Antelope Moon Puzzle: A 1000-Piece Round Jigsaw of the Moon

By Ali Kaya

Most jigsaw puzzles give you two kinds of help before you have placed a single piece: colour to sort by and four corners to start from. The Antelope Moon Puzzle takes both away. It is a thousand pieces of grey that close into a circle 26.5 inches across, about 67 centimetres, and the picture on it is the one face of the Moon we ever get to see.

Without colour you sort by brightness. The dark, smooth pieces belong to the maria, the old lava plains that people once took for seas; the pale, pitted ones belong to the highlands; and the pieces streaked with fine white lines sit somewhere along the rays of a young crater. By the time the circle is finished you can find the big seas without a map, which is more than most of us can say after a lifetime of looking up at the real thing.

One piece is about 97 kilometres

The Moon is 3,474.8 kilometres across and the puzzle is 67.3 centimetres across, so the scale is about 1 : 5.16 million and every centimetre of cardboard is roughly 52 kilometres of ground. A circle that size has an area of π × 33.65² ≈ 3,558 cm², which leaves about 3.6 square centimetres for each of the thousand pieces — a square a little under 1.9 centimetres on a side. Carry that back to the Moon and an average piece is about 97 kilometres wide. The crater Tycho, 85 kilometres from rim to rim, would fit on one of them.

The same scale is worth carrying a little further. Earth is 12,742 kilometres across, so next to this puzzle it would be a disc about 2.47 metres wide — taller than the door of the room you are building it in. And the average distance between the two, 384,400 kilometres, shrinks to 74 metres. Put the finished Moon on the table, walk three-quarters of a football pitch away, and that is where the Earth goes. The twelve people in the list of people who have walked on the Moon crossed that gap; on the puzzle, all six landing sites sit within 20 centimetres of the centre.

The pieces at the edge hold more Moon

There is a small lie in the paragraph above, and it is the interesting part. The puzzle is flat and the Moon is not. What is printed on the cardboard is a hemisphere pressed onto a disc, the way a camera far away sees it, so a piece in the middle looks straight down at the ground while a piece at the rim looks at ground that is tilting away. If a piece sits at an angle θ from the centre of the face, the surface it shows is stretched by a factor of 1 / cos θ.

The total makes the point quickly. The disc you assemble stands for πR² ≈ 9.48 million km², but the hemisphere it is a picture of has an area of 2πR² ≈ 18.97 million km² — exactly twice as much. So the average piece really carries about 19,000 square kilometres of Moon, and the pieces do not share it equally. A piece at the very centre holds about 9,500 square kilometres, a little more than Cyprus. A piece 29 centimetres out, where θ is 60°, holds double that. In the last centimetre before the rim the factor passes four, which is why the craters there are squeezed into thin ellipses and why the border is the slowest part of the build.

Why the circle is harder than the rectangle

The cut is what puzzle makers call a ribbon cut: the pieces run in rows and columns, as they do in an ordinary rectangular puzzle, and the circle is simply laid over that grid. On a rectangle the grid and the border agree, so every edge piece has one straight side and there are four corners to anchor them. Here the border is 211 centimetres of curve crossing the grid at a different angle everywhere, so no two edge pieces are quite the same shape and there is no corner to tell you where you are. I would still start with the rim, but expect it to behave like the middle of a normal puzzle.

The thing that helps is the image itself. The print is sharp enough that small craters stay crisp at arm's length, the finish is matte so a desk lamp does not glare off it, and the box includes a double-sided poster of the whole face to work from. Sort into three trays — dark, pale and rayed — and the puzzle starts to move.

The only side there is

A puzzle of Earth would have to choose a side. The Moon chose for us: it turns once on its axis in exactly the time it takes to go once around Earth, so the same hemisphere stays pointed at us and has done for billions of years. Because the orbit is slightly oval and slightly tilted, the Moon appears to rock a little from week to week, and over time that rocking lets us see about 59 percent of the surface instead of 50. The remaining 41 percent was not seen by anyone until 1959. The picture on this puzzle is the middle of that rocking — the average face, the one on every calendar.