A new puzzle turns the Earth into a Rubik's Cube, but more complex
Another orbit around the sun and we're back: back to where we started, but we've turned around – changed, maybe disturbed.
Henry Segerman, British-American mathematician and mathematical artist from Oklahoma State University, invented the puzzle for this puzzling annual event: Continental Drift, a 3D sliding puzzle that debuted earlier this year. The underlying geometric concept is holonomy: when you loop through a curved surface and return to the starting point, you arrive somewhat flipped, rotated, perhaps 180 degrees.
"Take a mathematical idea, can you make it happen?" - this question, said Dr. Segerman, is what drives his inventions.
He is passionate about visualizing mathematics, whether with 3D printing (he wrote a book on the subject) or through non-Euclidean virtual reality experiences. But Dr. Segerman suffers from aphantasia, an inability to construct mental images, or "visually hallucinate images at will", as he puts it. This could explain his passion for making concrete images, especially the impressive collection he produced in 2022.
Continental Drift is Earth in miniature, mapped on a truncated icosahedron - a soccer ball - with its regular patchwork of 12 pentagonal faces and 20 hexagonal faces.
Continental Drift Puzzle.CreditCredit...Brett Deering for The New York TimesThe design inspiration was a Victorian craze: the classic 15 Puzzle, in which square tiles numbered 1 through 15 are jumbled on a 4-by-4 grid, with one square left empty; you solve the puzzle by sliding the tiles in numerical order.
In Continental Drift, a spherical version of the 15 Puzzle, it is the hexagonal tiles that are shuffled. (The pentagons are indented and stand still.) "One of the hexagons, this one in the South Pacific, is sticking out," says Dr. Segerman on his YouTube channel. "We can then activate the San Andreas Rift and slide California south into the ocean. And we can continue, mixing all the continents together."
Holonomy occurs when a tile travels a complete loop along the curved surface of the puzzle: slide the tile with, say, Greenland all the way around the perimeter of a single pentagonal tile - perhaps the tile representing the 'North Atlantic. After a full loop, the Greenlanders return to their starting position rotated 60 degrees. If the loop encompasses two adjacent pentagons, the tile returns to the starting point with a rotation of 120 degrees. And so on.
Maker mathDr. Segerman's more formal research is in topology, the study of geometric objects without regard to lengths or angles. "All you're left with is how things are connected - how many holes a thing has, and so on," he said. As an old topology joke goes: "A topologist is someone who can't tell the difference between a coffee cup and a donut."
" Henry is a mathematician who likes to do,” said his younger brother and sometimes collaborator, Wil...
Another orbit around the sun and we're back: back to where we started, but we've turned around – changed, maybe disturbed.
Henry Segerman, British-American mathematician and mathematical artist from Oklahoma State University, invented the puzzle for this puzzling annual event: Continental Drift, a 3D sliding puzzle that debuted earlier this year. The underlying geometric concept is holonomy: when you loop through a curved surface and return to the starting point, you arrive somewhat flipped, rotated, perhaps 180 degrees.
"Take a mathematical idea, can you make it happen?" - this question, said Dr. Segerman, is what drives his inventions.
He is passionate about visualizing mathematics, whether with 3D printing (he wrote a book on the subject) or through non-Euclidean virtual reality experiences. But Dr. Segerman suffers from aphantasia, an inability to construct mental images, or "visually hallucinate images at will", as he puts it. This could explain his passion for making concrete images, especially the impressive collection he produced in 2022.
Continental Drift is Earth in miniature, mapped on a truncated icosahedron - a soccer ball - with its regular patchwork of 12 pentagonal faces and 20 hexagonal faces.
Continental Drift Puzzle.CreditCredit...Brett Deering for The New York TimesThe design inspiration was a Victorian craze: the classic 15 Puzzle, in which square tiles numbered 1 through 15 are jumbled on a 4-by-4 grid, with one square left empty; you solve the puzzle by sliding the tiles in numerical order.
In Continental Drift, a spherical version of the 15 Puzzle, it is the hexagonal tiles that are shuffled. (The pentagons are indented and stand still.) "One of the hexagons, this one in the South Pacific, is sticking out," says Dr. Segerman on his YouTube channel. "We can then activate the San Andreas Rift and slide California south into the ocean. And we can continue, mixing all the continents together."
Holonomy occurs when a tile travels a complete loop along the curved surface of the puzzle: slide the tile with, say, Greenland all the way around the perimeter of a single pentagonal tile - perhaps the tile representing the 'North Atlantic. After a full loop, the Greenlanders return to their starting position rotated 60 degrees. If the loop encompasses two adjacent pentagons, the tile returns to the starting point with a rotation of 120 degrees. And so on.
Maker mathDr. Segerman's more formal research is in topology, the study of geometric objects without regard to lengths or angles. "All you're left with is how things are connected - how many holes a thing has, and so on," he said. As an old topology joke goes: "A topologist is someone who can't tell the difference between a coffee cup and a donut."
" Henry is a mathematician who likes to do,” said his younger brother and sometimes collaborator, Wil...
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