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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 the area of a shape, the sheet is overlaid on the shape and the dots within the shape are counted.
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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 ).
Dots and boxes is a pencil-and-paper game for two players (sometimes more). It was first published in the 19th century by French mathematician Édouard Lucas, who called it la pipopipette. [1] It has gone by many other names, [2] including dots and dashes, game of dots, [3] dot to dot grid, [4] boxes, [5] and pigs in a pen. [6]
Initially, paper was ruled by hand, sometimes using templates. [1] Scribes could rule their paper using a "hard point," a sharp implement which left embossed lines on the paper without any ink or color, [2] or could use "metal point," an implement which left colored marks on the paper, much like a graphite pencil, though various other metals were used.
Graph paper, coordinate paper, grid paper, or squared paper is writing paper that is printed with fine lines making up a regular grid. It is available either as loose leaf paper or bound in notebooks or Graph Books. It is commonly found in mathematics and engineering education settings, exercise books, and in laboratory notebooks.
The dot pattern is a two-dimensional barcode; the most common is the proprietary Anoto dot pattern. In the Anoto dot pattern, the paper is divided into a grid with a spacing of about 0.3 mm, a dot is printed near each intersection offset slightly in one of four directions, a camera in the pen typically records a 6 x 6 groups of dots.
The Ben Day process is a printing and photoengraving technique for producing areas of gray or (with four-color printing) various colors by using fine patterns of ink on the paper. It was developed in 1879 [ 1 ] by illustrator and printer Benjamin Henry Day Jr. (son of 19th-century publisher Benjamin Henry Day ). [ 2 ]