Smithsonian museums continue to be closed to support the effort to contain the spread of COVID-19. Read a message from our director, and check our website and social media for updates.

Trapezium or Quadrilateral, Ross Surface Form

Trapezium or Quadrilateral, Ross Surface Form

<< >>
Usage conditions apply
This is one of a series of models of plane figures (surface forms) designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. This example, what Ross called a “trapezium,” is a quadrilateral with four unequal sides, none of them parallel. A diagonal groove joining two opposite vertices, dividing the quadrilateral into two triangles. Ross recommended finding the area of these triangles from the length of their sides.
A paper sticker attached to the model reads: Trapezium. Another sticker reads: SCALENE TRIANGLE. A second mark on this sticker reads: It is the only operation for which the Ross Blocks have no objective proof or illustration, such objective proof is probably impossible.
This model is not listed in Ross’s 1891 manual. Here he had written: “The trapezium is measured by dividing it up into triangles. This disposes of all the quadrilaterals.” He apparently revised this view.
If none of the angles of an arbitrary convex quadrilateral is known, knowing the length of the sides does not suffice to determine the area of the figure.
Compare models 1985.0112.190 through 1985.0112.202. For further information about Ross models, including references, see 1985.0112.191.
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 15.7 cm x 10 cm; 13/32 in x 6 3/16 in x 3 15/16 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.


Add a comment about this object