A new puzzle turns the Earth in a Rubik’s Cube. However, it’s much more difficult

Another orbit around Sun, and here we are again: back at the beginning but orbited around it – changed, possibly confused.

Henry Segerman was a British-American mathematician who also works as an artist at Oklahoma State University. He created the puzzle to be used in the annual puzzle contest, Continental Drift. It is a 3D sliding puzzle which debuted earlier this year. The basic engineering concept of inclusiveness is that you travel in a loop along a curving surface and return to your starting point, which can be interpreted as a turn or 180 degrees.

“Take a mathematical idea. Can you make it real?” – This question, Dr. Sigerman stated, is the impetus behind his inventions.

He loves to visualize mathematics, whether it is in 3D printing (he wrote a bookAbout it) or through Non-Euclidean virtual reality experiences. But Dr. Sigerman suffers from aphantasia, which is the inability to form mental images, or “visually hallucinating images at will,” as he puts it. This may explain his passion to create tangible images, including the impressive collection he produced 2022.

Continental Drift is the Earth as miniature, drawn in the form of an octahedron (a soccer ball) with a regular jumble 12 pentagons & 20 hexagons.

The conceptual inspiration was the Victorian craze: the classic 15 puzzle, in which square tiles numbered 1 to 15 are shuffled on a 4×4 grid, leaving one square blank; You can solve the puzzle by moving the tiles in numerical order.

Continental Drift is a spherical version the 15 puzzle. It is the hexagonal tiles which get shuffled. (The pentagons, which are sunken, stay still. “One hexagon comes out, this one in the South Pacific,” Dr. He explains on his YouTube channel. “We can then activate the San Andreas fault and push California south into the ocean. And we can continue to shuffle all the continents.”

Holonomy happens when tiles move in a complete circle along the curved surface. Move a tile that shows Greenland all of the way around one pentagonal square tile. Perhaps a tile that shows the North Atlantic. After completing the loop, the Greenlanders rotate 60 degrees to return to their original position. If the ring is made up of two adjacent pentagons the tiles will return their starting position by rotating 120°. And so on.

Math maker

Dr. Sigerman’s formal investigations are focused on topology, which is the study of geometric bodies without regard for lengths or angles. “All that’s left for you,” he said, “is how things relate to each other—how many holes are in the thing, etc.” Age Topology joke“A topologist is someone who cannot tell the difference between a coffee mug and a donut,” he said.

Will Sigerman, Will’s younger brother, said that Henry was a mathematician who also likes to make. Mr. Sigerman is a maker who loves mathematical forms and lives in Manchester, England. He studied fine arts, and now designs and makes escape rooms puzzles. The brothers’ creative process is asking questions about everything. Dr. Segerman always mentions a new project. He says it is always “very, very smart.” Mr. Segerman is still trying to find holes.

Dr. Sigerman proved that just a few years ago extensors: A kit for building extension mechanisms out of hinged parts that look like scissor-like. His brother was more gullible and said “Not stupid enough”. They added an activator handle at one end and a 4-pronged claw at the other. The result was released in April. grabber mechanism– the patent hanging.

Sabita MatsumotoGeorgia Institute of Technology applied mathematician Dr. Segerman contributed to the development of Extensor. Dr. Matsumoto stated that the math they have is “a very similar conversation.”

Collider of Ideas

Dr. Segerman, Kyle Vandeventer, and a former student present a twist on the scissors theme. Circular scissorsThis summer.

This invention was the solution to a problem: given a “self-similar” quadrilateral tile pattern—the same shape but rotated, translated, and resized—can the tiles be replaced by scissor joints (like a scissor lift), and can the structure then move?

There are two types. Proved“Dual parallelogram” and “surprisingly round quadrilateral”: Periodically means that all vertices within a quadrilateral are on a circle. Mr. Van Deventer, an aeronautical engineering at Aurora Flight Sciences in Manassas in Virginia, sees potential uses in the aerospace industry. He declined to give any details. clipper systemsThey have been used for space technologies, architecture, and satellite panels. One YouTube commenter suggested that the mechanism would be a “back scratcher”.

The d24 counting down is another example of a 24-sided die. It’s the latest invention from Dice Lab. This partnership was formed with Robert Fathauer, an Arizona mathematician and puzzle designer. The d24 countdownThis is used to keep track of points in the card game Magic: The Gathering.

One problem with countdown dice that are often in the form of an icosahedron, with 20 triangular sides is that the numerical path around it doesn’t follow any consistent pattern. This leaves you scrambling to find the number you want.

The d24 Countdown is a spherical, triangular conical shape that looks like a poorly-fitting soccer ball. It is then cut and rolled and glued together.

This invention was born out of a “clash between ideas”, just like many other creations by Dr. Sigerman. He had previously collaborated in the making of the rolling Circus acrobatsOn a biconical spherical foundation.

Two cones didn’t solve the fumble problem for the countdown die. Three cones solved it. The result shows a clear, winding path around the die that counts down from 24 to 1. It makes it easy to rotate the dashes to the number you desire.

Dr. Sigerman noted that the mold can “roll along its course”. The die moves in a perfect chronological order when it has the right slope, gravity, and thrust. Dr. Sigerman stated, “That was a surprise.” “Reality tends towards turning back.”

Fight or flight

Dr. Sigerman is not the first to be on the holistic block with Continental Drift. He did a job last summer. Dodecahedral labyrinthRecently, Helix cube puzzle. His psychology obsession began with musical scores on the 15th Puzzle that preceded Continental Drift. He added hinges to allow the tiles to rotate while sliding. This led to 15 + 4 puzzleAnd then Hyperbolic 29 puzzle.

“Just looking at this puzzle activates my fight-or-flight response,” one YouTube commenter wrote about the Hyperbolic 29 puzzle. Rick Rubinstein (a former professional juggler who is now semi-retired in software engineering in Sunnyvale Calif.), was Dr. Segerman’s friend. He wrote: “Henry Segerman. Mad Genius.”

As a Stanford University entertainer, Mr. Rubinstein became friends with Dr. Segerman. Dr. Sigerman can juggle five balls and takes 100 work breaks.

Rubinstein stated that “He’s actually quite reasonable and has a rather non-Euclidean humour.”

Although Dr. Segerman is aware that his puzzles can be solved, he doesn’t bother to solve them.

To give an idea of the complexity of Continental Drift, it has 7 x 10 states. A Rubik’s Cube has about four by ten degrees, whereas a Continental Drift has nearly as many moving parts. One YouTube viewer estimated that half of Continental Drift cases are possible.

Dr. Sigerman knows of only one person who has solved Continental Drift. He stated, “I solved it through unscrewing the removable portion of the frame that allows for you to slide out the tiles.” He then reassembled the puzzle, attaching the tiles and himself to it.