Computers & Business Machines

• 

  Geometric Model, L. Brill No. 90 a. Ser. 6 No. 19a, Third Order Space Curve

  Description

  In 1880, Ernst Lange, a student at the mathematical institute of the technical high school in Munich, working under the direction of Felix Klein, designed four plaster models of space curves of degree three drawn on cylinders with cross sections that were conic sections. All of these curves represented the intersection of a surface of degree two with the cylinder shown.

  This model, the first in the series, shows the intersection of a cone with an elliptic cylinder. The curve of intersection, called a cubic ellipse, is incised on the model. A paper tag on the model reads: Raumcurve 3. Ordnung. (/) Verl. v. L. Brill. 6. Ser. Nr. XIXa.

  Compare 1985.0112.061, 1990.0571.24, and 1990.0571.25. For another curve drawn on an elliptic cylinder, see 1982.0795.32

  References:

  L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, p. 13, 73-74.

  E. Lange, Mathematische Modelle XIX. Die vier Arten der Raumcurven dritter Ordnung, pp. 1-2. A copy of this document is available online through the website of the Göttingen collection of mathematical models. Accessed November 13, 2017.

  Mathematics Institute of Oxford University website. This indicates that the intersecting surfaces are an elliptic cylinder and a hyperbolic parabola.

  Ulf Hashagen, Walther von Dyck (1856-1934): Mathematik, Technik und Wissenschaftsorganisation an der TH München, Stuttgart: Franz Steiner, 2003, p. 90, 100, 102.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.061

  catalog number

  1985.0112.061

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Geometric Model, L. Brill No. 4, Ser. 10. 1, Disjoinable Ellipsoid

  Description

  This white plaster ellipsoid is divided in two along a circle that makes an angle of about 45 degrees with the major axis of the ellipse. Two metal rods protruding from the right portion fit into metal-lined holes in the left portion. The hollow elliptical wooden stand is painted black.

  Compare 1990.0571.02.

  This series of models was designed at the technical high school in Munich under the direction of Alexander Brill, and originally published in 1885.

  Reference:

  L. Brill, Catalog, 1892, p. 21, 57, 91.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.001

  catalog number

  1985.0112.001

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Geometric Model, L. Brill No. 37. Ser. 7 No. 8, Third Order Surface with Three Double Points

  Description

  This white plaster model of a third order surface has a square base and three symmetrically arranged peaks. The peaks come together at three points along their slopes, with a hollow area beneath. Various curves are indicated on the surface.

  A paper tag reads: 37. Another paper tag reads: Fl. 3. Ord. mit [. . .] reellen Knpktn. [. . .] (/) Verl. v. L. Brill. 7 Ser. Nr. 8 [. . .].

  This model, along with all the models of Series 7, is on the design of Carl Rodenberg of the technical high school in Munich.. It was first published by Brill in 1881.

  References:

  L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, p.14, 61.

  Accession file.

  G. Fischer, Mathematical Models, Braunschweig: Vieweg, 1986, vol. 1, p. 19, vol. 2, pp. 12-14.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.029

  catalog number

  1985.0112.029

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Geometric Models, L. Brill No. 99. Ser. 3 No. 9, Two Hyperboloids of Two Sheets

  Description

  In the nineteenth and early twentieth century, students studying technical subjects often learned about the representation of surfaces by equations in courses in solid analytic geometry. Schools in Europe, the United States, and Japan sometimes purchased models to illustrate such surfaces. These objects are part of series of models of quadric surfaces (surfaces of degree two) designed in 1878 by Rudolf Diesel, then a student at the technical high school in Munich. They were published by the firm of Ludwig Brill in Darmstadt. These examples were exhibited at the German Educational Exhibit at the Columbian Exposition held in Chicago in 1893, where they were purchased by Wesleyan University.

  The plaster models show a hyperboloid of two sheets. The surface can be represented by the equation x²/a² + y²/ b² + z²/c² = - 1. Sections parallel to the plane z=0 are ellipses. Sections by the planes x=0 and y=0, and planes parallel to these, are hyperbolas. Two metal rods hold together the two sheets of each model.

  Grids of perpendicular lines of curvature are shown. A paper tag on one models reads: 99. Paper tags on both of them read: Zweischaliges Hyperboloid. (/) Verl. v. L. Brill. 3. Ser. Nr. 9.

  Compare 1990.0571.07.

  References:

  Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 7, 77.

  Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, pp. 240-241.

  Gerard Fischer, Mathematical Models, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, vol. I, p. 62, vol. II, pp.25-28.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.072

  catalog number

  1985.0112.072

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Darling, Brown & Sharpe Open Triangle

  Description

  This steel 45°-45°-90° triangle is 8" tall and has an open interior. A hole near one vertex is for hanging. The instrument is marked: Darling, Brown & Sharpe (/) Providence, R.I. The firm operated under that name from 1866 to 1892. (Compare to 1977.0460.08 and 1977.0460.09.) It advertised this triangle in 1868 for $4.50 and for $4.00 in 1887 and 1899 (when the company was known as Brown & Sharpe). In 1884 the Physical Laboratory of the University of California in Berkeley purchased a triangle of this type from Darling, Brown & Sharpe for $4.25.

  Erasmus Darwin Leavitt Jr. (1836–1916), the renowned American mechanical engineer and designer of steam engines, owned this triangle. It was donated to the Smithsonian by his granddaughter.

  References: Kenneth L. Cope, intro., A Brown & Sharpe Catalogue Collection, 1868 to 1899 (Mendham, N.J.: The Astragal Press, 1997), 14, 118, 157; "Disbursements," in Annual Report of the Secretary to the Board of Regents of the University of California, for the Year Ending June 30, 1884 (Sacramento, 1884), 50.

  Location

  Currently not on view

  date made

  1866-1892

  maker

  Darling, Brown & Sharpe

  ID Number

  1977.0460.10

  catalog number

  336081

  accession number

  1977.0460

  Data Source

  National Museum of American History

• 

  Brunsviga Model C Calculating Machine

  Description

  In 1892 the German firm of Grimme, Natalis & Company in Braunschweig, which had specialized in sewing machines, purchased the rights to manufacture pinwheel calculating machines on the design of the Swede W. T. Odhner. Under the leadership of the engineer Franz Trinks, they began manufacturing and improving a machine called the Brunsviga. This is a relatively early example.

  The lever-set non-printing manually operated machine has a brass and steel mechanism and a metal frame, painted black, with an iron base. Seven slots in the front have levers moved forward to release pins on pinwheels below and set a number. A brass crank with a wooden handle on the right side of the machine rotates backward (clockwise) for addition and multiplication and forward (counterclockwise) for subtraction and division.

  At the front of the machine, a movable carriage carries ten windows that show dials of the result register on the right and eight windows for the revolution register on the left. Holes for decimal markers above the registers presently contain no markers. Depressing a lever at the front of the machine releases the carriage for shifting. An arrow on the left of the cover of the machine points to the wheel of the revolution counter that will be affected by turning the crank when the carriage is in any one position. Rotating wing nuts at the ends of the carriage zeros the registers on it.

  Marks on the top of the machine read: BRUNSVIGA, and: No1750. A mark at the top of a list of patents on the left side of the machine reads: Grimme, Natalis & Co.(/) Braunschweig - Brunswick (/) Patente:W.T. Odhner. The patents are from Germany, Belgium, England, Austria, Sweden, Norway, Switzerland, Hungary, Russia (no number), Luxembourg (no number), and the United States (no number).

  This machine came to the Smithsonian from the personal collection of Brooklyn high school teacher L. Leland Locke.

  References:

  E. Martin, The Calculating Machines (Die Rechenmaschinen), trans. P. A. Kidwell and M. R. Williams, Cambridge: MIT Press, 1992, pp. 109–113.

  E. Anthes, “Zur Datierung von Brunsviga-Rechenmaschinen, Leertaste, Nr. 6, August, 1982.

  F. Schellstede, “Brunsviga. Produktionxzahlen, Absatzzahlen, Werbung. Versuch einer kurzen geschichtlichen Darstellung,” Kassel, 1990.

  “Sixty Years of Brunsviga,” Business Equipment Topics vol. 80 (April, 1932), p. 46.

  Location

  Currently not on view

  date made

  ca 1898

  maker

  Grimme, Natalis & Co.

  ID Number

  MA.311947

  catalog number

  311947

  accession number

  155183

  maker number

  1750

  Data Source

  National Museum of American History

• 

  Geometric Model, L. Brill No. 22. Carton Ser. No. 5, Paraboloid Made from Cardstock

  Description

  In the nineteenth and early twentieth century, students studying technical subjects often learned about the representation of surfaces by equations in courses in solid analytic geometry. Schools in Europe, the United States, and Japan sometimes purchased models to illustrate such surfaces. The firm of Ludwig Brill in Darmstadt published this one as part of a series of paper models (the “Carton” series) designed by Alexander Brill and first issued in 1874. 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 green paper model of an elliptic paraboloid consists of portions of twelve circles intersecting portions of twelve other circles. It is stored flat in a gray paper envelope which also contains model 1985.112.004. The envelope is in a brown box with the other models in the Carton series. A mark on model reads: Verlag von L. Brill in Darmstadt.

  The surface shown can be represented by the equation x²/a² + y²/ b² = - 2z (when the model is mounted on the stand as shown, the z-axis goes cross-wise). It is displayed on a stand that is part of 1985.0112.005.

  References:

  Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 1, 59.

  Henry Burchard Fine and Henry Dallas Thompson, Coordinate Geometry, New York: Macmillan Company, 1931, p. 242.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.018

  catalog number

  1985.0112.018

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Microscope

  Description

  This is a compound monocular with sliding tube for coarse adjustment, micrometer screw for fine focus, inclination joint, rectangular stage covered with vulcanized rubber, sub-stage iris diaphragm, sub-stage mirror, horseshoe base, and wooden box with extra lenses. The inscription on the base reads “Bausch & Lomb Optical Co. / NEW YORK ROCHESTER, N.Y. CHICAGO.” The 24845 serial number indicates a date of around 1896. Bausch & Lomb termed this stand a Continental B; this example is of the simplest form.

  Ref: Bausch & Lomb, Microscopes and Accessories (Rochester and New York, 1895), pp. 4-5.

  Location

  Currently not on view

  date made

  ca 1896

  maker

  Bausch & Lomb

  ID Number

  2009.0116.11

  catalog number

  2009.0116.11

  accession number

  2009.0116

  Data Source

  National Museum of American History

• 

  Microscope

  Description

  Bausch & Lomb introduced their Large Continental in 1891, noting that “no efforts have been spared to make the stand the most complete and fitted with all modern improvements and appliances.” This example is a compound monocular with coarse and fine focus, triple nosepiece (but only one objective), inclination joint with clamp (the handle is made of celluloid), large circular stage, sub-stage Abbe condenser and iris diaphragm, and support for sub-stage mirror (the mirror is missing). The instrument is brass, the draw tube is nickel plated, and the stage is covered with vulcanized rubber. The inscription on the horseshoe base reads “Bausch & Lomb Optical Co. / ROCHESTER, N.Y. & NEW YORK CITY / 14317.” The serial number indicates a date around 1894.

  Ref: Henry Bausch, “New American Microscopes, Made by Bausch & Lomb Optical Co., Rochester, N.Y.,” Proceedings of the American Society of Microscopists 13 (1891): 116-119.

  Bausch & Lomb, Microscopes and Accessories (Rochester and New York, 1895), pp. 8-10.

  Henri Van Heurck, The Microscope (London, 1893), pp. 141-142.

  Location

  Currently not on view

  date made

  1894

  maker

  Bausch & Lomb Optical Company

  ID Number

  MG.M-12198

  accession number

  272522

  catalog number

  M-12198

  Data Source

  National Museum of American History

• 

  Geometric Model, L. Brill No. 12. Ser. 4, No. 2, Cylinder, Cone and Plane Transformable into One-Sheeted Hyperboloid and Hyperbolic Paraboloid

  Description

  From the early nineteenth century, mathematicians and engineers have studied surfaces generated by motion. The gold threads of this model form a cylinder, the red ones a double cone. Rotating the top circle of the frame twists the gold threads and untwists the red ones, forming surfaces called hyperboloids. The blue threads, which initially lie in a plane, become a hyperbolic paraboloid. This model was made in Germany and 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.

  Location

  Currently not on view

  Date made

  1893

  maker

  Brill, L.

  ID Number

  1985.0112.009

  accession number

  1985.0112

  catalog number

  1985.0112.009

  Data Source

  National Museum of American History

• 

  Geometric Model, L. Brill No. 200. Ser. 15 No. 5, Projection of a Polytope (Six Hundred-Cell)

  Description

  This string and wire model of a 600-cell consists of several wire polyhedra, one inside another. The innermost polyhedron appears to be a cube with a tetrahedron erected on each of its six sides. The second and third polyhedra are extremely complex, with triangular faces of differing dimensions. The fourth and outermost polyhedron appears to have 32 equilateral triangles for faces. The model originally sold with a skeleton of a tetrahedron on the outside, but that is missing on this example.

  In the late nineteenth century, several mathematicians thought of ways of envisioning four-dimensional surfaces in three-dimensional space. The German mathematician Victor Schlegel developed a series of wire and thread models for the purpose. The series was first published by Ludwig Brill in 1886.

  This model (presently misshapen and missing its threads) represents the 600-cell. It supposed to have 599 tetrahedra inside an outer tetrahedron.

  This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893.

  References:

  L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, pp. 31, 88.________.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.153

  catalog number

  1985.0112.153

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Geometric Model, L. Brill No. 101. Ser. 3 No. 16, Hyperbolic Parabaloid

  Description

  In the nineteenth and early twentieth century, students studying technical subjects often learned about the representation of surfaces by equations in courses in solid analytic geometry. Schools in Europe, the United States, and Japan sometimes purchased models to illustrate such surfaces. This object is part of series of models of quadric surfaces (surfaces of degree two) designed in 1878 by Rudolf Diesel, then a student at the technical high school in Munich. It 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.

  The saddle-shaped plaster model shows a hyperbolic paraboloid. The surface is represented by the equation: + y²/ b² - x²/a² = - 2z. Sections by any plane where x = c or y=c (c being an arbitrary constant) are parts of parabolas. Sections parallel to the plane z = 0 are parts of hyperbolas. A grid of perpendicular lines of curvature is shown on the model.

  A tag on the model reads: Hyperbolisches Paraboloid [. . .] (/) Verl. v. L. Brill. 3. Ser. Nr. 16.

  Reference:

  Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 7, 77.

  Gerard Fischer, Mathematical Models, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, vol. II, pp.25-28.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.074

  catalog number

  1985.0112.074

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Model of a Dissected Trapezoid, Ross Surface Form #6

  Description

  This is the sixth in a series of models of plane figures (surface forms) designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The unpainted rectangular wooden model is cut into two pieces at one corner. It may be arranged so that the pieces form either a rectangle or a trapezoid. A paper label attached to the model reads: Dissected Trapezoid 5x7.

  Ross argued that the area of the trapezoid equaled half the sum of its parallel sides, multiplied by its breadth.

  Compare models 1985.0112.190 through 1985.0112.202. For further information about Ross models, including references, see 1985.0112.190.

  Location

  Currently not on view

  date made

  ca 1895

  maker

  Ross, W. W.

  ID Number

  1985.0112.193

  accession number

  1985.0112

  catalog number

  1985.0112.193

  Data Source

  National Museum of American History

• 

  Geometric Model, L. Brill No. 36. Ser. 7 No. 7, Third Order Surface with Three Double Points

  Description

  This white plaster model of a third order surface has a square base and three symmetrically arranged peaks. Various colored lines are drawn on the surface.

  A paper tag on the model reads: 36. Another paper tag reads: Fl. 3. Ord. mit 3 reellen con. Knpktn. (/) Verl. v. L. Brill. 7. Ser. Nr. 7. This model, along with all the models of Series 7, is on the design of Carl Rodenberg of the technical high school in Munich.. It was first published by Brill in 1881.

  The object was exhibited at the German Educational Exhibit at the Columbian Exposition, a World’s Fair held in Chicago in 1893. It there was purchased by Wesleyan University in Connecticut, and subsequently was donated to the Smithsonian.

  References:

  L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, p.14, 61.

  Accession file.

  G. Fischer, Mathematical Models, Braunschweig: Vieweg, 1986, vol. 1, p. 17, vol. 2, pp. 12-14.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.028

  catalog number

  1985.0112.028

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Geometric Model, L. Brill No. 148. Ser. 10 No. 1h, Minimal Surface

  Description

  Students at the technical high school in Munich, working under the direction of Alexander Brill, developed a series of wire models of minimal surfaces that was first published by Ludwig Brill in 1885. A minimal surface is the surface of smallest area of all the surfaces bounded by a closed curve in space. Its mean curvature is zero. Minimal surfaces are often represented by soap films, as was the intention with this model. This, the eighth model in the series, is in the shape of a six-sided prism with alternate edges missing on the top and the bottom faces . A handle extends from the top.

  This example was exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893.

  References:

  L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, p. 21, 85.

  G. Fischer, Mathematical Models: Commentary, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, pp. 41-43.

  H.A. Schwarz, Bestimmung einer speciellen Minimalfläche, Berlin: F. Dümmler's Verlags-Buchhandlung, 1871. This source is mentioned in Brill’s catalog.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.113

  catalog number

  1985.0112.113

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Geometric Model, L. Brill No. 205. Ser. 17 No. 2b, Spherical Projection of a Plane Curve of Third Order

  Description

  This white plaster model shows the spherical projection of a plane curve of third order. It is a sphere with various colored and plain curves drawn on it. A mark on a paper tag on the model reads: Kugelprojection der ebenen Curven 3. Ord., (/) II. 3 Typen.(/) Verl. v. L. Brill. 17. Ser. Nr. 2b.; XVII. (/) 2b. The black wooden stand is round. The model was designed by Dollinger in Tűbingen under the direction of Alexander Brill.

  This example of the model was exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893.

  Reference:

  L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 40, 75.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.157

  catalog number

  1985.0112.157

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Pyramid and Frustrum of Pyramid, Ross Solid #11

  Description

  This is the eleventh in a series of models illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The unpainted wooden model has a square base and four equal triangles for sides. A plane parallel to the base divides it into a square pyramid and the frustum of a square pyramid. A paper label on the model reads: Frustum of a Pyramid. Another mark on this label reads: (See Metallic Frustum). A mark on another paper label reads: Pyramid.

  Compare models 1985.0112.205 through 2012.0112.217. For further information about Ross models, including references, see 1985.0112.190.

  Location

  Currently not on view

  date made

  ca 1895

  maker

  Ross, W. W.

  ID Number

  1985.0112.205

  catalog number

  1985.0112.205

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Chicago Stamping Co. Combination Rule and Paper Cutter, Advertising The Hartford Insurance Co.

  Description

  This convex orange-coated tin combination rule and paper cutter has a 9" scale divided to sixteenths of an inch along one long edge. The other long edge is shaped into a tube, which may serve as a handle while cutting or tearing paper. A small hole at the right end may be for hanging the rule. The rule is marked: Compliments (/) of (/) THE HARTFORD FIRE INS. Co. (/) HARTFORD, CONN. The company's logo of a stag appears between the words "HARTFORD" and "FIRE." The tube notes that the company had paid $33,000,00 for claims in New York City in 1835, Nantucket, Mass., in 1846, St. Louis, Mo., in 1849, Portland, Me., in 1866, Chicago in 1871, Boston in 1872, and St. John, New Brunswick, "and other places" in 1877. These were all historic destructive fires. The back of the rule is marked: AGENCIES IN ALL CITIES AND TOWNS THROUGHOUT THE COUNTRY (/) Commenced Buisness 1794 • Charter Perpetual (/) The Chicago Stamping Co. Combination Rule and Paper Cutter. Patent Sept. 8^th 1885. Hartford Fire Ins. Co. Sole Owner and Manufacturer. All Infringements prosecuted.

  Richard S. Thain (1845–1912) received the patent mentioned on the instrument. He fought for the Union in the Civil War, was advertising manager of a Chicago publication, Western Rural, and organized an advertising firm with George W. Sharp in 1868. He spent some time in New York City after the Chicago fire of 1871. From 1882 to 1889, he worked for a Chicago advertising agency, Lord & Thomas. Another ruler made from Thain's design is 293320.2815.

  The Chicago Stamping Company was in business from at least as early as 1868 to at least as late as 1911. The firm made enameled cylindrical tin containers, such as milk and trash cans; published sheet music and stationery items; and manufactured the United States Wheel brand of bicycles. Although text on the rule says The Hartford started selling fire insurance in 1794, the history on the company's website indicates it was not incorporated until May 10, 1810. The firm adopted its stag logo in 1875. As of 2013, it was one of the biggest insurance companies worldwide.

  References: Richard S. Thain, "Combination Ruler and Paper Cutter" (U.S. Patent 325,992 issued September 8, 1885); "Men of the Ninety-sixth Regiment with Millburn Connections," excerpted from Charles A. Partridge, ed., History of the Ninety-Sixth Regiment Illinois Volunteer Infantry (Chicago, 1887), Historic Millburn Community Association, http://www.hmca-il.org/k6men.htm; "The Hartford's Historical Timeline," http://www.thehartford.com/about/.

  Location

  Currently not on view

  date made

  ca 1890

  distributor

  Hartford Fire Insurance Company

  maker

  Chicago Stamping Company

  ID Number

  MA.293320.2814

  accession number

  293320

  catalog number

  293320.2814

  Data Source

  National Museum of American History

• 

  Geometric Model, L. Brill No. 68. Ser. 2 No. 6b, Kummer Surface

  Description

  In 1877, L. Brill published three plaster models designed by Karl Rohn (1855-1920), a student of Alexander Brill and Felix Klein at the technical high school in Munich. This is the second of them. Rohn would go on to make distinguished contributions to algebraic geometry, including the study of Kummer surfaces, both as a student and as a professor at German universities. A Kummer surface takes its name from the mathematician Eduard Kummer (1810-1893), who described them in an 1864 paper. It is a special kind of surface represented by an equation of degree four which has sixteen double points.

  Sometimes, as in this plaster model with metal supports, some of the double points are in the complex plane, and do not appear in a model in ordinary three-dimensional space. Eight double points are shown. The curves shown on the model represent lines of intersection between the surface and planes containing six of the double points. They are curves of degree two, that is to say conic sections.

  A paper tag on the model reads: 68. Another paper tag reads: Kummer'sche Fläche (/) [. . .] v. L. Brill. 2. Ser. Nr. VIb

  This example of the model was exhibited at the Columbian Exposition in Chicago in 1893.

  References:

  L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, p. 5, 66.

  G. Fischer, Mathematical Models: Commentary, Braunschweig / Wiesbaden: Friedr. Vieweg & Sohn, 1986, pp. 14-16.

  Mathematics Institute of Oxford University website.

  Ulf Hashagen, Walther von Dyck (1856-1934): Mathematik, Technik und Wissenschaftsorganisation an der TH München, Stuttgart: Franz Steiner, 2003.

  Location

  Currently not on view

  date made

  1892

  maker

  L. Brill

  ID Number

  1985.0112.052

  catalog number

  1985.0112.052

  accession number

  1985.0112

  Data Source

  National Museum of American History

• 

  Sixteen-Sided Regular Polygon, Ross Surface Form

  Description

  This is one of the models of plane figures (surface forms) designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The flat unpainted wooden object is in the shape of a regular polygon with sixteen sides. On the opposite side from the paper label, it has eight straight lines drawn joining opposite vertices, dividing the polygon into 16 equal triangles. The lines meet at a point. The label reads: POLYGON OF 16 SIDES.

  In constructing his visual demonstration of the area of a circle, Ross built several regular polygons, and showed that they had areas equal to the sum of the area of triangles with height equal to the radius of an inscribed circle and sides equal to the sides of the polygons. In other words, the area of the regular polygon equaled half the perimeter of the polygon times the radius of the inscribed circle.

  This is the example for a 16-sided figure. Compare 1985.0112.200 and 1985.0112.201. For the circle, see 1985.0112.203. For further information about Ross models, including references, see 1985.0112.190.

  Location

  Currently not on view

  date made

  ca 1895

  maker

  Ross, W. W.

  ID Number

  1985.0112.202

  catalog number

  1985.0112.202

  accession number

  1985.0112

  Data Source

  National Museum of American History

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