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Your search found 21 records from National Museum of American History collection.
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- Description
- This fixed string model shows a ruled surface, that is to say a surface swept out by a moving straight line. The model was published by the firm of Ludwig Brill in Darmstadt beginning in 1879. This example was exhibited at the German Educational Exhibit at the Columbian Exposition held in Chicago in 1893, where it was purchased by Wesleyan University.
- The surface is the saddle-shaped hyperbolic paraboloid, shown in red strings and bounded by a black metal frame. The frame has two straight edges along opposite bottom sides, joined by curved edges to form a four-sided base. Above the two opposite straight base edges are edges in the shape of a parabolas. The parabolas are joined at the top by a cross bar. A row of holes extends along each curved edge at the base and along each parabola.
- References:
- Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 9, 59-60.
- Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, pp. 243-244. An example of this model is shown in Figure 7.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.022
- catalog number
- 1985.0112.022
- accession number
- 1985.0112
-
- Description
- This is one of a set of four models of ruled surfaces originally published by Ludwig Brill in 1891. The series was designed by C. Tesch, an assistant to Christian Wiener (1826-1896), a professor at the technical high school in Karlsruhe. Tesch also designed Series 20 of Brill’s models (also published in 1891) and, after graduation, Series 22 (published in 1894, by which time Tesch is listed as an engineer with no academic affiliation).
- This, the third model in Brill's Series 18, has a black metal frame and red and green threads, with gold beads. The three sides are roughly straight, with complex curves on the top and bottom. One side is broken off. The threads in this example are presently broken.
- All the models in the series are meant to show ruled surfaces of degree three. As in #2, there should be two lines of intersection of the ruled surfaces, marked by beads, but these lines would meet only infinitely far from the model.
- This example of the model was exhibited at the Columbian Exposition, a World’s fair held in Chicago in 1893.
- Compare 1985.0112.179.
- References:
- L. Brill, Catalog, 1892, p. 64-65, 44-45.
- Richter, K., Online Collection of Mathematical Models, Martin-Luther-Universität Halle-Wittenberg. This collection has the web address: https://www2.mathematik.uni-halle.de/modellsammlung/. The example of this model shown there has number A3-032 in that collection.
- Tesch. C., Modelle der Regelfaechen dritten Gerades. A copy of this essay, which gives a brief historical account of the development of the model at Karlsruhe, is online at http://modellsammlung.uni-goettingen.de/data/Texts/M1/Modelle72-75_Tesch.pdf. It was posted in connection with the copy of the model at the University of Goettingen (their model 74).
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.185
- catalog number
- 1985.0112.185
- accession number
- 1985.0112
-
- Description
- The black metal frame of this string model has two opposite sides that are circles, two opposite sides that are H-shaped, and quadrilaterals on the top and the bottom. Most of the strings were missing from the object when it was received. The model has no maker’s tags.
- This is one of a series of models of ruled surfaces representing space curves of fourth order designed by Karl Rohn, professor of mathematics at the technical high school in Dresden. The series was first published by Brill in 1892.
- This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893.
- Compare models 1985.0112.181, 1985.0112.182, 1985.0112.183, and 1985.0112.184, and 1985.0112.186.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, pp. 40-42, 75.
- An example of the model by Brill’s successor, Martin Schilling, is in the collections of the University of Utrecht, which gives it the designation of Series 21, #2. See: https://www.uu.nl/en/research/3d-geometric-models/schilling-2102.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.182
- catalog number
- 1985.0112.182
- accession number
- 1985.0112
-
- Description
- This is one of a set of seven models of surfaces representing space curves of fourth order designed by Karl Rohn, professor of mathematics at the technical high school in Dresden. The series was first published by Brill in 1892. The black metal frame of this string model has two opposite sides that are circles, with two loops in each circle. The other two sides are H-shaped. The top and bottom contain a quadrilateral with curved sides. There are red and green strings, some with beads on them, many broken.
- This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893.
- Compare models 1985.0112.181, 1985.0112.182, 1985.0112.183, 1985.0112.184, and 1985.0112.186.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, pp. 40-42, 75.
- An example of this model, with tag, is in the collections of the University of Utrecht, giving it the Brill series 21, number 1 designation. See https://www.uu.nl/en/research/3d-geometric-models/schilling-2101.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.184
- catalog number
- 1985.0112.184
- accession number
- 1985.0112
-
- Description
- This is one of a set of seven models of surfaces representing space curves of fourth order designed by Karl Rohn, professor of mathematics at the technical high school in Dresden. The series was first published by Brill in 1892. The black metal frame of the string model has two round sides and two H-shaped sides. The top and bottom are in the general shape of quadrilaterals. The threads are green and red, with gold beads. At this writing, most threads are broken.
- This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893.
- Compare models 1985.0112.181, 1985.0112.182, 1985.0112.183, 1985.0112.184, and 1985.0112.186.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, pp. 40-42, 75.
- An example of this model is #8 in the Altgeld collection of mathematical models at the University of Illinois. An image of it has a tag with the Brill series 21, number 5 designation. See http://www.mathmodels.illinois.edu/cgi-bin/cview?SITEID=4&ID=372.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.183
- catalog number
- 1985.0112.183
- accession number
- 1985.0112
-
- Description
- The black metal frame of this string model has two opposite oval sides, with a loop in each oval. The other opposite sides are I-shaped (one I is very squat). The top and bottom are T-shaped. The bits of thread that remain (most are missing) are red and green. There is no maker's tag on this example.
- This is one of a series of models of ruled surfaces representing space curves of fourth order designed by Karl Rohn, professor of mathematics at the technical high school in Dresden. The series was first published by Brill in 1892. This model is a special case of model 5 in the series.
- This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893.
- Compare models 1985.0112.181, 1985.0112.182, 1985.0112.183, 1985.0112.184, and 1985.0112.186.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, pp. 40-42, 75
- An example of this model is #44 in the collection of mathematical models at the University of Illinois. An image of it has a tag with the the Brill series 21, number 6 designation. http://www.mathmodels.illinois.edu/cgi-bin/cview?SITEID=4&ID=355.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.181
- catalog number
- 1985.0112.181
- accession number
- 1985.0112
-
- Description
- This is one of a set of seven models of surfaces representing space curves of fourth order designed by Karl Rohn, professor of mathematics at the technical high school in Dresden. The series was first published by Brill in 1892. The object has a black metal frame and white threads, which appear to be plastic. The frame has a circular base and top. There are two overlapping ruled surfaces, each with 48 strings. There also is the framework for a second surface that would fit within the first. A tag on the model indicates it is part of Brill's series 21.
- This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893.
- Compare models 1985.0112.181, 1985.0112.182, 1985.0112.183, 1985.0112.184, and 1985.0112.186.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, pp. 40-42, 75.
- An example of this model is #38 in the Altgeld collection of mathematical models at the University of Illinois. An image of it has a tag with the series 21, number 3 designation. See http://www.mathmodels.illinois.edu/cgi-bin/cview?SITEID=4&ID=350.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.186
- accession number
- 1985.0112
- catalog number
- 1985.0112.186
-
- Description
- The German Karl Rohn (1855-1920) intended to become an engineer, but found the mathematical part of his studies at the polytechnic in Darmstadt more intriguing. He studied mathematics with Alexander von Brill and Felix Klein in Munich, and went on to a career as a professor of mathematics in Leipzig and Dresden.
- In 1886 and again in 1892, Rohn published sets of string models with the publisher and mathematical model distributor Ludwig Brill. Several models from the first set, Brill’s Series XIII, were exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893. This is one of them, number 4 in the series.
- The thread model has a metal frame. It shows two congruent hyperboloid-like ruled surfaces (in gold), and a vertical straight line that runs between them (in red).
- The model was received at the Smithsonian with one bit of thread and restrung.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, pp. 27-28, 68.
- “Mathematical Models of Surfaces,” University of Groningen, website accessed October 16, 2017. This site describes the mathematics of these surfaces in more detail. It illustrates them with examples of the models published by Brill’s successor, Martin Schilling - still as series XIII.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.132
- catalog number
- 1985.0112.132
- accession number
- 1985.0112
-
- Description
- The German Karl Rohn (1855-1920) intended to become an engineer, but found the mathematical part of his studies at the polytechnic in Darmstadt more intriguing. He studied mathematics with Alexander von Brill and Felix Klein in Munich, and went on to a career as a professor of mathematics in Leipzig and Dresden.
- In 1886 and again in 1892, Rohn published sets of string models with the publisher and mathematical model distributor Ludwig Brill. Several models from the first set, Brill’s Series XIII, were exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893. This is one of them, number 6 in the series.
- The model has a black metal frame. The top and bottom are four-pointed asterisks, while two opposite sides resemble the sides of 1985.0112.132. The two other sides are Y-shaped, like the top and bottom of 1985.0112.128. There are no labels and the red and gold strings are broken.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, pp. 27-28, 68.
- An example of this model, with strings, is #224 in the mathematics collections of the University of Dresden. In October of 2017, that collection had address http://www.math.tu-dresden.de/modellsammlung/. This model was described at http://www.math.tu-dresden.de/modellsammlung/karte.php?ID=224.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.133
- catalog number
- 1985.0112.133
- accession number
- 1985.0112
-
- Description
- The German Karl Rohn (1855-1920) intended to become an engineer, but found the mathematical part of his studies at the polytechnic in Darmstadt more intriguing. He studied mathematics with Alexander von Brill and Felix Klein in Munich, and went on to a career as a professor of mathematics in Leipzig and Dresden.
- In 1886 and again in 1892, Rohn published sets of string models with the publisher and mathematical model distributor Ludwig Brill. Several models from the first set, Brill’s Series XIII, were exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893. This is one of them, number 8 in the series.
- Two sides of the black metal frame are alike, two sides are partially mirror images, and the top and bottom are partially mirror images of one another. The model presently lacks strings.
- Reference:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, pp. 27-28, 69.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.131
- catalog number
- 1985.0112.131
- accession number
- 1985.0112
-
- Description
- The German Karl Rohn (1855-1920) intended to become an engineer, but found the mathematical part of his studies at the polytechnic in Darmstadt more intriguing. He studied mathematics with Alexander von Brill and Felix Klein in Munich, and went on to a career as a professor of mathematics in Leipzig and Dresden.
- In 1886 and again in 1892, Rohn published sets of string models with the publisher and mathematical model distributor Ludwig Brill. Several models from the first set, Brill’s Series XIII, were exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893. This is one of them, number 1 in the series.
- The thread model has a metal frame. It shows two congruent ruled surfaces (in gold), as well as two double lines (in red). Each of the lines has four pinch points, that is to say points for which every neighborhood is self-intersecting.
- The model was received at the Smithsonian with its threads broken and restrung.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, pp. 27-28, 68.
- “Mathematical Models of Surfaces”, University of Groningen, website accessed October 16, 2017. This site describes the mathematics of these surfaces in more detail. It illustrates them with examples of the models published by Brill’s successor, Martin Schilling.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.134
- catalog number
- 1985.0112.134
- accession number
- 1985.0112
-
- Description
- The German Karl Rohn (1855-1920) intended to become an engineer, but found the mathematical part of his studies at the polytechnic in Darmstadt more intriguing. He studied mathematics with Alexander von Brill and Felix Klein in Munich, and went on to a career as a professor of mathematics in Leipzig and Dresden.
- In 1886 and again in 1892, Rohn published sets of string models with the publisher and mathematical model distributor Ludwig Brill. Several models from the first set, Brill’s Series XIII, were exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893. This is one of them, number 7 in the series.
- Brill described this as a ruled surface with a triple line and two constant tangential planes along the line. The surface is ruled in gold threads, with the line in red.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, pp. 27-28, 69.
- “Mathematical Models of Surfaces,” University of Groningen, website accessed October 17, 2017. This site describes the mathematics of these surfaces in more detail. It illustrates them with examples of the models published by Brill’s successor, Martin Schilling - still as series XIII.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.129
- catalog number
- 1985.0112.129
- accession number
- 1985.0112
-
- Description
- This is one of a set of four models of ruled surfaces originally published by Ludwig Brill in 1891. The series was designed by C. Tesch, an assistant to Christian Wiener (1826-1896), a professor at the technical high school in Karlsruhe. Tesch also designed Series 20 of Brill’s models (also published in 1891) and, after graduation, Series 22 (published in 1894, by which time Tesch is listed as an engineer with no academic affiliation).
- This, the second model in Series 18, has a black metal frame and, at present, only a few red and gold fragments of string. The frame has two intersecting curved segments on the top and also on the bottom, two curved sides, and one cross-shaped side. A second cross-shaped side is detached. The remnants of a tag read: [. . .] gelfl[ae]che e. Grades. (II. Fall.) (/) [. . .] erl. v. L. Brill. 18. Ser. Nr. II.
- All the models in the series are ruled surfaces of degree three. If the model were restrung, lines of the intersection of the strings would be marked with beads to show a circle and as well as two straight lines that would intersect above the frame.
- This example of the model was exhibited at the Columbian Exposition, a World’s fair held in Chicago in 1893.
- Compare 1985.0112.185.
- References:
- L. Brill, Catalog, 1892, p. 44-45, 64-65.
- Richter, K., Online Collection of Mathematical Models, Martin-Luther-Universität Halle-Wittenberg. This collection has the web address: https://www2.mathematik.uni-halle.de/modellsammlung/, accessed August 28, 2020. The example of this model shown has number A3-031 in that collection.
- Tesch. C., Modelle der Regelfaechen dritten Gerades. – a copy of this essay, which gives a brief historical account of the development of the model at Karlsruhe, is online at http://modellsammlung.uni-goettingen.de/data/Texts/M1/Modelle72-75_Tesch.pdf. It was posted in connection with the copy of the model at the University of Goettingen.The web version of the document was accessed August 28, 2020.
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.179
- catalog number
- 1985.0112.179
- accession number
- 1985.0112
-
- Description
- The German Karl Rohn (1855-1920) intended to become an engineer, but found the mathematical part of his studies at the polytechnic in Darmstadt more intriguing. He studied mathematics with Alexander von Brill and Felix Klein in Munich, and went on to a career as a professor of mathematics in Leipzig and Dresden.
- In 1886 and again in 1892, Rohn published sets of string models with the publisher and mathematical model distributor Ludwig Brill. Several models from the first set, Brill’s Series XIII, were exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893. This is one of them, number 5 in the series.
- The model has two congruent components (both in gold threads), both of them self-intersecting. The two segments of intersection are collinear, and are included on a vertical line (in red threads on the model). This model is a special case of #1 in the series (1985.0112.134). It was received with broken strings and restrung.
- Compare Baker models MA.304722.30 and MA.211257.123 to 1985.0112.130.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, pp. 27-28, 68.
- “Mathematical Models of Surfaces,” University of Groningen, website accessed October 16, 2017. This site describes the mathematics of these surfaces in more detail. It illustrates them with examples of the models published by Brill’s successor, Martin Schilling - still as series XIII.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.130
- catalog number
- 1985.0112.130
- accession number
- 1985.0112
-
- Description
- The German Karl Rohn (1855-1920) intended to become an engineer, but found the mathematical part of his studies at the polytechnic in Darmstadt more intriguing. He studied mathematics with Alexander von Brill and Felix Klein in Munich, and went on to a career as a professor of mathematics in Leipzig and Dresden.
- In 1886 and again in 1892, Rohn published sets of string models with the publisher and mathematical model distributor Ludwig Brill. Several models from the first set, Brill’s Series XIII, were exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893. This is one of them, number 9 in the series. It has a black metal frame and gold strings.
- As described in the Brill catalog, the surface consists of a mantle on which there are two pieces of the double curve; the generators are partly real, partly ideal, double secants of the space curve of third order, including four tangents.
- Compare 1985.0112.128, MA.211257.122 and MA.304722.29. The last two models are by Richard P. Baker.
- References:
- L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, pp. 27-28, 69.
- An example of the model is shown in the website of the Dresden collection of mathematical models, accessed October 17, 2017. At that time, their copy of this model was described at http://www.math.tu-dresden.de/modellsammlung/karte.php?ID=557.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.128
- catalog number
- 1985.0112.128
- accession number
- 1985.0112
-
- Description
- From the early nineteenth century, mathematicians and engineers have studied surfaces generated by motion. In a complete form of this model, two sets of threads join the small circle (with its tangent line) at the top and the larger circle (with its tangent line) toward the bottom.
- One set of threads forms a cone and its tangent plane. The threads within it form a double cone. If the circle at the top or bottom is rotated, the tangent plane becomes a hyperbolic paraboloid and the double cone and outside cone become two different hyperboloids.
- Compare to model 1985.0112.009 (Brill’s Ser. 4, No. 2), in which the two metal circles are equal and the outer curve is a cylinder.
- This German model of a surface of second order is one of a series of five first introduced by Brill in 1879, rather early in the life of the company. This example was exhibited at the Columbian Exposition, the world's fair held in Chicago in 1893. It came to the Smithsonian from the mathematics department of Wesleyan University in Connecticut. It presently lacks weights and the strings are broken.
- Reference:
- Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 9-10, 58-59.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.010
- catalog number
- 1985.0112.010
- accession number
- 1985.0112
-
- Description
- This is one of four string models showing space curves of fourth order that were designed by the German mathematician Hermann Wiener (1857-1939) and first published by Ludwig Brill in 1884. The model has a metal frame painted black. There are no curves on the top and two pieces of metal along opposite sides of the bottom. Six curved metal segments come together at the center of two opposite sides. The other two sides have identical curved figures. The bits of string left on the model (most strings are missing) are red and gold. Several wires held in the frame have beads on them. This example has no maker's label.
- The model is intended to show the developable surface of the tangents to the curves shown in Brill's model 91 (e.g. model 1985.0112.065).
- This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893. It came to the Smithsonian from Wesleyan University in 1985.
- Examples of this model, with strings, are presently shown at websites of the University of Illinois (the Altgeld collection) and of the University of Groningen in the Netherlands.
- References:
- L. Brill, Catalog mathematischer Modelle..., Darmstadt: L. Brill, 1892, p. 24, 74.
- For images of the example of the model at the University of Illinois, see http://www.mathmodels.illinois.edu/cgi-bin/cview?SITEID=4&ID=358, accessed August 19, 2020.
- For the example of the model at the University of Groningen, see Series XII, nr. 2 at http://www.math.rug.nl/models/, accessed August 19, 2020.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.066
- catalog number
- 1985.0112.066
- accession number
- 1985.0112
-
- Description
- This adjustable string model with a metal frame shows a ruled surface, that is to say a surface swept out by moving straight lines. The model was published by the firm of Ludwig Brill in Darmstadt beginning in 1879. This example was exhibited at the German Educational Exhibit at the Columbian Exposition held in Chicago in 1893, where it was purchased by Wesleyan University.
- The model has a metal frame with two triangular metal pieces that can be opened to lie horizontally or raised to approach one another. These pieces are pivoted together at both ends and attached to a metal frame. Red and gold strings join opposite sides of the frame and each is held tight by a bead at one end and a weight at the other. When the triangular pieces lie flat, the strings are all in a plane; as the edges are raised, the surface becomes a doubly ruled hyperbolic paraboloid.
- References:
- Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 10, 60.
- Gerard Fischer, Mathematical Models, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, vol. I, p. 9, vol. II, pp.3-4.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.023
- catalog number
- 1985.0112.023
- accession number
- 1985.0112
-
- Description
- This string model with a metal frame shows two ruled surfaces, that is to say surfaces swept out by moving straight lines. On the outside, shown in gold threads, is a doubly ruled hyperboloid of one sheet with an elliptic base and top. On the inside is a doubly ruled elliptic double cone, erected on the same base and top and shown in red.
- The model was published by the firm of Ludwig Brill in Darmstadt. This example was exhibited at the German Educational Exhibit at the Columbian Exposition held in Chicago in 1893, where it was purchased by Wesleyan University.
- References:
- Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 9, 58.
- Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, pp. 251-253. An example of this model is shown in Figure 6.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.008
- catalog number
- 1985.0112.008
- accession number
- 1985.0112
-
- Description
- This model was shown at the German Universities Exhibit in Chicago at the 1893 World’s Fair: Columbian Exposition. The model, labeled 109, was manufactured by the Darmstadt publishing company of Ludwig Brill under the direction of the German mathematician Otto Staude.
- The mathematician Felix Klein came to Chicago as a representative of the Prussian Ministry of Culture and presented several lecture–demonstrations about the mathematical models on display there. After the World’s Fair, the models displayed in Chicago were purchased by Wesleyan University; they were donated to the museum about ninety years later.
- This white plaster model shows an ellipsoid and a hyperboloid. The visible part of the ellipsoid is the thickening around the hyperboloid. Looking at the front of the model (see AHB2016q011675.jpg) there are thin metal rods extending from the lower right and the underside of the upper left. The model originally had small eyes at the ends of the rods through each of which was a string that looped tightly around the plaster model; the two strings were of equal length.
- The model is listed in Brill’s 1892 catalog as “Model of Staude’s string construction of the ellipse from two confocal second order surfaces.” Otto Staude wrote a short article about the construction in Alexander von Brill’s ca. 1892 Discussions on the models for higher mathematical teaching published by the publishing house of L. Brill in Darmstadt. The confocal surfaces referred to are an ellipsoid and a hyperboloid of one sheet.
- This string, or thread, construction does not produce a string model in the usual sense, i.e., it is not a model of a ruled surface in which every point of which is on a straight line contained entirely in the surface. While the hyperboloid is such a surface, the ellipsoid, to which the thread construction refers, is not. Rather, the construction is analogous to the pencil and string construction of an ellipse. In that construction the two ends of a string are fixed at two points (the foci of the intended ellipse) and the string is kept taut by a pencil while drawing a curve with that pencil. In this model, the the analog of the piece of string whose ends are anchored at the foci of the ellipse is a loop of string that passes around the plaster model. The two eyes at the ends of the rods represent two different possibilities for the location of the analog of the pencil point that pulls the string tight.
- The short article by Staude describes the model as having a red piece of string attached to the rod on the lower right side and looped around the model as well as a yellow piece of string of the same length attached to the rod on the upper left side also looped around the model. Both strings are taut. A photograph in the mathematical models collection at the University of Groningen in Holland shows the placement of the threads looking at the back of the model (Series X, 2b).
- Staude describes the properties of two differently defined points that lie on the ellipsoid to be constructed. They are represented by the place on the rods where the red and the yellow thread would be anchored. All points on that ellipsoid must be constructed using a piece of string of the same length as the red and yellow pieces of string and must follow a path composed in the same way as one of the paths described below for the red or the yellow thread. In both cases the thread would leave the rod in two straight line segments, each of which is part of a line tangent to both the ellipsoid and the hyperboloid.
- When the red thread left the rod it ran in two line segments both of which first met the plaster on the ellipse at a point of tangency (the points of tangency with the hyperboloid occurs further along those lines). The line segment running from the right hand rod and to the front of the plaster met the ellipsoid near the upper curve of intersection of the ellipsoid and the hyperboloid, while the one that ran to the back met the ellipsoid near the lower curve of intersection. The line segments were continued by a geodesic (minimal length) curve on the ellipsoid that ran to the closer curve of intersection and was continued along the curve of intersection until the two parts of the thread were joined along another geodesic that ran between the two lines of intersection.The path of the thread that ran between the lines of intersection is visible on the left side of the ellipse in AHB2016q011676.jpg.
- When the yellow thread left the rod it also ran in two line segments. Starting from the left hand rod it ran to the back of the plaster model, met the hyperboloid, continued as a line segment until it met the ellipsoid, traveled on a geodesic curve seen on the ellipsoid (visible on the left side of the model in AHB2016q011678.jpg) to the lower curve of intersection of the ellipsoid and the hyperboloid, traveled along the lower curve of intersection onto another geodesic curve as it ran along a geodesic curve on the ellipsoid until it met the line segment that took it back to the rod.
- Reference:
- “Modell zur Fadenconstructionen des Ellipsoids aus zwei gegeben confocalen Flächen zweiten Grades” by Dr. O. Staude, 2 pp. In Alexander von Brill, Abhundlungen zu den durch die Verslagshandlung von L. Brill in Darmstadt veröffentlichten Modellen für den höheren matheatischen Unterricht. Darmstadt: Brill, ca. 1892.
- Location
- Currently not on view
- date made
- 1892
- maker
- L. Brill
- ID Number
- 1985.0112.077
- catalog number
- 1985.0112.077
- accession number
- 1985.0112
Pages
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