Trapezium or Quadrilateral, Ross Surface Form

Description:

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 1985.0112.190.

Date Made: ca 1895

Maker: Ross, W. W.

Location: Currently not on view

Place Made: United States: Ohio, Fremont

Subject: Mathematics

Subject:

See more items in: Medicine and Science: Mathematics, Science & Mathematics, Arithmetic Teaching

Exhibition:

Exhibition Location:

Credit Line: Gift of Wesleyan University

Data Source: National Museum of American History

Id Number: 1985.0112.199Catalog Number: 1985.0112.199Accession Number: 1985.0112

Object Name: geometric model

Physical Description: wood (overall material)Measurements: overall: 1 cm x 15.7 cm x 10 cm; 13/32 in x 6 3/16 in x 3 15/16 in

Guid: http://n2t.net/ark:/65665/ng49ca746a5-1820-704b-e053-15f76fa0b4fa

Record Id: nmah_694076

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.