Dissected Square, Ross Surface Form #11
date: label: date made
content: ca 1895
name: label: maker
content: Ross, W. W.
notes: label: Description
content: This is the eleventh in a series of models of plane figures (surface forms) designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The unpainted wooden square is bisected along one diagonal, with wooden dowels to hold the pieces together. Along the other diagonal, one of the triangles is bisected. On the back, an inscribed circle is indicated as well as the radius of the circle and a square inscribed inside it. A paper label glued to the object reads: SQUARE 6x6.
label: Description
content: This is the first in a series of models in which Ross considered the area of a regular polygon to be made up of isosceles triangles, with base equal to the length of the side of the polygon and height equal to the radius of the inscribed circle. Summing the area of the triangles, he found that the total area equaled half the perimeter of the polygon times the radius. In this case, each of the four triangles had base 6, height 3 (the radius of the inscribed circle), and area 9. The perimeter is 4x6 or 24, half the perimeter is 12, and the area is 36. This was the same area found by multiplying the length of the sides of the square.
label: Description
content: Although they are not listed in his 1891 <I>Manual</I>, Ross also would make models of regular polygons with 8 and with 16 sides, similarly divided into triangular sectors. Examples of these have catalog numbers 1985.0112.201 and 1985.0112.202. He then, like A. H. Kennedy before him, generalized the dissection to represent the area of a circle (see 1985.0112.203).
label: Description
content: For further information about Ross models, including references, see 1985.0112.190.
label: Location
content: Currently not on view
place: label: place made
content: United States: Ohio, Fremont
topic: label: Subject
content: Mathematics
setName: label: See more items in
content: Medicine and Science: Mathematics
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content: Science & Mathematics
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content: Arithmetic Teaching
creditLine: label: Credit Line
content: Gift of Wesleyan University
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 1985.0112.200
label: catalog number
content: 1985.0112.200
label: accession number
content: 1985.0112
objectType: label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: wood (overall material)
label: Measurements
content: overall: 1 cm x 15.3 cm x 15.3 cm; 13/32 in x 6 1/32 in x 6 1/32 in