclic quadrilateral”, cyclic means that all the vertices of the quadrilateral lie on a circle. Mr. VanDeventer, now an aerospace engineer at Aurora Flight Sciences in Manassas, Virginia, sees potential applications in the aerospace industry; he declined to elaborate, for proprietary reasons. Scissor system It has been used in construction, space technology and satellite panels. In YouTube comments, one viewer said the mechanic would be “one hell of a backstop.”

Also consider the Countdown d24, a 24-sided die that is the latest invention from Dice Lab, a business partnership with math artist and puzzle designer Robert Fasol of Apache Junction, Arizona. countdown d24 Used to keep track of points, for example in the card game Magic: The Gathering.

One problem with some countdown dice (usually the icosahedron shape with 20 triangular sides) is that the paths of numbers around the shape don’t follow a consistent pattern, leaving you fumbling to find the number you want.

The Countdown d24 overcomes this problem by being a sphere made from a three-cone shape, like an awkwardly shaped football, which is then cut, twisted and glued back together.

Like many of Dr. Segerman’s creations, this invention arose from a “collision of ideas.”He previously co-produced a scroll circus acrobatic equipment Based on a biconical sphere.

For countdown dice, two cones won’t solve the fumbling problem, but three cones will. The result shows a clear path that zigzags up and down the dice, counting down from 24 to 1, and easily spins the dice to the number you want.

It turns out that the dice can “roll along its path,” Dr. Segman noted. Given the correct slope, gravity, and nudge, the dice will swing along a perfectly timed countdown. “It was a surprise,” Dr. Segerman said. “Reality tends to bite back.”

Continental Drift isn’t Dr. Segerman’s first foray into full blocks.Last year, he produced complete dodecahedron maze and the most recent Spiral Cube Puzzle. His full craze began with a riff on 15 Puzzle before Continental Drift.He added hinges so the tiles could rotate as they slid, creating 15+4 puzzle After that Hyperbolic 29 Puzzle.

“Just looking at this puzzle triggers my fight-or-flight response,” wrote one YouTube commenter about the Hyperbolic 29 puzzle. Dr. Segman’s friend Rick Rubenstein, a former professional vaudevillian and semi-retired software engineer in Sunnyvale, California, went on to say: “Henry Segman, mad genius. “

Mr. Rubinstein met Dr. Sigman while at Stanford University, when he was an amateur juggler. Dr. Segman can catch five balls at a steady pace, and he often rests after 100 catches.

“He’s actually a very reasonable guy with a slightly non-Euclidean sense of humor,” Mr Rubinstein said.

Indeed, while Dr. Segerman knew his puzzles were solvable, he didn’t bother with the task of finding a solution.

Still, for a rough measure of the complexity of continental drift, he calculated that it has 7 × 10³¹ states, or possible configurations. (The Rubik’s Cube has about the same number of moving parts, only about 4 × 10^1⁹ states.) One YouTube viewer calculated that half the states of Continental Drift are reachable.

As far as Dr. Segman knows, only one person has solved the problem of continental drift so far. “I got around this by unscrewing the removable part of the frame so you can take out the tiles,” he says. He then reorients himself and the tile, screwing the puzzle back into place.



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