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Date: circa 1958

Inventory Number: 1997-1-1597

Classification: Mathematical Model

Subject:

Maker: Walter Balcke

Cultural Region:

Place of Origin:

City of Use:

Dimensions:

2 x 29 x 12 cm (13/16 x 11 7/16 x 4 3/4 in.)

Material:

Accessories: in library folder (Lib 4927):
-twenty-one letters from Joseph L. Walsh, mathematics professor at Harvard University, to Walter Balcke, dated between 27 May 1957 and 24 January 1964 (letters thank Balcke for the many mathematical models he gifted to the Mathematics Department, praise his skill and ingenuity, many invite him to faculty and personal luncheons, and one letter provides an analytic solution to the "13-point problem" behind one of Balcke's models)
-three letters from Garret Birkhoff (then Chairman of the Harvard Mathematics Department) dated 3 March 1954, 4 January 1955, and 10 January 1955, each expressing gratitude (and in one case, an official department thank you) for the many mathematical models he gifted to the mathematics department
-photocopy of original envelope in which correspondence between mathematics department and Walter Balcke was stored (original was destroyed on 13 July 1997)
-photocopy of instructional card for object 1997-1-1671
- seven instructional cards that accompany the following Balcke models: Pascal's Theorem, Brianchon's Concurrent Lines, Trisector, Twelve Point Ellipse, Rolling Parabola, unknown, Equation Solution with a 'Constant' Variable and Thread
- photograph of the display case containing Balcke's models in the Harvard Mathematics department

DescriptionThe demonstration toy is mounted on a rectangular black plastic platform. There is a wedge of beige plexiglass fixed to the platform with its wide base at the bottom. The wedge is divided into four strips by black lines inscribed parallel to the leftmost edge of the wedge. Each of the main lines is numbered, 1 through 4. Each strip is further subdivided in ten by black lines, every fifth of which is bolder.

There is a clear plexiglass lever emerging from the left-hand edge of the object. A piece of white string is tied to the free end of the lever through a small hole lined with blue plexiglass. The other end of the string is tied to a round blue plexiglass knob fixed near the left edge of the platform. The string can be used to move the lever.

The lever attaches to the plexiglass base with a pivot labeled E. At the point of the pivot, there is a bend in the lever. The end of the segment after the bend is marked with a point labeled C. Point C is in a cut-out plexiglass track. As the lever is moved up and down (between a position nearly parallel to the left edge of the toy and 45° up from that edge) the point C slides back and forth in its curved track. Point C and the lever pivot E are attached to a white plexiglass piece below, shaped a bit like a horse's head. As the point C slides back and forth in its track, this white piece also rotates up and down, with E as its fixed pivot of rotation. The points labeled B and D are attached to a second white plexiglass piece beneath, shaped like a rectangle with two extensions from the bottom edge. As the lever moves up and down, this white piece also slides up and down, with each of B and D sliding up and down in a cut-out track. The motion of the white plexiglass pieces is imparted to another clear piece, with a point marked A at the top. A slides from side to side in a cut-out arc track.

As A rotates back and forth, a long clear ruler slides back and forth across the beige plexiglass wedge below. There is a black line down the center of the rule that intersects with the lines drawn on the wedge. As the rule slides across the wedge, the intersection points change with it.

There is a clear plexiglass lever emerging from the left-hand edge of the object. A piece of white string is tied to the free end of the lever through a small hole lined with blue plexiglass. The other end of the string is tied to a round blue plexiglass knob fixed near the left edge of the platform. The string can be used to move the lever.

The lever attaches to the plexiglass base with a pivot labeled E. At the point of the pivot, there is a bend in the lever. The end of the segment after the bend is marked with a point labeled C. Point C is in a cut-out plexiglass track. As the lever is moved up and down (between a position nearly parallel to the left edge of the toy and 45° up from that edge) the point C slides back and forth in its curved track. Point C and the lever pivot E are attached to a white plexiglass piece below, shaped a bit like a horse's head. As the point C slides back and forth in its track, this white piece also rotates up and down, with E as its fixed pivot of rotation. The points labeled B and D are attached to a second white plexiglass piece beneath, shaped like a rectangle with two extensions from the bottom edge. As the lever moves up and down, this white piece also slides up and down, with each of B and D sliding up and down in a cut-out track. The motion of the white plexiglass pieces is imparted to another clear piece, with a point marked A at the top. A slides from side to side in a cut-out arc track.

As A rotates back and forth, a long clear ruler slides back and forth across the beige plexiglass wedge below. There is a black line down the center of the rule that intersects with the lines drawn on the wedge. As the rule slides across the wedge, the intersection points change with it.

Signedunsigned

FunctionThis toy is designed to demonstrate the relationship between various mechanical motions through the motion of the single black line drawn down the center of a clear plastic rule across an inscribed scale on the beige wedge beneath.

Walter Balcke built and gifted many mathematical models to the Mathematics department at Harvard University. According to substantial correspondence between mathematics professors and Balcke, the models were sometimes used in classes, circulated around the department for observation, and eventually put on display in the mathematics library.

Walter Balcke built and gifted many mathematical models to the Mathematics department at Harvard University. According to substantial correspondence between mathematics professors and Balcke, the models were sometimes used in classes, circulated around the department for observation, and eventually put on display in the mathematics library.

Curatorial RemarksThis object is clearly visible in a Polaroid photograph taken in August 1961. The photograph is labeled "Exhibit of mathematical models and devices designed and constructed by Mr. Walter H. Balcke of Winchester, Mass. Department of Mathematics, Harvard University. August 1961" (in Lib. 4927). The display was set up in the Harvard Mathematics Department Library.

ProvenanceFrom the Department of Mathematics, Harvard University.

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