Computers & Business Machines
Imagine the loss, 100 years from now, if museums hadn't begun preserving the artifacts of the computer age. The last few decades offer proof positive of why museums must collect continuously—to document technological and social transformations already underway.
The museum's collections contain mainframes, minicomputers, microcomputers, and handheld devices. Computers range from the pioneering ENIAC to microcomputers like the Altair and the Apple I. A Cray2 supercomputer is part of the collections, along with one of the towers of IBM's Deep Blue, the computer that defeated reigning champion Garry Kasparov in a chess match in 1997. Computer components and peripherals, games, software, manuals, and other documents are part of the collections. Some of the instruments of business include adding machines, calculators, typewriters, dictating machines, fax machines, cash registers, and photocopiers

Model of Babbage's Difference Engine No. 1  Replica
 Description
 This is a replica of the portion of a difference engine built by Charles Babbage in 1832. Babbage, an English mathematician, hoped to compute and to print astronomical tables by machine. He proposed to estimate the value of functions using polynomials, and to use the method of finite distances to compute results.
 Babbage never completed either a difference engine or a more complex, programmable instrument he dubbed an analytical engine.
 The machine has three columns of discs. The leftmost column has six discs, each with the numbers from 0 to 9. The middle column has seven discs. The six lower ones each have the digits from 0 to 9. The uppermost disc is marked as indicated. The rightmost column has five discs numbered from 0 to 9. Above these are four discs, similarly numbered, that are immediately adjacent to one another. On the top of the machine are a gear train and a handle. The machine has a metal framework and a wooden base. The replica has containers for springs, but no springs.
 The overall dimensions include the handle. Without it, the dimensions are: 59 cm. w. x 43.5 cm. d. x 72 cm. h.
 The replica was built for display in the first exhibition devoted to mathematics and computing at the Museum of History and Technology (now the National Museum of American History). A similar replica is in the collections of IBM Corporation.
 The original on which this replica is based is at the Science Museum in London. That museum also displays a more recent attempt to build a working version of Babbage’s difference engine.
 References:
 Merzbach, Uta C., Georg Scheutz and the First Printing Calculator, Washington, D.C.: Smithsonian Institution Press, 1977.
 D. Pantalony, “Collectors Displays and Replicas in Context What We Can Learn from Provenance Research in Science Museums,” in The Romance of Science: Essays in Honour of Trevor H. Levere, eds. Jed Buchwald and Larry Stewart, Cham: Springer, 2017, pp.257275, esp. pp.268273. This article discusses replicas of the Babbage difference engine, but not the one at the Smithsonian, which was by a different maker than other replicas provided by IBM.
 Swade, Doron. The Difference Engine: Charles Babbage and the Quest to Build the First Computer, New York: Viking, 2000.
 Location
 Currently not on view
 date made
 ca 1963
 date received
 1963
 maker
 Daniel I. Hadley & Associates
 ID Number
 MA.323584
 accession number
 252309
 catalog number
 323584
 Data Source
 National Museum of American History

Keuffel and Esser DeciLon Slide Rule
 Description
 This Keuffel and Esser DeciLon slide rule is a model 68 1100 with 10inch scales. The rule is made of a shatterproof synthetic material while the indicator is made of clear plastic with metal edges. Markings are in red and black. The front face is printed with 13 scales: Sq1, Sq2, DF, CF, CIF, L, CI, C, D, Ln0, Ln1, Ln2, Ln3. The reverse face is also printed with 13 scales: Ln3, Ln2, Ln1, Ln0, A, B, T, SRT, S, C, D, DI, and K scales. Printed on the reverse face and located on the right side of the lower rail is the serial number 178687 and located on the leftside of the center rail, made in U.S.A. When not in use, it is stored in an orange, stitched leather case with belt carrier. An imprint of the donor’s last name can be detected on the front of the case under the model name.
 The donor purchased this slide rule from the Cornell University bookstore in September 1969. He used it in his coursework for physics engineering as well as nuclear engineering. After earning a master’s degree in nuclear engineering, he served for 42 years in the U.S. Navy.
 References:
 http://www.mccoyskecatalogs.com/KECatalogs/1962/1962kecatp10.htm
 http://www.mccoyskecatalogs.com/KECatalogs/1967/1967kecatp12.htm
 http://www.sliderules.info/collection/10inch/020/1025decilon.htm
 Accession file.
 Location
 Currently not on view
 date made
 ca 1969
 maker
 Keuffel & Esser Co.
 ID Number
 2018.0283.02
 accession number
 2018.0283
 catalog number
 2018.0283.02
 Data Source
 National Museum of American History

Four Articles on Educational Games
 Description
 These four sheets are photocopies of reprints of the articles listed below:
 1. "Games and programmed instruction" by Layman E. Allen  reprinted from The Arithmetic Teacher> for March, 1965.
 1." Programmed Games and the Learning of ProblemSolving Skills: The WFF 'N PROOF Example" by Layman E. Allen, Robert W. Allen, James C. Miller, reprinted from The Journal of Educational Research, September, 1966, pp.2225.
 3. "The ALL Project (Accelerated Learning of Logic)" by Layman E. Allen, Robin B. S. Brooks, James W. Dickoff and Patricia A. James, reprinted from the
, May, 1961, 68: 497500.  4. " Academic Ganes: Play as You Learn" by John Egerton, reprinted from Southern Education Report (no date).
 Location
 Currently not on view
 date made
 19611966
 maker
 Allen, Layman E.
 ID Number
 MA.317891.31
 accession number
 1975317891
 catalog number
 317891.31
 Data Source
 National Museum of American History

Prism Binoculars
 Description
 This is a steel instrument with black plastic fittings and black leather on the barrels. The left eye plate is marked “CARL / ZEISS/ 8 x 30.” The objective lenses are 30 mm diameter. The eyepieces are separately adjustable as is the interocular distance. The barrel on the right has been bisected to show the internal structure.
 Location
 Currently not on view
 date made
 ca 1963
 maker
 Zeiss
 ID Number
 PH.323152
 catalog number
 323152
 accession number
 250105
 Data Source
 National Museum of American History

LOCI2 Punch Card
 Description
 This is one of a series of fortycolumn perforated punch cards designed for use with the programmable Wang LOCI2 electronic calculator. Each card is marked in the bottom left corner: IBM D56709. Each card is marked on the left side: LOCI (LOGARITHMIC COMPUTER) PROGRAM.
 For the calculator, see 1980.0096.01. For the card reader, see 1980.0096.01.1. For the card punch, see1980.0096.02.
 Location
 Currently not on view
 date made
 1965 or later
 maker
 IBM
 ID Number
 1980.0096.03.5
 catalog number
 1980.0096.03.5
 accession number
 1980.0096
 Data Source
 National Museum of American History

Booklet, Instructions MonroMatic Monroe IQ Calculator
 Description
 This illustrated pamphlet is the third (1963) printing of an instruction book first published in 1961. It describes use of the MonroeModel IQ213 calculating machine.
 The document was received with an example of this machine that has museum number 1988.0663.01.
 Location
 Currently not on view
 date made
 ca 1963
 ID Number
 1988.0663.02
 accession number
 1988.0663
 catalog number
 1988.0663.02
 Data Source
 National Museum of American History

Pickett Trig Slide Rule Instruction Manual
 Description
 This 64page booklet was received with 1993.0559.01. Its citation information is: Maurice L. Hartung, How to Use . . . Trig Slide Rules (Chicago: Pickett & Eckel Inc., 1960). It sold separately for fifty cents. Hartung was the University of Chicago professor who was closely associated with Pickett & Eckel in the company's early years and who wrote several instruction manuals for the firm's slide rules.
 The booklet discusses slide rule operation, use of certain special scales, applications of trigonometry, and the principles underlying slide rules. Hartung focused on the operations of the instrument rather than on mathematical theory. There are problem sets at the end of each section, with answers in the back of the manual, and a few sets of "practical" (word) problems. Another copy of the booklet is scanned at http://sliderulemuseum.com/Manuals/M104_Pickett_HowToUseTrig_1960.pdf.
 Reference: "Maurice Leslie Hartung," Mathematics Genealogy Project, http://www.genealogy.math.ndsu.nodak.edu/id.php?id=7964. Hartung received a life achievement award from the Illinois Council of Teachers of Mathematics in 1977, http://ictm.org/ictmawards/lifeachievement.html.
 Location
 Currently not on view
 date made
 1960
 publisher
 Pickett Industries
 author
 Hartung, Maurice L.
 ID Number
 1993.0559.01.01
 accession number
 1993.0559
 catalog number
 1993.0559.01.01
 Data Source
 National Museum of American History

New Math Flash Cards, Subtraction
 Description
 From the 1950s, particularly after the launch of the Sputnik satellite in 1958, American mathematicians and mathematics educators introduced a variety of reforms in mathematics teaching dubbed “The New Math.” This set of flash cards reflects the way of presenting subtraction problems that emerged.
 The set consists of fifty cards, printed with subtraction problems on each side. The problems are written crosswise, with a box for the answer. The solution is printed in red in the upper left corner on the back. Another card lists basic subtraction facts (vertically), and three cards give work sheets and directions.
 A mark on the paper box reads: MILTON BRADLEY (/) NEW MATH (/) FLASH CARDS (/) SUBTRACTION. Another mark reads: [copyright] 1965. A third mark reads: 4592.
 These and several other sets of flash cards were donated by elementary school teacher Marjorie A. Naidorf.
 Compare 2005.0055.06, 2005.0055.07, 2005.0055.08, and 2005.0055.09.
 Location
 Currently not on view
 date made
 ca 1965
 maker
 Milton Bradley Company
 ID Number
 2005.0055.06
 catalog number
 2005.0055.06
 accession number
 2005.0055
 Data Source
 National Museum of American History

LOCI2 Punch Card
 Description
 This is one of a series of fortycolumn perforated punch cards designed for use with the programmable Wang LOCI2 electronic calculator. Each card is marked in the bottom left corner: IBM D56709. Each card is marked on the left side: LOCI (LOGARITHMIC COMPUTER) PROGRAM.
 For the calculator, see 1980.0096.01. For the card reader, see 1980.0096.01.1. For the card punch, see1980.0096.02.
 Location
 Currently not on view
 date made
 1965 or later
 maker
 IBM
 ID Number
 1980.0096.03.6
 catalog number
 1980.0096.03.6
 accession number
 1980.0096
 Data Source
 National Museum of American History

Hologram of Toy Train
 Description
 This glass plate records the hologram, “Toy Train” by Emmett Leith and Juris Upatnieks. Made in late 1963, this hologram demonstrated their method of making highresolution threedimensional images of threedimensional objects. Their success at the University of Michigan’s Willow Run Laboratory came after several years work on advanced radar techniques and lensless photography for defense purposes.
 Leith and Upatnieks created this transmission hologram by exposing a black and white photographic plate to the laser light reflected from a toy train model. The image is reconstructed in three dimensions when the correct laser light shines through the glass. When they displayed this hologram at a conference in April 1964, other scientists linedup to see their breakthrough. “Toy Train” was not the first hologram ever made, but the quality of the image stunned everyone. And so it became the first hologram many people heard about. Since then, many other types of holograms have been devised.
 In 1948, British scientist Dennis Gabor had used two beams of electrons to record a microscopic image. He then tried to make images of larger objects using filtered light from an arc lamp but obtained poor results. The invention of lasers in 1960 gave researchers a better light source for making threedimensional photographs and spurred Leith and Upatnieks’ work.
 Location
 Currently not on view
 date made
 1963
 maker
 Leith, Emmett N.
 ID Number
 PG.69.186.05
 catalog number
 69.186.5
 accession number
 285032
 Data Source
 National Museum of American History

Keuffel & Esser 40703 Polyphase Duplex Trig Slide Rule
 Description
 This teninch mahogany duplex slide rule is coated with white celluloid and held together with metal endpieces that are significantly corroded. On one side, the base has DF, D, and L scales, with CF, CIF, CI, and C scales on the slide. The top of the base is marked in faded red: KEUFFEL & ESSER CO.; PATS. 2,500,460 2,168,056 2,170,144 PAT. PEND.; MADE IN U.S.A. The right end of the slide is marked in red: © (/) K + E; < 40703 >. On the other side, the base has K, A, D, and DI scales, with B, T, ST, and S scales on the slide. The left end of the slide has a serial number: 952594. The top and bottom of the base are both marked at the left end: 594. The indicator is glass with plastic edges; it is so corroded that it has fallen apart and is no longer on the rule.
 There is a green leather case with white inlays on the holder for the flap. The flap is marked: K + E. Inside the flap is written in ink: Jeffery (/) Smith (/) P 68. An orange chamois case holds a magnifier with two lenses and a metal frame. On one side, the frame is marked: K + E. On the other side, the frame is marked: PAT. NO. 2556806. A green cardboard box, missing one end, holds the rule, its case, the magnifier, and its case.
 For information on the patents on the rule, see 1993.0482.01 and 2007.0181.01. Paul E. Gaire of Manasquan, N.J., received a patent for the magnifier in 1951, replacing his earlier attempt at a magnifier, which could only be used on one side of a slide rule at a time. This double magnifier was first advertised in Keuffel & Esser's 1954 catalog and first pictured in the 1962 catalog; it sold for $5.50. K&E sold this version of the model 40703 slide rule from 1952 to 1962, at a price of $20.50.
 References: Paul E. Gaire, "Magnifying Runner for Slide Rules" (U.S. Patent 2,556,806 issued June 12, 1951); K + E Catalog, 42nd ed. (New York: Keuffel & Esser Co., 1954), 276–277; Keuffel & Esser Co., Slide Rules, Catalog 8 (Hoboken, N.J., 1962), 29–30; Clark McCoy, ed., "K&E Catalogs and Price Lists for Slide Rules," http://www.mccoyskecatalogs.com/KEmain.htm.
 Location
 Currently not on view
 date made
 19541962
 maker
 Keuffel & Esser Co.
 ID Number
 1990.0317.03
 catalog number
 1990.0317.03
 accession number
 1990.0317
 Data Source
 National Museum of American History

Burroughs Series P Adding Machine
 Description
 This fullkeyboard printing electric adding machine has a tan steel frame and eight columns of tan and brown square plastic keys. To the left of these is a column of keys with the numbers 71 through 79 (there is a 65 instead of a 75), presumably denoting years. Left of this is a column with four keys for the months of quarterly statements (DEC, SEP, JUN, and MAR) and two keys labeled MR and CHK respectively. There are function bars and keys to the right of the number the keys.
 Above the keyboard are four number wheels. Behind them is a twocolored ribbon and a printing mechanism, an adjustable wide carriage, and narrow paper tape. The type wheel for months has all 12 months on it. The ribbon and its spools are covered, with screws holding the covers in place. Plastic knobs at the ends of the carriage are rotated to advance the platen. On the right side of the machine is a place for inserting a crank, although there is no crank. At the back on the right side is a lock for the machine, with the key in it. There also is a lock at the left front of the machine.
 The machine is marked on the front: Burroughs. The serial number, on a metal tag on the back of the machine, is: P366728D It is from after 1960. Another metal tag on the back of the machine is marked: SERIES P (/) BURROUGHS CORPORATION (/) DETROIT, MICHIGAN MADE IN U.S. America.
 Location
 Currently not on view
 date made
 ca 1960
 maker
 Burroughs Corporation
 ID Number
 1987.0285.02
 catalog number
 1987.0285.02
 accession number
 1987.0285
 Data Source
 National Museum of American History

Replica of a Mariner's Astrolabe from about 1603
 Description
 This metal mariner's astrolabe is a replica of one associated by some with the French explorer Samuel de Champlain (ca 15671635). It was made for the museum.
 Location
 Currently not on view
 date made
 1964
 1963
 ID Number
 MA.323718
 catalog number
 323718
 accession number
 252316
 Data Source
 National Museum of American History

WFF 'N PROOF: The Game of Modern Logic
 Description
 This set of 21 games taught principles of modern logic. Players learned to combine grammatically correct logical statements called wellformed formulae (WFFs) into logical proofs. WFF 'N Proof was developed by Layman E. Allan of Yale University Law School under a grant from the Carnegie Corporation for ALL (Accelerated Learning of Logic). Allen applied for a trademark for WFF ‘N Proof in August 1961; it was registered the following year but has now expired. The game sold from 1962.
 The set includes 18 wooden cubes with small letters, representing sentences, and 18 with large letters, representing logical rules of inference. The simplest of the games in WFF ‘N Proof were designed to teach young children how to arrange these cubes on a series of paper mats to form WFFs. The remaining games were meant to teach how to argue logically. These games involve assuming the truth of WFFs of certain forms and concluding the truth of WFFs of other forms using logical rules of inference. Thus players proved theorems but did not use that terminology. The most advanced of these games were designed to challenge college students.
 The set also includes a timer, a book of instructions written by Allen, WFF ‘N Proof: The Game of Modern Logic (New Haven: Autotelic Instructional Materials Publishers, 1970), and a leaflet describing "Games for Thinkers" from WFF 'N PROOF Publishers of Turtle Creek, Pennsylvania. All these materials are stored in a plastic case that is marked on the cover: WFF'N PROOF (/) The Game of Modern Logic.
 In 1968 Layman Allen moved from Yale to the University of Michigan with a joint appointment in the Law School and the Mental Health Research Institute, where he continued his work on instructional games. Over the years the name and location of the distributor of WFF ‘N Proof changed, although the phrase “Games for Thinkers” has been associated with it from before Allen’s move to Ann Arbor. Price lists in the WFF ‘N PROOF Newsletters (part of the documentation in accession 317891) indicate that at first the game was distributed by WFF ‘N PROOF in New Haven, Connecticut, and sold for $6.00. In 1970 the price was raised to $8.00 and in 1971 the game was distributed by WFF ‘N PROOF through Maple Packers in Turtle Creek, Pennsylvania. At some point a firm called Learning Game Associates of Ann Arbor took over distribution of the game and donated this example to the Smithsonian in 1975. Later the Accelerated Learning Foundation of Fairfield, Iowa, became the distributor.
 Reference: Games For Thinkers Website.
 Location
 Currently not on view
 date made
 ca 1970
 developer
 Allen, Layman E.
 maker
 Learning Games Associates
 ID Number
 MA.335302
 accession number
 317891
 catalog number
 335302
 Data Source
 National Museum of American History

Felsenthal FAE15 Stadia Computer Circular Slide Rule
 Description
 This white plastic circular slide rule consists of a disc riveted to a square backing. The backing has a logarithmic scale of readings of a stadia rod used with a transit telescope, in feet. The disc has two logarithmic scales of angles. The first scale gives the difference in elevation of the transit and the stadia rod, in feet. It represents multiplying the stadia reading by 1/2 sin 2A, where A is the vertical angle of the transit telescope. The second scale finds the horizontal distance of the rod in feet and represents multiplying the stadia reading by the square of cos A. There is no indicator.
 The instrument is marked on the front: STADIA COMPUTER. The interior of the disc has DIRECTIONS FOR USE and a table providing the quantity to be added when a constant is used in measuring stadia. On the back, the rule is marked: 66756644676 (/) CONTRACT NO. DSA 70068MAF86 (/) FELSENTHAL INSTRUMENTS CO. (/) CHICAGO, ILLINOIS (/) 22040 (/) MFR'S PART NO. FAE15. It has a blue plastic case with snaps and a holder for a label. This object was donated with a second, duplicate Felsenthal stadia computer, which was assigned the same catalog number.
 The instrument resembles Cox's Stadia Computer (see 1987.0221.01 and 1987.0221.02). Donor Ben Rau dated the object to 1968, which is consistent with the form of the company name on the instrument. For Felsenthal company history, see 1977.1141.01 and 1977.1141.02.
 References: Deborah J. Warner, “Browse by Maker: Felsenthal,” National Museum of American History Physical Sciences Collection: Navigation , http://americanhistory.si.edu/collections/navigation/maker.cfm?makerid=173; accession file.
 Location
 Currently not on view
 date made
 ca 1968
 maker
 Felsenthal Instrument Co.
 ID Number
 1977.1141.41
 catalog number
 336425
 accession number
 1977.1141
 Data Source
 National Museum of American History

Book, The Attractive Universe: Gravity and the Shape of Space
 Description
 This is a book by Evans G. Valens, published in New York by World Publishing Company in 1969. It comes from the library of the artist David Crockett Johnson. An figure on p. 135 was the basis of two of Crockett Johnson's paintings. One is entitled Law of Motion (Galileo). The painting has museum catalog number 1979.1093.46 and high definition image number 20082482. The second painting is entitled Velocities and Right Triangles (Galileo). This painting has museum catalog number 1979.1093.64 and high definition image number 20082535.
 Location
 Currently not on view
 date made
 1969
 maker
 Valens, Evans G.
 ID Number
 1979.3083.06.79
 catalog number
 1979.3083.06.79
 nonaccession number
 1979.3083
 Data Source
 National Museum of American History

LongPeriod Horizontal Seismometer (WWSSN)
 Description
 Working at the Lamont Geological Observatory, a Columbia University facility in Palisades, N.Y., Frank Press and his mentor, Maurice Ewing, designed seismometers that responded to surface waves of longperiod and smallamplitude whether caused by explosions or by earthquakes. Their horizontal seismometer was of the “gardengate” form: here, the horizontal boom attaches to the lower end of a vertical post, and a diagonal wire extends from the upper end of the post to the outer end of the boom. The first example was installed in 1953.
 This example was made for the World Wide Standard Seismological Network. Established in 1961, the WWSSN was designed to detect underground nuclear tests, and generate valuable information about the earth’s interior and its dynamic processes. The WWSSN was a key component of VELA Uniform, a Cold War project that was funded by the Advanced Research Projects Agency (ARPA), a branch of the Department of Defense. It was managed by the U.S. Coast and Geodetic Survey and then by the U.S. Geological Survey. That agency transferred this instrument to the Smithsonian in 1999.
 Each of the 120 stations in the WWSSN had two horizontal seismometers of this sort (one to capture the eastwest component of the earth’s motions, and one to capture the northsouth component). This example was used Junction City, Tx. It would have been linked to a matched galvanometer (such as 1999.0275.09) and a photographic drum recorder (such as 1999.0275.10). The “Sprengnether Instrument Co.” signature refers to a firm in St. Louis, Mo., that specialized in seismological instruments.
 Ref: United States Coast and Geodetic Survey, Instrumentation of the WorldWide Seismograph System, Model 10700 (Washington, D.C., 1962).
 W.F. Sprengnether Instrument Co., Inc., General Discription (sic) Long Period Horizontal Seismometer ([St. Louis], n.d.).
 W.F. Sprengnether Instrument Co., Inc., Sprengnether Horizontal Component Seismometer, Series H ([St. Louis], n.d.).
 TaLiang Teng, “Seismic Instrumentation,” in Methods of Experimental Physics, vol. 24 part B, Geophysics (1987), pp. 5658.
 Location
 Currently not on view
 date made
 19611962
 maker
 Geotechnical Corporation
 W. F. Sprengnether Instrument Co.
 ID Number
 1999.0275.04
 catalog number
 1999.0275.04
 accession number
 1999.0275
 Data Source
 National Museum of American History

Painting  Bouquet of Triangle Theorems (Euclid)
 Description
 The mathematician Euclid lived around 300 BC, probably in Alexandria in what is now Egypt. Like most western scholars of his day, he wrote in Greek. Euclid prepared an introduction to mathematics known as The Elements. It was an eminently successful text, to the extent that most of the works he drew on are now lost. Translations of parts of The Elements were used in geometry teaching well into the nineteenth century in both Europe and the United States.
 Euclid and other Greek geometers sought to prove theorems from basic definitions, postulates, and previously proven theorems. The book examined properties of triangles, circles, and more complex geometric figures. Euclid's emphasis on axiomatic structure became characteristic of much later mathematics, even though some of his postulates and proofs proved inadequate.
 To honor Euclid's work, Crockett Johnson presented not a single mathematical result, but what he called a bouquet of triangular theorems. He did not state precisely which theorems relating to triangles he intended to illustrate in his painting, and preliminary drawings apparently have not survived. At the time, he was studying and carefully annotating Nathan A. Court's book College Geometry (1964). Court presents several theorems relating to lines through the midpoints of the side of a triangle that are suggested in the painting. The midpoints of the sides of the large triangle in the painting are joined to form a smaller one. According to Euclid, a line through two midpoints of sides of a triangle is parallel to the third side. Thus the construction creates a triangle similar to the initial triangle, with one fourth the area (both the height and the base of the initial triangle are halved). In the painting, triangles of this smaller size tile the plane. All three of the lines joining midpoints create triangles of this small size, and the large triangle at the center has an area four times as great.
 The painting also suggests properties of the medians of the large triangle, that is to say, the lines joining each midpoint to the opposite vertex. The three medians meet in a point (point G in the figure from Court). It is not difficult to show that point G divides each median into two line segments, one twice as long as the other.
 To focus attention on the large triangle, Crockett Johnson executed it in shades of white against a background of smaller dark black and gray triangles.
 Bouquet of Triangle Theorems apparently is the artist's own construction. It was painted in oil or acrylic and is #26 in the series. It was completed in 1966 and is signed: CJ66. It is signed on the back: Crockett Johnson 1966 (/) BOUQUET OF TRIANGLE THEOREMS (/) (EUCLID).
 Reference: Nathan A. Court, College Geometry, (1964 printing), p. 65. The figure on this page is not annotated.
 Location
 Currently not on view
 date made
 1966
 referenced
 Euclid
 painter
 Johnson, Crockett
 ID Number
 1979.1093.19
 catalog number
 1979.1093.19
 accession number
 1979.1093
 Data Source
 National Museum of American History

Painting  Square Roots to Sixteen (Theodorus of Cyrene)
 Description
 Greek mathematicians knew that numbers could not always be represented as simple ratios of whole numbers. They devised ways to describe them geometrically. The title of this painting refers to Theodorus of Cyrene (about 465–398 BC), a Greek geometer who, according to the Greek mathematician Theaetetus (about 417–369 BC), constructed the square roots of the numbers from 3 through 17. Crockett Johnson's painting follows a diagram in Evans G. Valens's The Number of Things that stops with the square root of 16.
 The construction of this oil or acrylic painting, #45 in the series, begins with a vertical line segment of length one. Crockett Johnson then drew a right angle at the base of the segment and an adjacent line with length one. From the Pythagorean theorem, it follows that a line from the center of the spiral has length equal to the square root of 2. The construction was continued until the last hypotenuse displayed length equal to the square root of 16.
 The painting, which looks like a seashell, shows a specific color pattern. The three dark gray triangles have hypotenuses whose lengths are whole numbers (the square roots of 4, 9, and 16). The six white triangles have hypotenuses whose lengths are irrational and are square roots of even integers. Finally, the six tan triangles have hypotenuses whose lengths are irrational and the square roots of odd integers.
 The painting dates from 1967 and is signed: CJ67. It is marked on the back: Crockett Johnson (/) SQUARE ROOTS TO SIXTEEN (/) (THEODORUS OF CYRENE).
 Location
 Currently not on view
 date made
 1967
 referenced
 Theodorus of Cyrene
 painter
 Johnson, Crockett
 ID Number
 1979.1093.32
 catalog number
 1979.1093.32
 accession number
 1979.1093
 Data Source
 National Museum of American History

Painting  Multiplication through Imaginary Numbers (Gauss)
 Description
 This painting was inspired by ideas of Carl Friedrich Gauss (1777–1855). In his 1797 doctoral thesis, Gauss proved what is now called the fundamental theorem of algebra. He showed that every polynomial with real coefficients must have at least one real or complex root. A complex number has the form a+bi, where a and b are real numbers and i represents the square root of negative one. The French mathematician René Descartes (1596–1650) called such numbers "imaginary", which explains the reference in the title. Gauss demonstrated that, just as real numbers can be represented by points on a coordinate line, complex numbers can be represented by points in the coordinate plane.
 The construction of this painting echoes a figure in an article on Gauss by Eric Temple Bell in J. R. Newman's The World of Mathematics that illustrates the representation of points on a plane. This book was in Crockett Johnson's library, and the figure is annotated.
 In Bell's figure, real numbers c and c are plotted on the x axis, the imaginary numbers ci and ci are plotted on the y axis, and the complex number a+bi is shown in the first quadrant. The figure is meant to show that if a complex number a+bi is multiplied by the imaginary number i then the product is a complex number on the same circle but rotated ninety degrees counterclockwise. That is, i(a+bi) = ai+bi² = b+ai. Thus, this complex number lies in the second quadrant. If this process is repeated the next product is abi, which lies in the third quadrant. It is unknown why Johnson did not illustrate the fourth product.
 The colors of opposite quadrants of the painting are related. Those in quadrant three echo those of quadrant one and those of quadrant four echo those of quadrant two.This oil painting is #40 in the series. It is signed: CJ67.
 References:
 James R. Newman, The World of Mathematics (1956), p. 308. This volume was in Crockett Johnson's library. The figure on this page is annotated.
 Location
 Currently not on view
 date made
 1967
 painter
 Johnson, Crockett
 ID Number
 1979.1093.28
 catalog number
 1979.1093.28
 accession number
 1979.1093
 Data Source
 National Museum of American History
Pages
Filter Your Results
Click to remove a filter:

topic
 Science 336
 Slide Rules 71
 Rule, Calculating 62
 Art 53
 Computers & Business Machines 36
 Education 33
 Punch Cards 31
 Tabulating Equipment 29
 Arithmetic Teaching 27
 Calculating Machines 27
 Scientific apparatus and instruments 27
 Women Teaching Math 26
 Women's History 26
 Modern Physics 21
 Mathematical Recreations 18
 Artificial satellites 17
 Energy & Power 17
 Trigonometry 16
 Adding Machines 13
 object type
 date
 place
 culture

set name
 Medicine and Science: Mathematics 352
 Science & Mathematics 336
 Slide Rules 71
 Art 53
 Crockett Johnson 47
 Computers & Business Machines 36
 Punch Cards 31
 Tabulating Equipment 29
 Arithmetic Teaching 27
 Calculating Machines 27
 Women Teaching Math 26
 Medicine and Science: Modern Physics 21
 Energy & Power 17
 Sputnik 17
 Trigonometry 16
 Medicine and Science: Computers 15
 Adding Machines 13
 Measuring & Mapping 13
 Flowcharting Templates 12
 Work and Industry: Electricity 12