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Drawn Mathematics

Mathematics you can see, draw, and fold.

Borrow These Drawings

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The diagrams and data files that Drawn Mathematics makes itself are free to reuse. Put them in a worksheet, a slide, a quilt pattern or a book, change them, sell what you make, and give credit.

The site's own diagrams and data files

The site's own diagrams, and the CSV files offered with its articles, are released under the Creative Commons Attribution 4.0 International license (CC BY 4.0, https://creativecommons.org/licenses/by/4.0/). You may copy, adapt and republish them for any purpose, including commercial use, as long as you give credit.

Each diagram carries two credits. The short one sits under the figure:

Diagram: Drawn Mathematics, CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

The full credit line, which you can copy, takes this form:

"[figure title]" by Drawn Mathematics, [article URL], licensed under CC BY 4.0, https://creativecommons.org/licenses/by/4.0/

Use the full line when you republish a diagram. Credit a CSV file the same way, with the address of the article it comes from. A link back to the article is one reasonable way to give that credit and is appreciated, but it is not a condition added on top of the license.

The license covers only what this site draws. When a diagram lays construction lines over a public-domain painting, the license covers the overlay alone, and the painting underneath is credited as public domain with its basis. The credit for such an overlay reads "The license covers the overlay only. Base image:" followed by the full credit for the painting. When a diagram is drawn over an image licensed CC BY-SA, the combined image follows that image's ShareAlike license, and its credit line names that license instead of CC BY.

Paintings, plates and photographs from other sources

Images from museums, archives and open collections keep their own licenses. Each one is credited in full under the image, in this form:

"[title]" by [creator] — [source page] — [license] ([license URL])

When an image was cropped, adjusted or marked up, its credit ends with "; modified:" and a list of the changes. The credit names the creator, not the institution or the person who uploaded the file, unless the source asks for that.

A public-domain image states why it is public domain, usually the creator's year of death and the jurisdiction, for example "Public domain (author d. 1472; PD worldwide)". A painting from a museum that releases its images under CC0 is credited as public domain, with the painter's year of death and a note that the museum released the image under CC0.

Images are used only if they are in the public domain or under CC0, the Public Domain Mark, CC BY or CC BY-SA. Images under NonCommercial or NoDerivatives licenses are not used. If you reuse one of these images, follow its own license and credit rather than the CC BY terms above, and confirm them on the source page named in the credit.

Data and reference sources

  • Natural Earth coastline data (version 5.1.2) is in the public domain. Coastline lengths that this site computes from it are marked as the site's own illustrative measurements, with Natural Earth named as the source.
  • Markus Kuhn, "A4 paper format / International standard paper sizes" (https://www.cl.cam.ac.uk/~mgk25/iso-paper.html) is licensed CC BY 4.0. Paper-size values on this site are recalculated from their definition; wherever that page is cited or adapted, it is credited with Markus Kuhn's name, the page address and CC BY 4.0.
  • Rijksmuseum collection data, The Metropolitan Museum of Art Open Access data and National Gallery of Art (Washington) open data are released under CC0. Facts taken from them, such as dates, materials, dimensions and object numbers, are credited to the museum by name and object number. No credit implies that any museum endorses this site.
  • The National Gallery, London publishes the key facts about its paintings, such as date, medium and dimensions, under CC0. Facts taken from them are credited to the gallery by name and inventory number, for example NG1314.
  • Wolfram MathWorld is copyrighted. It is consulted for checking only: no text, figure or table from it is reproduced here.

Scene illustrations

A small share of the pictures on the site are scene illustrations. They are not released under CC BY. Each one carries this credit and these use terms:

Illustration: Drawn Mathematics. Generated scene illustration — not a photograph, historical image or researched reconstruction. Use terms: may be reused with credit to "Drawn Mathematics"; provided without any claim of historical accuracy.

These pictures set a scene and nothing more. Their clothing, buildings and objects are not evidence of anything in the text, and on share images they carry an Illustration label.

Fonts

The typefaces are STIX Two Text for headings, Open Sans for body text and Commit Mono for data and captions. All three are released under the SIL Open Font License 1.1 (https://openfontlicense.org/open-font-license-official-text/), and all three are served from this site.

Mathematical symbols that these typefaces lack, such as √, ≈ and ∠, come from STIX Two Math, also released under the SIL Open Font License 1.1 and served from this site. A browser downloads it only when a page uses one of those symbols.

Citing a page

Every article carries a Cite this page block. It gives the site name, the article title, the date of first publication, the date of the last substantial revision and the page's permanent address, plus the date you accessed it. Cite the page by that address: Drawn Mathematics does not issue DOIs, and no citation here carries one.

When an article is substantially revised, the revision date in its citation block changes, and the change is listed on Corrections and redraws.