mathematical model, parabola ?
Date: 1952-1964
Inventory Number: 1997-1-1612
Classification: Model
Subject:
Maker: Walter Balcke
Cultural Region:
Place of Origin:
City of Use:
Dimensions:
2 x 22 x 5 cm (13/16 x 8 11/16 x 1 15/16 in.)
Material:
DescriptionThe model is mounted in between two arms. The base arm is constituted of a mahogany bar with two parallel metal wires along the top that extend on one side and are supported by a brass plate. A rounded brass hook sticks out and upward from the other side of the mahogany bar. The top arm is constituted of brass, with two parallel wires running underneath it for the full length. There is a round black disc with a white dot in the center at the very end of this arm. The two arms are connected at the brass extension end of the bas arm by a pivot, permitting variability in the angle between them.
Two identical and parallel chains are attached to the bottom arm, above the wooden section. Each chain is attached to one of the parallel wires above the arm. Each chain consists of two round white plexiglass discs, each with a round pink bead on top, followed by one rounded rectangular white plexiglass piece, followed by four more round white discs with pink beads on top. Each of the pieces is connected to the next by a black plexiglass pivot. A hole is cut through each of the pink beads on the tops of the white discs. A blue plastic cord with a brass bead at each end, is strung through the blue beads on each chain.
Two straight metal wires, each with a 90° bend at one end, are fixed to each chain, and intersect with one of the parallel wires hung beneath the main upper brass arm of the model. Each pair of wires intersects each other and intersects an upper wire in the same place, held together by a small brass cylinder.
As the angle between the two main arms is altered, i.e. they are pushed together or pulled apart, the four wires in between are pushed and pulled as well. They impart this motion to the chains below. The chains are therefore pulled, in tandem, into different configurations ranging from nearly flat to a slightly oblique half circle.
Two identical and parallel chains are attached to the bottom arm, above the wooden section. Each chain is attached to one of the parallel wires above the arm. Each chain consists of two round white plexiglass discs, each with a round pink bead on top, followed by one rounded rectangular white plexiglass piece, followed by four more round white discs with pink beads on top. Each of the pieces is connected to the next by a black plexiglass pivot. A hole is cut through each of the pink beads on the tops of the white discs. A blue plastic cord with a brass bead at each end, is strung through the blue beads on each chain.
Two straight metal wires, each with a 90° bend at one end, are fixed to each chain, and intersect with one of the parallel wires hung beneath the main upper brass arm of the model. Each pair of wires intersects each other and intersects an upper wire in the same place, held together by a small brass cylinder.
As the angle between the two main arms is altered, i.e. they are pushed together or pulled apart, the four wires in between are pushed and pulled as well. They impart this motion to the chains below. The chains are therefore pulled, in tandem, into different configurations ranging from nearly flat to a slightly oblique half circle.
Signedunsigned
FunctionWalter 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.
This particular model may be designed to show parabolas of various configurations. Further, each of the four wires that pass between the two main arms is tangent to any parabola created by the model. It may also point to information about the tangents of parabolas.
It is known that Walter Balcke produced a model of the catenary (the idealized curve of a chain or rope hanging between two points). According to a cardboard card from the display case in the mathematics department (CHSI library, Lib.4927), the stand that supported the chain was too large to be put on display. It is possible that this parabola model and the catenary model came together (possibly referred to together in letter from J.L. Walsh, dated February 11, 1953), although this is not certain. The models are not there mentioned by name.
This particular model may be designed to show parabolas of various configurations. Further, each of the four wires that pass between the two main arms is tangent to any parabola created by the model. It may also point to information about the tangents of parabolas.
It is known that Walter Balcke produced a model of the catenary (the idealized curve of a chain or rope hanging between two points). According to a cardboard card from the display case in the mathematics department (CHSI library, Lib.4927), the stand that supported the chain was too large to be put on display. It is possible that this parabola model and the catenary model came together (possibly referred to together in letter from J.L. Walsh, dated February 11, 1953), although this is not certain. The models are not there mentioned by name.
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" (CHSI library, Lib.4927). The display was set up in the Harvard Mathematics Department Library.
ProvenanceFrom the Department of Mathematics, Harvard University.