Dissected Circle Transformable into Parallelogram

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.

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