mathematics demonstration model, tumble chain (?)
Date1963
Inventory Number1997-1-1650
ClassificationMathematical Model
Subject
Attributed to
Walter Balcke
?
Cultural Region
Place of Origin
Place of Use
Dimensionsopen: 11.9 × 32.3 × 4.7 cm (4 11/16 × 12 11/16 × 1 7/8 in.)
closed: 12.3 × 32.3 × 4.7 cm (4 13/16 × 12 11/16 × 1 7/8 in.)
closed: 12.3 × 32.3 × 4.7 cm (4 13/16 × 12 11/16 × 1 7/8 in.)
Material
Accessoriesmahogany lid
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)
- one letter from J.L. Walsh may pertain directly to this object, dated March 21, 1963
-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 model is mounted on a thin rectangular mahogany base board. A mahogany cover fits on top of the base board. There is a brass hook on each edge of the cover that hook onto brass hooks at either end of the base board to keep the case closed.
The model is constituted of variously colored plexiglass components lodged in between two rectangular clear triangular plexiglass panels, flush with the base board. The panes are, in turn, lodged between two dark red plexiglass bars fixed to the raised center of the mahogany baseboard.
There are nine blue plexiglass spikes at various angles in between the external plexiglass panes. The blue peaks slide back and forth individually in a horizontal track that prevents their order from changing. In between each pair of blue peaks is a red plexiglass wedge held by a clear plexiglass circle in another horizontal track. The wedge track is attached at one end by a pivot and so can be moved up and down. There is a plexiglass rule with a ten-inch scale marked on it in black across the top of the instrument. In between the rule cross beam and the track for the red wedges is a window through which users can manually move the blue and red pieces.
The ruler has become unattached at one end and so pivots around the instrument. It is not clear whether this was intended or not. A red piece of unknown origin accompanies the instrument in a zip lock bag.
The model is constituted of variously colored plexiglass components lodged in between two rectangular clear triangular plexiglass panels, flush with the base board. The panes are, in turn, lodged between two dark red plexiglass bars fixed to the raised center of the mahogany baseboard.
There are nine blue plexiglass spikes at various angles in between the external plexiglass panes. The blue peaks slide back and forth individually in a horizontal track that prevents their order from changing. In between each pair of blue peaks is a red plexiglass wedge held by a clear plexiglass circle in another horizontal track. The wedge track is attached at one end by a pivot and so can be moved up and down. There is a plexiglass rule with a ten-inch scale marked on it in black across the top of the instrument. In between the rule cross beam and the track for the red wedges is a window through which users can manually move the blue and red pieces.
The ruler has become unattached at one end and so pivots around the instrument. It is not clear whether this was intended or not. A red piece of unknown origin accompanies the instrument in a zip lock bag.
Signedunsigned
Curatorial RemarksIt is not verified that this object was constructed by Walter Balcke for the Mathematics Department at Harvard University. However, it is constructed in the same style and same materials as other confirmed Balcke models and is very likely one of them.
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.
It is unknown what this model was specifically designed to demonstrate. It may have something to do with the relations between triangles. The space in between each pair of blue plexiglass peak is a triangle of variable characteristics, and the wedges in each such space may serve to make those changing characteristics visible. The ruler at the top indicates that measurements along the horizontal were relevant to the demonstration.
A letter from J.L. Walsh to Walter Balcke, dated 21 March 1963, refers to a "Tumble Chain" and indicates that it "is highly unusual and many of our students have enjoyed experimenting with it and, I am sure, few, if any, have been able to devise a theory for it". This letter could potentially refer to this object.
It is unknown what this model was specifically designed to demonstrate. It may have something to do with the relations between triangles. The space in between each pair of blue plexiglass peak is a triangle of variable characteristics, and the wedges in each such space may serve to make those changing characteristics visible. The ruler at the top indicates that measurements along the horizontal were relevant to the demonstration.
A letter from J.L. Walsh to Walter Balcke, dated 21 March 1963, refers to a "Tumble Chain" and indicates that it "is highly unusual and many of our students have enjoyed experimenting with it and, I am sure, few, if any, have been able to devise a theory for it". This letter could potentially refer to this object.
ProvenanceFrom the Department of Mathematics, Harvard University.
Walter Balcke
Date: 1958
Accessories: mahogany case with plastic top; cardboard instruction card;
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)
- one letter from J.L. Walsh pertains directly to this object, dated January 30, 1958
-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
Object number: 1990-5-0029
Walter Balcke
Date: circa 1958
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
Object number: 1997-1-1597
Walter Balcke
Date: 1953
Accessories: mahogany box; cardboard instruction card;
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)
- one letter from J.L. Walsh directly related to this object, the "modified slide rule", dated February 11, 1953
-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
Object number: 1997-1-1609
Walter Balcke
Date: 1959
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)
- one letter from J.L. Walsh pertains directly to this object, dated April 21, 1959
-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
Object number: 1990-5-0030
Walter Balcke
Date: circa 1958
Accessories: wooden case; blue pencil; pink eraser
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
Object number: 1997-1-1671
Walter Balcke
Date: 1953
Accessories: mahogany box; cardboard instruction card;
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)
- one letter from J.L. Walsh pertains directly to this object, dated October 27, 1953
-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
Object number: 1997-1-1610
Walter Balcke
Date: circa 1958
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 (pertains directly to this object), 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
Object number: 1990-5-0031
Walter Balcke
Date: 1959-1960
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)
- one letter from J.L. Walsh, dated November 17, 1959 anticipates Balcke's construction of models to demonstrate Pascal and Brianchon's theorems; another letter from J.L. Walsh, dated Januaray 18, 1960 thanks Balcke for the Pascal Model; another letter from J.L. Walsh, dated February 29, 1960 thanks Balcke for the Brianchon model;
-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 (may pertain directly to this object), Brianchon's Concurrent Lines (may pertain directly to this object), 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
Object number: 1997-1-1603
Panelvision Corporation
Date: 1984
Accessories: single-board display controller
cable for display (1997-1-0686c)
shipping ticket/ hand carry pass dated June 11, 1997 (in instrument file)
letter to Dr. Richard V. Kollarits from William Andrewes dated June 16, 1997 regarding donation of MiniGraphic display and letter to William Andrewes from Dr. Richard V. Kollarits that accompanied the object upon donation on June 11, 1997 (in instrument file)
four sample color prints made with this display on micro-encapsulated photographic paper. 1. man in business suit, 2. woman crouching next to lawn ornament, 3. two clowns painting a third's face, 4. woman in winter hat and scarf (in instrument file)
copies of two articles by AT&T Bell Laboratories staff (Richard V. Kollarits, William, H. Ninke, David C. Gibbon) on color imaging and printing (in instrument file)
Panelvision pamphlet introducing the MiniGraphic multipurpose flat panel display, including instrument specifications, consumer prices, functioning and features (in instrument file)
1984 article by Panelvision employees (Peter Brody Fang-Chen Luo, Paul Malmberg) on active matrix technology (in instrument file)
Panelvision Corporation Fact Sheet, including details of company history and recent developments (in instrument file)
article about commercial debut of active matrix technology from Design Engineering newspaper, June 18, 1984 (in instrument file)
full circuit diagram and schematic for MiniGraphic Display Controller (in instrument file)
instruction manual and description of MiniGraphic Display Controller (two copies, in instrument file)
circuit diagrams and instruction manuals for the MiniGraphic Display (two booklets, in instrument file)
Object number: 1997-1-0686a
Panelvision Corporation
Date: 1984
Accessories: control for Panelvision MiniGraphic display (1997-1-0686a)
shipping ticket/ hand carry pass dated June 11, 1997 (in instrument 1997 - 0686a file)
letter to Dr. Richard V. Kollarits from William Andrewes dated June 16, 1997 regarding donation of MiniGraphic display and letter to William Andrewes from Dr. Richard V. Kollarits that accompanied the object upon donation on June 11, 1997 (in instrument 1997 - 0686a file)
four sample color prints made with this display on micro-encapsulated photographic paper. 1. man in business suit, 2. woman crouching next to lawn ornament, 3. two clowns painting a third's face, 4. woman in winter hat and scarf (in instrument 1997 - 0686a file)
copies of two articles by AT&T Bell Laboratories staff (Richard V. Kollarits, William, H. Ninke, David C. Gibbon) on color imaging and printing (in instrument 1997 - 0686a file)
Panelvision pamphlet introducing the MiniGraphic multipurpose flat panel display, including instrument specifications, consumer prices, functioning and features (in instrument 1997 - 0686a file)
1984 article by Panelvision employees (Peter Brody Fang-Chen Luo, Paul Malmberg) on active matrix technology (in instrument 1997 - 0686a file)
Panelvision Corporation Fact Sheet, including details of company history and recent developments (in instrument 1997 - 0686a file)
article about commercial debut of active matrix technology from Design Engineering newspaper, June 18, 1984 (in instrument 1997 - 0686a file)
full circuit diagram and schematic for MiniGraphic Display Controller (in instrument file)
instruction manual and description of MiniGraphic Display Controller (two copies, in instrument 1997 - 0686a file)
circuit diagrams and instruction manuals for the MiniGraphic Display (two booklets, in instrument 1997 - 0686a file)
Object number: 1997-1-0686b
Louis Dupin
Date: circa 1849
Accessories: book shaped storage case; six photographs and negatives of case and models with ruler scale (in instrument file)
Object number: 1996-1-0006
Electronic Assistance Corporation
Date: 1960-1965
Accessories: operator's Manual, published by the Department of the Army on 16 January 1961.
Object number: 2004-1-0414