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mathematical demonstration, angle divider (trisector ?)
Date: 1952-1964
Inventory Number: 1990-5-0028
Classification: Mathematical Model
Subject:
Maker: Walter Balcke ?
Cultural Region:
Place of Origin:
City of Use:
Dimensions:
case: 14.1 × 32 × 2.5 cm (5 9/16 × 12 5/8 × 1 in.)
Material:
Accessories: mahogany case; two circular protractors; clear plexiglass rule with serated edge
DescriptionThe demonstration set is mounted on a rectangular plexiglass base that is in turn mounted on a rectangular mahogany base. A mahogany lid fits onto the base, forming a case for the set.
Two concentric white plexiglass circles are fixed in the center of the base. Two spokes (or arms) emerge from each disc, pointing in the general direction of the four corners of the base. The discs can rotate, causing the spokes to slide back and forth across the plexiglass base, changing the angle between the spokes on each side of the apparatus.
Each of the spokes has a straight track (or groove) cut along its center. A blue, trapezoidal shaped plexiglass "slide" accompanies the set. It has three brown posts attached to three of its corners. These brown posts are the appropriate size to fit in the tracks of the spokes. A straight white line is etched along the long edge of the slide, between two of the brown posts. In between two of the spokes on one side of the apparatus is a raised plexiglass edge. The blue slide has a groove cut in its bottom panel that fits onto this track. The track can be used to limit the slide's degrees of freedom when the apparatus is in use.
The set also includes seven rectangular blue plexiglass strips with rounded edges. These act as "links" in the set. Three of these links have a brown post at each end. These posts are the appropriate size to fit in tracks on the spokes. The other four blue links have small holes at each end. These holes fit onto the top part of the posts. The blue slide, and the blue links fit together by holes and poles to create a linkage on the surface of the apparatus.
The set also includes two circular clear plastic protractors. Each one is divided into 360° by blue lines around the circumference. Every tenth degree is labeled with the appropriate numeral. Each protractor is further marked with the compass directions. N(orth) lines up with 0°, E(ast) lines up with 90°, S(outh) lines up with 180°, and W(est) lines up with 270°. A clear plastic attachment has been added to the 0° point on each protractor. Each attachment has a small rounded groove cut in its outmost edge. The attachments would have been used to attach the protractors to the set. It is no longer clear where and to what they would have been attached.
The set is also accompanied by a clear plexiglass bar with one serrated edge, whose use is unknown.
Two concentric white plexiglass circles are fixed in the center of the base. Two spokes (or arms) emerge from each disc, pointing in the general direction of the four corners of the base. The discs can rotate, causing the spokes to slide back and forth across the plexiglass base, changing the angle between the spokes on each side of the apparatus.
Each of the spokes has a straight track (or groove) cut along its center. A blue, trapezoidal shaped plexiglass "slide" accompanies the set. It has three brown posts attached to three of its corners. These brown posts are the appropriate size to fit in the tracks of the spokes. A straight white line is etched along the long edge of the slide, between two of the brown posts. In between two of the spokes on one side of the apparatus is a raised plexiglass edge. The blue slide has a groove cut in its bottom panel that fits onto this track. The track can be used to limit the slide's degrees of freedom when the apparatus is in use.
The set also includes seven rectangular blue plexiglass strips with rounded edges. These act as "links" in the set. Three of these links have a brown post at each end. These posts are the appropriate size to fit in tracks on the spokes. The other four blue links have small holes at each end. These holes fit onto the top part of the posts. The blue slide, and the blue links fit together by holes and poles to create a linkage on the surface of the apparatus.
The set also includes two circular clear plastic protractors. Each one is divided into 360° by blue lines around the circumference. Every tenth degree is labeled with the appropriate numeral. Each protractor is further marked with the compass directions. N(orth) lines up with 0°, E(ast) lines up with 90°, S(outh) lines up with 180°, and W(est) lines up with 270°. A clear plastic attachment has been added to the 0° point on each protractor. Each attachment has a small rounded groove cut in its outmost edge. The attachments would have been used to attach the protractors to the set. It is no longer clear where and to what they would have been attached.
The set is also accompanied by a clear plexiglass bar with one serrated edge, whose use is unknown.
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 apparatus is a model designed to divide a given angles into a certain number of equal parts. This object may be an angle Trisector. A cardboard instruction card is kept in the CHSI library, Lib.4927, for such an object and reads "TRISECTOR / Can be used for dividing an angle into / 2, 3, 4, 5, 6 equal parts".
This object is very similar in design to object 1997-1-1601, designed to divide angles into various equal parts. Users set the initial angle, using the protractors and adjusting the plexiglass spokes. An appropriate linkage is then set up using the links and slide such that a new angle will be produced and can be measured with the protractor. The links transfer motion to the slide which pivots and pushes or pulls the spokes closer together or further apart. The details of this specific model are unknown. While there may be some differences, the functioning of this object is very similar to that of 1997-1-1601 whose instruction card is copied below.
"ANGLE DIVIDER / For any number of parts to thirteen / The basic angle between the arms is / varied by the slide; multiples of the angle / by the attached moving links. / The even multiples result when line AB*, / on the slide, is held at right angles to / one arm by using the side of the slide / having an extra pin for the arm groove. / The odd multiples result when line AB* / is held at right angles to the bisecting / line by the groove on the slide. / To divide an angle into a given number / of equal parts the slide is moved until / the angle is formed by the links for / that multiple. The base angle is one part. / When the given angle is outside the / range of the device an easily obtainable / fraction or multiple may be used. / To assure seating, tap links very lightly / before measuring the angles. / FRAGILE / Dust may cause binding. Do not force / the movement but assist the individual / parts if required. / Avoid striking the switch when closed."
* Line AB is shown in a diagram on the instruction card to be the white engraved line along the long edge of the blue slide.
This particular apparatus is a model designed to divide a given angles into a certain number of equal parts. This object may be an angle Trisector. A cardboard instruction card is kept in the CHSI library, Lib.4927, for such an object and reads "TRISECTOR / Can be used for dividing an angle into / 2, 3, 4, 5, 6 equal parts".
This object is very similar in design to object 1997-1-1601, designed to divide angles into various equal parts. Users set the initial angle, using the protractors and adjusting the plexiglass spokes. An appropriate linkage is then set up using the links and slide such that a new angle will be produced and can be measured with the protractor. The links transfer motion to the slide which pivots and pushes or pulls the spokes closer together or further apart. The details of this specific model are unknown. While there may be some differences, the functioning of this object is very similar to that of 1997-1-1601 whose instruction card is copied below.
"ANGLE DIVIDER / For any number of parts to thirteen / The basic angle between the arms is / varied by the slide; multiples of the angle / by the attached moving links. / The even multiples result when line AB*, / on the slide, is held at right angles to / one arm by using the side of the slide / having an extra pin for the arm groove. / The odd multiples result when line AB* / is held at right angles to the bisecting / line by the groove on the slide. / To divide an angle into a given number / of equal parts the slide is moved until / the angle is formed by the links for / that multiple. The base angle is one part. / When the given angle is outside the / range of the device an easily obtainable / fraction or multiple may be used. / To assure seating, tap links very lightly / before measuring the angles. / FRAGILE / Dust may cause binding. Do not force / the movement but assist the individual / parts if required. / Avoid striking the switch when closed."
* Line AB is shown in a diagram on the instruction card to be the white engraved line along the long edge of the blue slide.
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.
ProvenanceFrom the Department of Mathematics, Harvard University.