demonstration for exponential curve y=(x^n)
Date1961
Inventory Number1997-1-1638
ClassificationDemonstration
Subject
Maker
Walter Balcke
?
Cultural Region
Place of Origin
Place of Use
Dimensions0.4 x 5.8 x 5.8 cm (3/16 x 2 5/16 x 2 5/16 in.)
Material
DescriptionThis diagrammatic model is constructed on the surface of a white plexiglass square with beveled edges. Two perpendicular black axes are drawn onto the square with black felt pen, each parallel with two sides, meeting in the center. The axes are labeled to form a unit axis: the intersection between each end of each axis and the edge of the square is labeled 1 or -1. The top and right intersections are labeled 1, and the bottom and left intersections are labeled -1. The axes divide the square into four quadrants: the top right quadrant is I, the bottom right quadrant is II, the bottom left quadrant is III, and the top left quadrant is IV.
In quadrant IV is written the equation y = (x^n), which is described by the curves in the graph. In each of quadrants I, II, and III are drawn seven lines, each for a certain value of n. The central line in each of the quadrants is straight (representing y = (x^1) or y = x). The surrounding six lines in each quadrant represent y = (x^n) for n = 1/5, 1/3, 1/2, 2, 3, and 5. These values of n are labeled in quadrant I. The resulting curves each begin at the origin, and meet at a single point near the corner of each quadrant. A forest green plexiglass pane the exact shape and size of the area inside the outermost two curves in each of the three quadrants is attached to the top of the plexiglass square. Each looks like a leaf. There is a single line in quadrant IV, representing y = (x^2). This line is doubled with a raised green plexiglass thread and looks like a stem. The result is a three-leafed plant representation of the equation y = (x^n).
In quadrant IV is written the equation y = (x^n), which is described by the curves in the graph. In each of quadrants I, II, and III are drawn seven lines, each for a certain value of n. The central line in each of the quadrants is straight (representing y = (x^1) or y = x). The surrounding six lines in each quadrant represent y = (x^n) for n = 1/5, 1/3, 1/2, 2, 3, and 5. These values of n are labeled in quadrant I. The resulting curves each begin at the origin, and meet at a single point near the corner of each quadrant. A forest green plexiglass pane the exact shape and size of the area inside the outermost two curves in each of the three quadrants is attached to the top of the plexiglass square. Each looks like a leaf. There is a single line in quadrant IV, representing y = (x^2). This line is doubled with a raised green plexiglass thread and looks like a stem. The result is a three-leafed plant representation of the equation y = (x^n).
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.
This particular model is an artistic rendering of exponential curves of the form y = (x^n). Like most of Balcke's models, it likely had demonstrative, pedagogical, and aesthetic purposes. A letter from J.L. Walsh to Balcke, dated December 5, 1961, indicates that the model would have been circulated in an undergraduate mathematics class after discussing exponential curves. (See CHSI library, Lib.4927)
This particular model is an artistic rendering of exponential curves of the form y = (x^n). Like most of Balcke's models, it likely had demonstrative, pedagogical, and aesthetic purposes. A letter from J.L. Walsh to Balcke, dated December 5, 1961, indicates that the model would have been circulated in an undergraduate mathematics class after discussing exponential curves. (See CHSI library, Lib.4927)
ProvenanceFrom the Department of Mathematics, Harvard University.
Walter Balcke
Date: 1955
Accessories: mahogany box with plexiglass lid; pencil; eraser; box of lead; putty ball; cleaning cloth; cardboard instruction card
Object number: 1997-1-1619
Anthoine Mestrel
Date: 1551
Accessories: old velvet pouch
Object number: DW0592
Antonius Giamin
Date: early 20th Century
Object number: DW0590
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
G. Winckler
Date: 1790
Accessories: Leather covered rectangular case and 4 leveling screws. Paper with calculations in pencil and printed "KUNSTAUKTIONSHAUS Math. Lempertz ...Koln " loose in case.
Object number: 7106
American
Date: 1900-1950
Object number: 1998-1-0029
Hickok Electrical Instrument Company
Date: 1955-1965
Object number: 1998-1-0879
