In the event of a government shutdown, American History will remain OPEN through at least Saturday, October 7, by using prior year funds. Visit for updates.

Sixteen-Sided Regular Polygon, Ross Surface Form

Sixteen-Sided Regular Polygon, Ross Surface Form

<< >>
Usage conditions apply
This is one of the models of plane figures (surface forms) designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The flat unpainted wooden object is in the shape of a regular polygon with sixteen sides. On the opposite side from the paper label, it has eight straight lines drawn joining opposite vertices, dividing the polygon into 16 equal triangles. The lines meet at a point. The label reads: POLYGON OF 16 SIDES.
In constructing his visual demonstration of the area of a circle, Ross built several regular polygons, and showed that they had areas equal to the sum of the area of triangles with height equal to the radius of an inscribed circle and sides equal to the sides of the polygons. In other words, the area of the regular polygon equaled half the perimeter of the polygon times the radius of the inscribed circle.
This is the example for a 16-sided figure. Compare 1985.0112.200 and 1985.0112.201. For the circle, see 1985.0112.203. For further information about Ross models, including references, see 1985.0112.190.
Currently not on view
Object Name
geometric model
date made
ca 1895
Ross, W. W.
place made
United States: Ohio, Fremont
Physical Description
wood (overall material)
overall: 1 cm x 15 cm x 15 cm; 13/32 in x 5 29/32 in x 5 29/32 in
ID Number
catalog number
accession number
Credit Line
Gift of Wesleyan University
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Arithmetic Teaching
Data Source
National Museum of American History
Nominate this object for photography.   

Our collection database is a work in progress. We may update this record based on further research and review. Learn more about our approach to sharing our collection online.

If you would like to know how you can use content on this page, see the Smithsonian's Terms of Use. If you need to request an image for publication or other use, please visit Rights and Reproductions.

Note: Comment submission is temporarily unavailable while we make improvements to the site. We apologize for the interruption. If you have a question relating to the museum's collections, please first check our Collections FAQ. If you require a personal response, please use our Contact page.