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Science & Mathematics

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

"Science & Mathematics - Overview" showing 22 items.

Page 1 of 3

## Model for the "Devil's Coffin" Diagram Relating to Computing the Volume of a Parallelepiped, Ross Solid

- Description
- This wooden model is one in a series illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The incomplete unpainted wooden model has two pieces. One is a cube, the second is part of a parallelepiped with one square face the same size as the cube. A paper label pasted to a square side of both pieces of the model reads: DEVIL’S COFFIN (/) Phillips & Fisher, p. 305 Van Velzer & Shutts, p. 300 (/) Wentworth, p. 303 Wells, p. 278. This is a reference to four American geometry textbooks published between 1894 and 1899.

- In the course of the 19th century, American geometry textbooks came to be more than reproductions of British works. By the 1890s, several texts discussing solid geometry used a figure demonstrating the volume of a parallelepiped that apparently arose in the United States.

- In this construction, the volume of an arbitrary parallelepiped is first compared to one constructed having the same altitude and rectangular bases equal in area to those of the original solid. This figure is then compared to a third parallelepiped, this with the same altitude and six rectangular sides. John Farrar, following A.-M. Legendre, proposed such a construction in his
*Elements of Geometry*. By the 1890s, the figure had taken a rather different form. Perhaps because it was difficult imagine from a two dimensional drawing, it was known as “the devil’s coffin.”

- Ross’s model of the construction had three parts, a parallelepiped with six sides in the shape of equilateral parallelograms, a parallelepiped with two square sides and four rhombic sides, and a cube. The parallelepipeds are dissected. The two models in the Smithsonian collections are the cube and one piece of one of the parallelepipeds.

- This model is not mentioned in Ross’s original manual for his surface forms and solids. The texts referred were published several times, but show the devil’s coffin construction on the pages indicated on the model on editions published between 1894 and 1899. Hence the date of about 1900 assigned to the model.

- References:

- A.-M. Legendre,
*Éléments de géométrie, avec des notes*, Paris: Didot, 1794, pp. 178–184, Plate 8.

- John Farrar,
*Elements of geometry, by A. M. Legrendre. Translated from the French for the use of the students at the University at Cambridge, New England*, Boston : Hilliard and Metcalf printers, 1819, pp. 134–139, plates IX and X.

- Thomas Heath, ed.,
*The Thirteen Books of Euclid’s Elements*, vol. 3, Book XI, propositions 29 and 30, especially the commentary on Proposition 30, New York: Dover, 1956, esp. pp. 333–336.

- Andrew Wheeler Phillips and Irving Fisher,
*Elements of Geometry*New York: American Book Company, 1896, p. 305–306.

- C. A. Van Velzer and George C. Shutts,
*Plane and Solid Geometry Suggestive Method*Madison, WI: Tracy Gibbs, 1894, p. 300.

- Webster Wells,
*The Elements of Geometry*, rev. ed., Boston: Leach, Shewell and Sanborn, 1894, p. 278.

- George A. Wentworth,
*Plane and Solid Geometry*, rev. ed., Boston: Ginn, 1899, p. 303.

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Ross, W. W.

- ID Number
- 1985.0112.217

- catalog number
- 1985.0112.217

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model of An Oblong or Rectangle, Ross Surface Form #3

- Description
- In 1891, William Wallace Ross (1834–1906), the superintendent of schools in Fremont, Ohio, published a set of “dissected surface forms and geometrical solids” for teaching practical geometry and measurement in schools and colleges. He also prepared a manual that describes their use. Ross extended earlier work of Albert H. Kennedy, including a much larger number of surfaces. His models would be distributed at least as late as 1917, when they were listed in the catalog of the Atlas School Supply Company of Chicago, Illinois.

- In his manual, Ross listed eighteen “surface forms”, eighteen solids or volumes, and the five Platonic or regular solids. By the time of the 1917–1918 catalog, a set of the model reportedly contained fifty pieces. The Smithsonian collections include thirteen of the surface forms, ten of which correspond to objects in the 1891 list. They also contain all or part of twelve of the solid forms, at least five of which correspond to the 1891 list.

- This is the second of Ross’s surface forms, a rectangle (or, in Ross’s language, an oblong) that measures 6 inches by 1 inch. The first surface form was a square one inch on a side. Taking the area of this square to be one square inch, students were to observe that the area of the rectangle was six square inches. A paper label attached to the model reads: Oblong 1x6.

- Compare models 1985.0112.190 through 1985.0112.202.

- References:

- W. W. Ross,
*Mensuration Taught Objectively with Lessons on Form . . . Manual for the Use of the Author’s Dissected Surface Forms and Geometrical Solids*, Fremont, Ohio, 1891.

- Atlas School Supply Company,
*Catalog No. 39 1917-18*, Chicago, Illinois, 1917, p. 86.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.190

- accession number
- 1985.0112

- catalog number
- 1985.0112.190

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model of a Rectangle or Oblong, Ross Surface Form #2

- Description
- This is the third 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 model is a 6 inch by 4 inch rectangle, divided into 24 one inch by one inch squares. A paper label attached to the model reads: Oblong 4x6.

- Comparing its area to that of a 6 inch by 1 inch rectangle (1985.0112.191), Ross noted that the area was four times 6 square inches, or 24 square inches. He generalized to argue that the area of a rectangle equaled the number of square units corresponding to the product of the length times the breadth.

- Compare models 1985.0112.190 through 1985.0112.202. For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.191

- accession number
- 1985.0112

- catalog number
- 1985.0112.191

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model of a Rectangle Bisected into Two Right Triangles, Ross Surface Form #8

- Description
- This is the eighth 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 rectangular wooden model is bisected along a diagonal. A paper label pasted to the model reads: Oblong 4x6 Bisected. According to Ross, this model demonstrates that a right-angled triangle with unequal sides adjacent to the right angle has half the area of a rectangle.

- Compare models 1985.0112.190 through 1985.0112.202. For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.192

- accession number
- 1985.0112

- catalog number
- 1985.0112.192

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model of a Dissected Trapezoid, Ross Surface Form #6

- Description
- This is the sixth 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 rectangular wooden model is cut into two pieces at one corner. It may be arranged so that the pieces form either a rectangle or a trapezoid. A paper label attached to the model reads: Dissected Trapezoid 5x7.

- Ross argued that the area of the trapezoid equaled half the sum of its parallel sides, multiplied by its breadth.

- Compare models 1985.0112.190 through 1985.0112.202. For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.193

- accession number
- 1985.0112

- catalog number
- 1985.0112.193

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Dissected Polygon, Probably a Ross Surface Form

- Description
- This unpainted wooden model consists of two doweled pieces that can be arranged as a quadrilateral. The model is incomplete. It resembles other Ross surface forms.

- Compare models 1985.0112.190 through 1985.0112.202, especially 1985.0112.193. For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.194

- accession number
- 1985.0112

- catalog number
- 1985.0112.194

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Rectangle Transformable Into an Obtuse Triangle, Probably a Ross Surface Form

- Description
- This is apparently is one 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 three doweled pieces of this unpainted wooden model can be arranged either as a rectangle or as an obtuse-angled triangle.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.195

- accession number
- 1985.0112

- catalog number
- 1985.0112.195

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Dissected Rhomboid, Ross Surface Form #5 (incomplete)

- Description
- This is the fifth 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 model is divided into two pieces, with the smaller piece missing.

- With the smaller piece, the model could be arranged either as a parallelogram or a rectangle. A paper label attached to the model reads: Dissected Rhomboid 4x6.

- Ross argued that the parallelogram (or, in his terminology, rhomboid), like the rectangle, was the product of its length and its altitude.

- Compare models 1985.0112.190 through 1985.0112.202.

- For further information about Ross models, including references, see 1985.0112.191.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.196

- accession number
- 1985.0112

- catalog number
- 1985.0112.196

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Dissection of a Parallelogram into Triangles, Ross Surface Form #9

- Description
- This is the ninth 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 parallelogram (rhomboid in Ross’s terminology) is bisected along a diagonal into two scalene triangles. A paper label attached to the model reads: Rhomboid A 4x6 Bisected. According to Ross, the model shows that if a rhomboid (parallelogram) is cut diagonally through the opposite acute angles, two equal obtuse-angled triangles result.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.197

- catalog number
- 1985.0112.197

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Dissection of a Parallelogram into Triangles, Ross Surface Form #10

- Description
- This is the tenth 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 rhomboid (parallelogram) is bisected along a diagonal into two scalene triangles. Two adjacent sides on the left are equal, as are two adjacent sides on the right. A paper label attached to the model reads: Rhomboid B 4x6 Bisected. According to Ross, the model shows that if a rhomboid is cut diagonally through the obtuse angles, two equal scalene triangles result.

- Location
- Currently not on view

- date made
- ca 1895

- maker
- Ross, W. W.

- ID Number
- 1985.0112.198

- catalog number
- 1985.0112.198

- accession number
- 1985.0112

- Data Source
- National Museum of American History, Kenneth E. Behring Center