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The game starts with an arbitrary number (n) of dots or crosses. At each turn, the player chooses to add either a dot, or a cross, along the line they have just drawn. The duration of the game lays between (2n) and (5n − 2), depending on the number of dots or crosses having been added. For n = 1, starting with a dot, the game will end after 2 ...
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When counting dots near the boundary of the shape as 1/2, there are 69 interior dots and 20 boundary dots for an estimated area of 79, close to the actual area of 25 π ≈ 78.54. A dot planimeter is a device used in planimetrics for estimating the area of a shape, consisting of a transparent sheet containing a square grid of dots. To estimate ...
Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Pages in category "Unsolved problems in geometry" The following 48 pages are in ...
Thus a single line can be drawn connecting all nine dots—which would appear as three lines in parallel on the paper, when flattened out. [18] It is also possible to fold the paper flat, or to cut the paper into pieces and rearrange it, in such a way that the nine dots lie on a single line in the plane (see fold-and-cut theorem). [17]