We are back where we started, but this time it's different and maybe deranged.
The Continental Drift, a 3-D sliding puzzle that made its debut earlier this year, was invented by Henry Segerman, a British American mathematician and mathematical artist. When you travel a loop on a curved surface and return to the starting point, you arrive in a different way.
"Can you make it real?" is a question that motivates his inventions.
He is fond of using 3-D printing and virtual reality to visualize mathematics. Dr. Segerman has aphantasia, an inability to build mental pictures orvisually hallucinate images at will. He produced an impressive collection of concrete pictures.
There are 12 pentagonal faces and 20 hexagonal faces on Continental Drift.
The concept was inspired by the classic 15 Puzzle, in which squares numbered 1 to 15 are scrambled on a grid with one square left empty, and you solve the puzzle by sliding tiles around into numerical order.
The hexagonal tiles in Continental Drift are scrambled. The pentagons aren't moving. One of the hexagons comes out in the South Pacific. It is possible to slide California into the ocean. We can mix up all of the world.
When a tile travels a full loop along the curved surface of the puzzle, it's called holonomy. The Greenlanders return to their starting position after a full loop. The tile goes back to the starting point if the loop includes two adjacent pentagons. So on.
The study of geometric objects without regard for length or angle is what Dr. Segerman does. He said that all you have left is how things are connected. A topologist is someone who can't tell the difference between a coffee mug and a doughnuts.
Will Segerman said that Henry is a mathematician who likes making. Mr. Segerman studied fine art and is a maker who likes mathematical shapes. The brothers are asking everything, "But what if..." Mr. Segerman looks to poke holes whenever Dr. Segerman mentions a new project.
Dr. Segerman showed how to make extending mechanisms from scissor-like hinges. His brother wanted more silliness. There was a four-pronged claw on the other side. The patent on the Grabber Mechanism is pending.
A mathematician at the Georgia Institute of Technology gave input into the creation of the contraption. It's a common conversation between them.
A variation on the scissor theme was presented by Dr. Segerman and Kyle VanDeventer.
The answer to the problem was given by this invention: Can the tiles be replaced with scissor linkage and the structure moved?
The two classes of shapes are boring parallelograms andsurprising cyclic quadrilaterals. Mr. VanDeventer, an engineer at Aurora Flight Sciences, sees potential applications in the industry, but he wouldn't say what they were. Satellite panels have been used with scissor systems. The viewer said that this mechanism would serve as a back-scratcher.
The latest invention to emerge from the Dice Lab, a business partnership with Robert Fathauer, a mathematical artist and puzzle designer, is the Countdown d 24. There is a card game called Magic: The Gathering that uses the Countdown d24.
One problem with some countdown dice is that they don't follow a consistent pattern, which makes it hard to find the number you want.
The Countdown d 24 is a sphericon, made from a triple-cone shape, which is then cut up, twisted around and glues back together.
The invention was the result of a collision of ideas. He collaborated with another person to make a rolling circus acrobatics apparatus.
Two cones didn't solve the problem, but three did. The result shows a clear path, with a zigzagging up and down around the die, making it easy to change the number on the die.
The die can roll along its path. The die wiggles along a chronological count. The doctor said that it was a surprise. Reality often bites back.
Dr. Segerman has been around the block before. He made the dodecahedral maze last year. The 15 Puzzle was the beginning of his craze. The 15+4 Puzzle and the Hyperbolic 29 Puzzle were created by adding hinges to the tiles.
The Hyperbolic Puzzle 29 was commented on by a person who said that it activated his fight-or-flight response. "Henry Segerman, Mad Genius" was written by Dr. Segerman's friend Rick Rubenstein.
Mr. Rubenstein and Dr. Segerman were both jugglers. Dr. Segerman takes a lot of work breaks.
He has a non-Euclidean sense of humor.
Dr. Segerman doesn't bother himself with the task of finding solutions to his puzzles.
For a rough measure of Continental Drift's complexity, he calculated that it has seven or more states. The cube has 4 1019 states. Half of Continental Drift's states are doable, according to a viewer.
One person has solved Continental drift so far. He said that he solved the problem by removing the part of the frame that was removed. He rearranged himself and the tiles to get the puzzle back together.
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