Dissected Circle Transformable into Parallelogram
date: label: date made
content: ca 1900
name: label: maker
content: Kennedy, Albert H.
notes: label: Description
content: 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.
label: Description
content: 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.
label: Description
content: In 1882, the German mathematician Lindemann demonstrated that no exact geometric squaring of the circle is possible. His work undoubtedly was unknown to Kennedy.
label: Description
content: The object has no maker's marks.
label: Description
content: Compare 2005.0054.01, 2005.0054.02, 2005.0054.03 and 2005.0054.04.
label: Description
content: References:
label: Description
content: <I>Arithmetic of Practical Measurements for Teachers' Instruction and Class Work in Mensuration. Published by Western School Supply House</I>, 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.
label: Description
content: C. L. F. von Lindemann, “Über die Zahl π,” <I> Mathematische Annalen</I>, 20 (1882), 215.
label: Description
content: “Paintings Presented to Local Schools,” <I>Rockport Journal</I> May 15, 1964.
label: Description
content: P. A. Kidwell, "American Mathematics Viewed Objectively: The Case of Geometric Models," in <I>Vita Mathematica: Historical Research and Integration with Teaching</I>, ed. Ronald Calinger, Washington, D.C.: Mathematical Association of America, 1996, pp. 197–207.
label: Location
content: Currently not on view
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 Jeremiah P. Farrell
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 2005.0054.01
label: catalog number
content: 2005.0054.01
label: accession number
content: 2005.0054
objectType: label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: wood (overall material)
label: Physical Description
content: cloth (overall material)
label: Physical Description
content: metal (overall material)
label: Measurements
content: overall: 2.5 cm x 16 cm x 16 cm; 31/32 in x 6 5/16 in x 6 5/16 in