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.
 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.
 Location

Currently not on view
 date made

ca 1895
 maker

Ross, W. W.
 ID Number

1985.0112.199
 catalog number

1985.0112.199
 accession number

1985.0112