Editing Graph paper

{{short description|Writing paper with a grid}}
[[File:Graph-paper-10sqsm-5sqin-4sqin.jpg|thumb|upright=1.35|Three styles of [[loose leaf]] graph paper: 10 squares per centimeter ("millimeter paper"), 5 squares per inch (“engineering paper"), 4 squares per inch (“quad paper")]]

'''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 [[notebook]]s or graph books.

It is commonly found in mathematics and engineering education settings, [[exercise book]]s, and in [[laboratory notebook]]s. 

The lines are often used as guides for [[mathematical notation]], plotting [[graph of a function|graphs of function]]s or [[experimental data]], and drawing [[curve]]s.

== History ==
The [[Metropolitan Museum of Art]] owns a pattern book dated to around 1596 in which each page bears a grid [[woodblock printing|printed with a woodblock]]. The owner has used these grids to create block pictures in black and white and in colour.<ref>John Boardley, [https://ilovetypography.com/2019/07/27/the-first-fashion-books-renaissance-pixel-fonts-and-the-invention-of-graph-paper/ 'The first fashion books, Renaissance pixel fonts & the invention of graph paper'], ''I Love Typography'', 27 July 2019.</ref>

The first commercially published "coordinate paper" is usually attributed to a Dr. Buxton of England, who patented paper printed with a rectangular coordinate grid, in 1794.<ref>{{cite web |url=http://www.math.yorku.ca/SCS/Gallery/milestone/milestone.pdf |title=Milestones in the history of thematic cartography, statistical graphics, and data visualization |publisher=York University |first1=Michael |last1=Friendly |first2=Daniel J. |last2=Denis |page=13 |date=5 July 2006}}</ref> A century later, E. H. Moore, a distinguished mathematician at the University of Chicago, advocated usage of paper or [[exercise book]]s with "squared lines" by students of high schools and universities.<ref>{{cite web |url=https://micromath.wordpress.com/2008/08/07/graphed-paper/ |title=Graphed Paper |work=Mathematics under the Microscope |first=Alexandre |last=Borovik |date=7 August 2008 |access-date=25 March 2017}}</ref> The 1906 edition of ''Algebra for Beginners'' by H. S. Hall and S. R. Knight included a strong statement that "the squared paper should be of good quality and accurately ruled to inches and tenths of an inch. Experience shows that anything on a smaller scale (such as 'millimeter' paper) is practically worthless in the hands of beginners."<ref name="pballew-graph">{{cite web |url= https://www.academia.edu/41452953|title= Notes on the History of Graph Paper|last= Ballew|first= Pat|date= January 2011|website= www.academia.edu|publisher= [[academia.edu]]|access-date= 8 June 2020}}</ref>

The term "graph paper" did not catch on quickly in American usage. ''A School Arithmetic'' (1919) by H. S. Hall and F. H. Stevens had a chapter on graphing with "squared paper". ''Analytic Geometry'' (1937) by W. A. Wilson and J. A. Tracey used the phrase "coordinate paper". The term "squared paper" remained in British usage for longer; for example it was used in ''Public School Arithmetic'' (2023) by W. M. Baker and A. A. Bourne published in London.<ref name="pballew-graph"/>

== Formats ==
* '''Quad paper''', sometimes referred to as '''quadrille paper''' from French quadrillé, 'large square',<ref>{{cite encyclopedia |url=https://en.oxforddictionaries.com/definition/quadrille#quadrille_Noun_300 |archive-url=https://web.archive.org/web/20160924215232/https://en.oxforddictionaries.com/definition/quadrille#quadrille_Noun_300 |url-status=dead |archive-date=24 September 2016 |title=quadrille |encyclopedia=Oxford Living Dictionaries |publisher=Oxford University Press |year=2017}}</ref> is a common form of graph paper with a sparse grid printed in light blue or gray and right to the edge of the paper. In the [[United States|U.S.]] and [[Canada]], it often has two, four or five squares per inch for work not needing too much detail. In [[Europe]], it usually has 5 [[Millimetre|mm]] by 5 mm squares. It is used in mathematical [[exercise book]]s and [[Lab notebook]]s.
* '''Dot grid paper''' uses dots at intersections instead of gridlines. It is often used for [[Bullet Journal|bullet journalling]].
* '''Engineering paper''', or an '''engineer's pad''',<ref name="mit-pset">{{cite web |url=http://web.mit.edu/me-ugoffice/communication/pset-format.pdf |title=The Preparation of Engineering Problem Sets |publisher=Massachusetts Institute of Technology |agency=Technical Communications in Mechanical Engineering |access-date=25 March 2017}}</ref> is traditionally printed on light green or tan translucent paper. It may have four, five or ten squares per inch. The grid lines are printed on the back side of each page and show through faintly to the front side.  Each page has an unprinted margin.  When [[Photocopier|photocopied]] or [[Image scanner|scanned]], the grid lines typically do not show up in the resulting copy, which often gives the work a neat, uncluttered appearance.  In the U.S. and Canada, some engineering professors require student [[homework]] to be completed on engineering paper.<ref name="mit-pset"/><ref>{{cite web |url=http://eng.auburn.edu/cheweb/student/Homework_Format.pdf |title=Required Homework Format |agency=Department of Chemical Engineering |publisher=Auburn University |access-date=25 March 2017}}</ref>
* '''Millimeter paper''' has ten squares per centimeter and is used for [[technical drawing]]s.
* '''Hexagonal paper''' shows regular hexagons instead of squares. These can be used to map geometric [[Tiling by regular polygons|tiled or tesselated]] designs among other uses.
* '''Isometric graph paper''' or '''3D graph paper''' is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. The triangles are arranged in groups of six to make hexagons. The name suggests the use for [[isometric projection|isometric views]] or pseudo-three-dimensional views. Among other functions, they can be used in the design of trianglepoint [[embroidery]]. It can be used to draw angles accurately.
* '''Logarithmic paper''' has rectangles drawn in varying widths corresponding to [[logarithmic scale]]s for [[semi-log plot]]s or [[log-log plot]]s.
* '''Normal [[probability]] paper''' is another graph paper with rectangles of variable widths. It is designed so that "the graph of the normal distribution function is represented on it by a straight line", i.e. it can be used for a [[normal probability plot]].<ref name="eom-prob">{{cite encyclopedia |url=http://www.encyclopediaofmath.org/index.php?title=Probability_graph_paper&oldid=11790 |title=Probability graph paper |encyclopedia=Encyclopedia of Mathematics |first=A. V. |last=Prokhorov |year=2011 |access-date=18 January 2014}}</ref>
* '''Polar coordinate paper''' has concentric circles divided into small arcs or 'pie wedges' to allow plotting in [[polar coordinate system|polar coordinates]].
* '''Ternary (triangular) graph paper''' has an equilateral triangle, divided into smaller equilateral triangles with usually 10 or more divisions per edge. It is used to plot compositional percentages of in systems that have three constituents or three dimensions. (see [[ternary plot]])

In general, graphs showing grids are sometimes called '''Cartesian''' graphs because the square can be used to map measurements onto a [[Cartesian coordinate system|Cartesian]] coordinate system.

== Examples ==
<gallery mode="packed" heights="180px">
File:graph-paper.svg|Regular graphing paper
File:Log paper.svg|Log-log graphing paper
File:LogPapierY.PNG|Semi-log graphing paper
File:Probability Graph Paper Template-landscape.png|Normal Probability paper
</gallery>

<gallery mode="packed" heights="180px">
File:Isometric graph paper, US letter size SVG.svg|Isometric graphing paper
File:PolarPapier.PNG|Polar coordinate paper
File:Engineering-pad-simulation.gif|Engineering paper
File:Ternary graph paper - 50 divisions per side.png|Ternary graph paper
</gallery>

<gallery mode="packed" heights="180px">
File:Russian school graph paper.jpg|Squared [[exercise book]] used in [[Russia]]n schools (12 and 18 sheets)
File:Graph-ruled_composition_book,_4_squares_per_inch,_80_pages.jpg|Graph [[exercise book|composition book]] used in the [[United States]] (80 sheets)
File:Two styles of graph paper (5843580902).jpg|Two styles of [[loose leaf]] graph paper
</gallery>

== See also ==
* [[Ruled paper]]
* [[Examination book]]

== References ==
{{reflist}}

== External links ==
{{commons category|Graph paper}}
* [http://www.print-graph-paper.com/ Graph paper downloads] at Print-graph-paper.com

{{Paper}}

{{Use dmy dates|date=March 2017}}

{{DEFAULTSORT:Graph Paper}}
[[Category:Printing and writing paper]]
[[Category:Engineering equipment]]
[[Category:Technical drawing]]
[[Category:Mathematical tools]]