#
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 2797 items.

Page 121 of 280

## Dissected Circle Transformable into Parallelogram

- Description
- In the years following the Civil War, a handful of American educators designed and sold wooden solids or flat shapes hinged or doweled so that they could be transposed into other shapes that had areas known to students. One of them was Albert H. Kennedy (1848–1940), Superintendent of Schools in Rockport, Indiana. He sold this business to the Rockport School Desk Company. Modified forms of the solids would be sold by the Western School Supply House of Des Moines, Iowa, A. Cowles and Company of Chicago, Illinois, and the American School Furniture Company of Chicago.

- From ancient times, mathematicians sought to find a polygon with straight sides equal in area to the circle. This model represents Kennedy’s attempt to demonstrate that the area of a circle equaled half of the product of its circumference and its radius. It consists of a dissected circle, transformable into a parallelogram. The circle has of two semicircular portions. Each portion is divided into eight equal wooden segments, which are held together by cloth tape that is nailed to each segment around the circumference. Rearranging the pieces gives a rough parallelogram that has one side equal to half the circumference of the circle and a height equal to the radius. Multiplying the two factors together gives the desired area.

- In 1882, the German mathematician Lindemann demonstrated that no exact geometric squaring of the circle is possible. His work undoubtedly was unknown to Kennedy.

- The object has no maker's marks.

- Compare 2005.0054.01, 2005.0054.02, 2005.0054.03 and 2005.0054.04.

- References:

*Arithmetic of Practical Measurements for Teachers' Instruction and Class Work in Mensuration. Published by Western School Supply House*, Des Moines: Iowa Printing Co., 1893. This reportedly was ”To accompany Kennedy’s improved dissecting mathematical blocks. 20th ed.” A copy of the sixteenth edition, which has the same date, is 2005.3099.01.

- C. L. F. von Lindemann, “Über die Zahl π,”
*Mathematische Annalen*, 20 (1882), 215.

- “Paintings Presented to Local Schools,”
*Rockport Journal*May 15, 1964.

- P. A. Kidwell, "American Mathematics Viewed Objectively: The Case of Geometric Models," in
*Vita Mathematica: Historical Research and Integration with Teaching*, ed. Ronald Calinger, Washington, D.C.: Mathematical Association of America, 1996, pp. 197–207.

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Kennedy, Albert H.

- ID Number
- 2005.0054.01

- catalog number
- 2005.0054.01

- accession number
- 2005.0054

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

## Dissected Cylinder Transformable into Block

- Description
- In the years following the Civil War, a handful of American educators designed and sold wooden solids or flat shapes hinged or doweled so that they could be transposed into other shapes that had areas known to students. One such educator was Albert H. Kennedy (1848–1940), superintendent of schools in Rockport, Indiana. He sold this business to the Rockport School Desk Company. Modified forms of the solids were later offered by the Western School Supply House of Des Moines, Iowa, A. Cowles and Company of Chicago, Illinois, and the American School Furniture Company of Chicago.

- This model is a generalization on Kennedy’s model showing the area of a circle, applied to the problem of finding the volume of a cylinder. The cylinder consists of two semicylindrical portions. Each portion is divided into eight equal wooden segments, which are held together by two pieces of cloth tape that are nailed around the circumference. Rearranging the pieces gives a rough block that has one side equal to half the circumference of the circle, one side height equal to the radius, and one side equal to the height of the cylinder. Multiplying the three factors together gives the desired volume.

- The object has no maker's marks.

- Compare 2005.0054.01, 2005.0054.02, 2005.0054.03 and 2005.0054.04.

- References:

*Arithmetic of Practical Measurements for Teachers' Instruction and Class Work in Mensuration. Published by Western School Supply House*, Des Moines: Iowa Printing Co., 1893. This reportedly was ”To accompany Kennedy’s improved dissecting mathematical blocks. 20th ed.” A copy of the sixteenth edition, which has the same date, is 2005.3099.01.

- “Paintings Presented to Local Schools,”
*Rockport Journal*May 15, 1964.

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Kennedy, Albert H.

- ID Number
- 2005.0054.02

- catalog number
- 2005.0054.02

- accession number
- 2005.0054

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

## Dissected Cone

- Description
- In the years following the Civil War, a handful of American educators designed and sold wooden solids or flat shapes hinged or doweled so that they could be transposed into other shapes that had areas known to students. One such person was Albert H. Kennedy (1848–1940), superintendent of schools in Rockport, Indiana. He sold this business to the Rockport School Desk Company. Modified forms of the solids were sold by the Western School Supply House of Des Moines, Iowa, A. Cowles and Company of Chicago, Illinois, and the American School Furniture Company of Chicago.

- This model is of a dissected cone. The cone consists of twelve wooden triangular pyramids, with an extra section at the bottom of each prism. The pyramids are held together by cloth tape that is nailed around the circumference at the bottom.

- The object has no maker's marks.

- Compare 2005.0054.01, 2005.0054.02, 2005.0054.03 and 2005.0054.04.

- References:

*Arithmetic of Practical Measurements for Teachers' Instruction and Class Work in Mensuration. Published by Western School Supply House*, Des Moines: Iowa Printing Co., 1893. This reportedly was ”To accompany Kennedy’s improved dissecting mathematical blocks. 20th ed.” A copy of the sixteenth edition, which has the same date, is 2005.3099.01.

- “Paintings Presented to Local Schools,”
*Rockport Journal*May 15, 1964.

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Kennedy, Albert H.

- ID Number
- 2005.0054.03

- catalog number
- 2005.0054.03

- accession number
- 2005.0054

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

## Dissected Sphere

- Description
- In the years following the Civil War, a handful of American educators designed and sold wooden solids or flat shapes hinged or doweled so that they could be transposed into other shapes with areas known to students. One such person was Albert H. Kennedy (1848-1940), superintendent of schools in Rockport, Indiana. He sold this business to the Rockport School Desk Company. Modified forms of the solids would be sold by the Western School Supply House of Des Moines, Iowa, A. Cowles and Company of Chicago, Illinois, and the American School Furniture Company of Chicago.

- This model is of a sphere dissected into eight wedges, each wedge being subdivided into four segments that are roughly square pyramids. It has a red leather base and eight bands of coated cloth tape nailed to hold the segments together. A string at the top goes around nails protruding from each of the wedges to hold them together.

- The object has no maker's marks.

- Compare 2005.0054.01, 2005.0054.02, 2005.0054.03 and 2005.0054.04.

- References:

- “Paintings Presented to Local Schools,”
*Rockport Journal*May 15, 1964.

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Kennedy, Albert H.

- ID Number
- 2005.0054.04

- catalog number
- 2005.0054.04

- accession number
- 2005.0054

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

## New Math Flash Cards, Subtraction

- Description
- From the 1950s, particularly after the launch of the Sputnik satellite in 1958, American mathematicians and mathematics educators introduced a variety of reforms in mathematics teaching dubbed “The New Math.” This set of flash cards reflects the way of presenting subtraction problems that emerged.

- The set consists of fifty cards, printed with subtraction problems on each side. The problems are written crosswise, with a box for the answer. The solution is printed in red in the upper left corner on the back. Another card lists basic subtraction facts (vertically), and three cards give work sheets and directions.

- A mark on the paper box reads: MILTON BRADLEY (/) NEW MATH (/) FLASH CARDS (/) SUBTRACTION. Another mark reads: [copyright] 1965. A third mark reads: 4592.

- Compare 2005.0055.06, 2005.0055.07, 2005.0055.08, and 2005.0055.09.

- Location
- Currently not on view

- date made
- ca 1965

- maker
- Milton Bradley Company

- ID Number
- 2005.0055.06

- catalog number
- 2005.0055.06

- accession number
- 2005.0055

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

## New Math Flash Cards, Addition-Subtraction

- Description
- From the 1950s, particularly after the launch of the Sputnik satellite in 1958, American mathematicians and mathematics educators introduced a variety of reforms in mathematics teaching dubbed “The New Math.” This set of flash cards reflects the way of presenting addition and subtraction problems that emerged.

- The set consists of flash cards showing sums written out horizontally on one side and differences written out horizontally on the other. A blank square indicates where the answer is to go. The cards are numbered from 1 to 81, with several missing and some duplicates. One unnumbered card may be card one. The cards are cut off at one corner, like punch cards. Another card lists on one side "Basic Addition Facts" for sums as large as 9 + 9, and "Basic Subtraction Facts" on the reverse side. Two further cards provide explanation.

- An explanation card for a similar set of flash cards for teaching multiplication and division is included, but none of these cards. Seven further cards, apparently from another set, give sums and differences written vertically.

- A mark on the cardboard box holding the cards reads: MILTON BRADLEY COMPANY (/) SPRINGFIELD (/) MASSACHUSETTS. Another mark reads: NEW MATH(/)FLASH CARDS. Another mark reads: ADDITION-SUBTRACTION. A further mark reads: [copyright] 1965. The set has the maker’s number: 7020.

- Compare 2005.0055.06, 2005.0055.07, 2005.0055.08, and 2005.0055.09.

- Location
- Currently not on view

- date made
- ca 1965

- date received
- 2003

- maker
- Milton Bradley Company

- ID Number
- 2005.0055.07

- catalog number
- 2005.0055.07

- accession number
- 2005.0055

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

## New Math Multiplication Flash Cards

- Description
- From the 1950s, particularly after the launch of the Sputnik satellite in 1958, American mathematicians and mathematics educators introduced a variety of reforms in mathematics teaching dubbed “The New Math.” This set of flash cards reflects the way of presenting arithmetic problems that emerged.

- The set consists of 50 flash cards showing products of one-digit numbers. A product is written out horizontally on each side of each card. The sides are numbered from 1 to 50 on one side and from 50 to 100 on the other. A "sliding number cover" fits over a card to cover one term in the "number sentence." The child is to figure out the answer. A window in the back of the cover reveals the correct answer written on the back of the card. In addition to these cards, there is a card listing "Basic Multiplication Facts" (written vertically, with answers) and "Basic Multiplication Combinations" (written vertically, without answers). Four cards give tips and instructions for teachers and parents.

- A mark on the cardboard box holding the flash cards reads: NEW MATH (/) MULTIPLICATION (/) FLASH CARDS. Another mark reads: [copyright]1966 ED-U-CARDS MFG. CORP., L.I.C., N.Y. A third mark reads: No. 263.

- Compare 2005.0055.06, 2005.0055.07, 2005.0055.08, and 2005.0055.09.

- Location
- Currently not on view

- date made
- ca 1966

- maker
- Ed-U-Cards Manufacturing Corporation

- ID Number
- 2005.0055.09

- accession number
- 2005.0055

- catalog number
- 2005.0055.09

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

## Stern Structural Arithmetic Kit Supplement

- Description
- Catherine Stern, a physicist by training and the founder of a Montessori school in her native Germany, designed this apparatus. Stern and her husband were of Jewish descent, and emigrated to New York City in 1938 to avoid persecution by the Nazis. There she developed these materials, described in her 1949 book
*Children Discover Arithmetic*. The equipment was used in preschools and later in primary schools.

- This is a supplement to Stern’s Structural Arithmetic Kit A. It includes wooden cubes, rods, and cases, as well as paper cards and styrofoam squares. The painted cubes are 11/16” (1.8 cm.) on a side, and the rods are of integer multiples of this length. The rods are painted green (1), violet (2), white (3), brown (4), yellow (5), red (6), light blue (7), orange (8), black (9) and dark blue (10). There are ten rods of each color except dark blue, with 11 of these). There also are ten unit cubes in each of the colors white, red, dark blue, and black. Included is a unit box with 19 rods (as in the other kit). A grooved wooden number track reaches from 0 to 100. It is in 10 pieces held together with dowels, with two end pieces as well.

- For teaching two-digit numbers,Stern designed a “dual board” that holds up to ten 10-rods in one square and up to 10 unit cubes in an adjacent groove. Two notched wooden “standards” hold up the dual board. To teach about hundreds, Stern used ten styrofoam pieces, each a 10x10 square. The kit also includes two sets of cards showing single digits, and a third set of cards showing two-digit numbers (the latter incomplete). Cards of the first set fold, and are intended for teaching multiplication. The other cards fit in grooved blocks, one designed to hold two-digit numbers and the other for three-digit numbers. All of these materials fit in a cardboard box.

- The apparatus also includes a square wooden case, painted gray, called the 20-case, and used especially to teach the properties of the numbers from 11 to 20.

- For related objects see 2005.0229.01. For related documentation, see nonaccession 2005.3100.

- Location
- Currently not on view

- date made
- 1966

- maker
- Stern, Catherine

- ID Number
- 2005.0229.02

- catalog number
- 2005.0229.02

- accession number
- 2005.0229

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

## Ken + Add Adding Machine

- Description
- This four-wheeled stylus-operated adding machine has two copper-colored wheels for cents and two silver-colored wheels for dollars. There are numbers on the cover around each wheel. No complementary digits are indicated. Above the wheels are four windows that indicate the total. At the back is a plastic container for the metal stylus. Inside the lid of the case is a so-called magic slate for jotting down and erasing numbers. The adding machine, stylus, and slate fit in an aluminum case. The instrument is marked: Ken + Add MACHINES CO. DULUTH, MINN. U.S.A. PATENT APPLIED FOR.

- An account of the Ken + Add appeared in
*Mathematics Teacher*in December 1952, where it was recommended not only as a practical adding machine but as a fascinating toy and an aid to arithmetic teaching. It was advertised in*Arithmetic Teacher*as late as 1956.

- Reference:

- P. A. Kidwell, A. Ackerberg-Hastings, and D. L. Roberts,
*Tools of American Mathematics Teaching 1800-2000*, Baltimore: Johns Hopkins University Press, 2008, pp. 248-249.

- Location
- Currently not on view

- date made
- 1950s

- maker
- Ken + Add Machines Co.

- ID Number
- 2005.0278.01

- catalog number
- 2005.0278.01

- accession number
- 2005.0278

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

## Arithmetic of Practical Measurements to Accompany Kennedy's Improved Dissecting Mathematical Blocks

- Description
- In the years following the Civil War, a handful of American educators designed and sold hinged or doweled wooden solids or flat shapes that they could be transposed into other shapes having areas known to students. One of them was Albert H. Kennedy (1848–1940), the superintendent of schools in Rockport, Indiana.

- This small paper pamphlet describes an improved form of Kennedy's models for teaching the arithmetic of practical measurement. Drawings show a model of a rectangle, as well as dissected models designed to show related areas of a parallelogram, a trapezoid and a circle. Other drawings show a model of a rectangular solid and related volumes of a cylinder, a cone, a pyramid, and a sphere, and another model relating to the cone and the cylinder. Further models are described for finding square roots, cube roots, and the area of right triangles. Several practical examples are given for each model described. The pamphlet also includes tables of non-metric weights and measures.

- For related objects, obtained separately, see 2005.0055.

- Location
- Currently not on view

- date made
- 1893

- maker
- Western School Supply House

- ID Number
- 2005.3099.01

- accession number
- 2005.3099

- catalog number
- 2005.3099.01

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