Index of Mathematical Objects

Although students might initially assume that mathematics is only written in texts, the discipline's history and practice includes a rich material culture. Convergence's library of Mathematical Treasures thus encompasses not only books and documents, but also instruments for calculating, observing, and measuring as well as other tangible artifacts. These objects have been gathered into a separate list to help instructors identify physical "things" they may wish to discuss and illustrate in their classrooms. One tool for teaching students how to analyze historical objects is this worksheet based upon Frederick D. Drake and Sarah Drake Brown, "A Systematic Approach to Improve Students' Historical Thinking," The History Teacher 36, no. 4 (2003): 465–489. For suggestions on teaching mathematics with objects and images of objects, see "Online Museum Collections in the Mathematics Classroom," by Amy Ackerberg-Hastings and Amy Shell-Gellasch.

Devices for Teaching and Representing Mathematics

• Demonstration Metric Grain Measures by Shakers of West Gloucester (later Sabbathday), Maine (1877–1900)
• Models for Descriptive Geometry by A. Jullien (ca 1880)
• Model for Soap Film Minimal Surface by L. Brill (ca 1892)
• Paper model of elliptic paraboloid by L. Brill (1892)
• Hypotrochoid kinematic model by Martin Schilling (ca 1900)
• Model of a thermodynamic surface by Richard P. Baker (ca 1906–1935)
• Geometric model from paper by A. Harry Wheeler (1915)
• Dissected rhombic dodecahedron by A. Harry Wheeler (1930s)
• Transformable plane dissections by A. Harry Wheeler (1931)
• Boole Senior Blocks by Edith Dummer Mintzer (ca 1935)
• Model of spherical triangle by A. Harry Wheeler (1945)
• Model of Elongated Pentagonal Pyramid by Michael Berman (mid-20th century)
• Add-A-Count Scale from Child Guidance Toys (1950s)
• Arithmetic Teaching Machine by B. F. Skinner (1954)
• Number line designed by Loraine McMillan and sold by Houghton-Mifflin Company (ca 1972)
• Blackboard triangles by Safe-T (2000)

Devices for Counting, Calculating, and Computing

• Mesopotamian accounting tokens (ca 4000–3100 BCE)
• English tally sticks (1296)
• Inca quipus (ca 1400–1650)
• Jetons for counting board, some associated with Hans Schultes or Hans Krauwinckel (ca 1490–1635)
• Counting board (16th century)
• Sangi rods and computing grid (17th–19th centuries)
• Set of Napier rods or bones (17th century)
• Pascal's Calculator, or Pascaline, by Blaise Pascal (1645)
• Stylus-operated Adding Machine, by Jean Lepine (1725)
• English gauger's scale (ca 18th century)
• Slide rule and gauging sticks (18th century)
• English-style sector from Jesse Ramsden's workshop (1765–1800)
• Korean sangi rods (19th century)
• Key-driven adding machine patent model by Thomas Hill (1857)
• Thomas Arithmometer by Charles Thomas (1867)
• Logic piano (mechanical computer) by William Stanley Jevons (1869)
• Troncet Arithmographe by Louis Troncet (1889/1895)
• Stepped Reckoner by Gottfried Wilhelm Leibniz (20th century replica of 1671 design)
• Simplex Mannheim slide rule by A. W. Faber (later Faber-Castell) (1900–1908)
• Ritty cash register by James and John Ritty (by 1904)
• Consul, the Educated Monkey (1915)
• Chinese abacus (ca 1925)
• Product integraph by Vannevar Bush and colleagues (ca 1925)
• IBM statistical tabulator by Benjamin Wood (1929)
• Class 3000 Bookkeeping Machine by National Cash Register Company (1938)
• Factor Stencil Punch Cards designed by Derek N. Lehmer and John D. Elder (1939)
• Trigonometer for Use with Artillery (ca 1942)
• Wang desktop programmable calculator by An Wang (ca 1965)
• Roman hand abacus (1977 reconstruction of 1st century design)
• HP28S Handheld Electronic Calculator by Hewlett-Packard (1988)
• Difference Engine by Charles Babbage (late-20th century construction of 1853 design)

Devices for Measuring, Drawing, and Observing

• Italian compass (15th century)
• Manuscript illustrations of measurement tools (15th century)
• Italian armillary sphere (1550)
• Italian astrolabe by Bernard Sabeus (1558)
• Gunter quadrant (17th century)
• Austrian weights (18th century)
• German protractor (1700)
• Austrian measuring rod (1732)
• Protractor, set square, and sector by Michael Butterfield (ca 1750)
• Set square by Claude Langlois (ca 1750)
• Astrolabe quadrant signed by Aḥmad ibn Ibrāhīm al-Sharbatlī (1840–1841)
• Hinged parallel rule by William Field (1854/1923)
• Grunow spherometer by William and Julius Grunow (1860s)
• Combination ruler, protractor, and calculating device patent model by Nels Ockerlund (1870)
• Japanese protractor (1876)
• Polar planimeter by Jacob Amsler (1880s)
• Captain Field's Improved Hinged Parallel Rule from Henry Hughes & Son (1923)
• Suspension Pantograph by G. Coradi (ca 1928)
• Trammel Ellipsograph by Keuffel & Esser (ca 1930)
• RCA Flowcharting Template (ca 1960)
• Proportional dividers by Maurice Kidjel (ca 1962)

Miscellaneous Objects

• Mathematical paintings by Crockett Johnson (1965 and 1968)
• Promotional Pen from Rubik's Cube Museum (1988–1991)