Science & Mathematics

Chemical Balance

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

Date: 1960s

Painting - Curve Tangents (Fermat)

The French lawyer and mathematician Pierre de Fermat (1601–1665) was one of the first to develop a systematic way to find the straight line which best approximates a curve at any point. This line is called the tangent line.
Description
The French lawyer and mathematician Pierre de Fermat (1601–1665) was one of the first to develop a systematic way to find the straight line which best approximates a curve at any point. This line is called the tangent line. This painting shows a curve with two horizontal tangent lines. Assuming that the curve is plotted against a horizontal axis, one line passes through a maximum of a curve, the other through a minimum. An article by H. W. Turnbull, "The Great Mathematicians," published in The World of Mathematics by James R. Newman, emphasized how Fermat's method might be applied to find maximum and minimum values of a curve plotted above a horizontal line (see his figures 14 and 16). Crockett Johnson owned and read the book, and annotated the first figure. The second figure more closely resembles the painting.
Computing the maximum and minimum value of functions by finding tangents became a standard technique of the differential calculus developed by Isaac Newton and Gottfried Leibniz later in the 17th century.
Curve Tangents is painting #12 in the Crockett Johnson series. It was executed in oil on masonite, completed in 1966, and is signed: CJ66. The painting has a wood and metal frame.
Location
Currently not on view
date made
1966
referenced
Fermat, Pierre de
painter
Johnson, Crockett
ID Number
1979.1093.07
catalog number
1979.1093.07
accession number
1979.1093

Dalton E-6B Dead Reckoning Computer by Jeppesen

In this instrument a white rectangular plastic sheet slides between two white discs that are held together with black plastic bars and metal grommets.
Description
In this instrument a white rectangular plastic sheet slides between two white discs that are held together with black plastic bars and metal grommets. The sheet is marked in green on both sides, with a polar grid and rectangular grid on one side and a polar grid on the other side. The front disc has scales for altitude computations at the top and for air speed computations at the bottom. The back disc has a scale to correct direction readings for wind and a scale for converting temperature readings from degrees Centigrade to Fahrenheit. The center of the back disc is clear for viewing the grid. A salmon plastic sheath stores the instrument.
The device is marked on the front: DALTON DEAD RECKONING COMPUTER (/) TYPE E-6B. It also is marked: WEEMS SYSTEM OF NAVIGATION (/) (A DIVISION OF JEPPESEN & CO.) (/) DENVER, COLORADO; PAT. NO. 2,097,118. The grid is marked in pencil: FL[IGH]T OFF COURSE (/) 2 MILES/SQUARE. The back of the disc is also marked in pencil. The three lines in the clear part of the disc are illegible, but below the temperature conversion scale, the marks read: 3.5° F/1000'. A ring at the top of one black plastic bar is marked: U.S. PAT. 3,112,875.
Naval Reserve pilot Philip Dalton, in consultation with navigation instructor Philip Van Horn Weems, developed the Dalton dead reckoning computer for the U.S. Army Air Corps and received a patent in 1937. The device was widely used during World War II.
After the war, many manufacturers in the United States and Europe made the E-6B. Elrey Borge Jeppesen, a pilot for what became United Airlines, founded his company in 1934 and moved it to Denver in 1941. Jeppesen & Co. made aeronautical charts and navigational tools and guides. It became a subsidiary of Boeing in 2000. The patent number on the back of this object refers to the design of the computer with the gridded rectangular sheet and two discs. The patentees were employed by Felsenthal Instruments Co., which frequently supplied companies with the plastic for manufacturing Dalton computers in the 1950s and 1960s.
The donor purchased this object around 1965 and used it for about two years in airplane navigation.
References:
Paul McConnell, "Some Early Computers for Aviators," Annals of the History of Computing 13, no. 2 (1991): 155–177, on 156. Philip Dalton, "Plotting and Computing Device" (U.S. Patent 2,097,116 issued October 26, 1937).
Ben Van Caro and Burton L. Fredriksen, "Computer Slide Construction" (U.S. Patent 3,112,875 issued December 3, 1963). "E6B," http://en.wikipedia.org/wiki/E6B.
"Jeppesen," http://en.wikipedia.org/wiki/Jeppesen.
"On the Beam," advertisement for Dalton Dead Reckoning Computer, Felsenthal Plastics, Flying 35, no. 2 (August 1944): 10.
Paul Sanik, "U.S. Army Air Corps Aerial Dead Reckoning type E-6B," Journal of the Oughtred Society 6, no. 2 (1997): 32–34 .
Location
Currently not on view
date made
1960s
maker
Jeppesen & Co.
ID Number
1995.0087.03
accession number
1995.0087
catalog number
1995.0087.03

Box with Sheet, for Log Log Magnifier Slide Rule

By the 1960s, when this cardboard box was made, slide rules were an established symbol of the technical education of young Americans. They came with considerable packaging – not only a leather or plastic case but a set of instructions and a guarantee.
Description
By the 1960s, when this cardboard box was made, slide rules were an established symbol of the technical education of young Americans. They came with considerable packaging – not only a leather or plastic case but a set of instructions and a guarantee. This box, made by the American firm of Pickett, was designed for the company’s model N4M-ES slide rule. The N indicates that the cursor was nylon, the M that it magnified the portion of the scales below it, and the ES that it was in “eye saver” yellow rather than the more usual white. The box also holds a guarantee – but no slide rule or case.
Location
Currently not on view
date made
ca 1965
maker
Pickett Industries
ID Number
1995.3023.07
nonaccession number
1995.3023
catalog number
1995.3023.07

Felsenthal FDD-7 Nautical Course Protractor Manufactured for Danforth/White

This white plastic circular protractor is mounted on a clear plastic square plotting board with green grid lines. The board bears a white arc for correcting against compass errors of VARIATION, divided to single degrees and marked by tens from 30 to 0 to 30.
Description
This white plastic circular protractor is mounted on a clear plastic square plotting board with green grid lines. The board bears a white arc for correcting against compass errors of VARIATION, divided to single degrees and marked by tens from 30 to 0 to 30. The letters E and W are printed above the 25° points. The protractor is divided by single degrees and marked by tens from 0° to 350°. A compass rose, with an arrow at North and the letters E, S, and W inside triangles, appears inside the degree circle.
An extending arm is affixed to the center of the protractor. The end of the arm on the protractor is marked with +2 (in black), +4 (in green), and +1 (in black). The arm also bears an arc for correcting against compass errors of DEVIATION, divided by single degrees and marked by tens from 20 to 0 to 20. The letters E and W are printed above the 15° points.
The part of the arm that extends for 9-3/4" beyond the protractor is divided by tenths and labeled for NAUT[ICAL] MILES. Markings by ones from 1 to 5 are for a scale of 1:40,000 n.m.; markings by ones (in green) from 1 to 10 are for a scale of 1:80,000 n.m.; and markings by ones from 1 to 2 are for a scale of 1:20,000 n.m. The arm is marked with instructions for use: Set 0 on compass circle to variation on square base. Align arm with course. Align cross lines on base with any meridian or parallel on chart so arrow on base points north. Read compass course on compass circle opposite deviation on arm. Deviation may be marked inside compass circle.
A sheet of instructions is also provided with the instrument and its clear plastic sheath. The arm is marked with the object's name—DE LUXE COURSE PROTRACTOR (/) PAT. PENDING—the Danforth/White company logo—the letters DW with the slogan, THE MARK OF SAFETY AFLOAT—and the maker's mark: DANFORTH/WHITE (/) PORTLAND, MAINE (/) ©1959, by R. S. Danforth. Felsenthal Instruments Co. manufactured this protractor for Danforth/White, which made well-regarded nautical compasses in the 1960s. Since the 1980s, the company has sold weather stations and instruments under the name Maximum Inc. For Felsenthal, this protractor was product number FDD-7.
See also 1977.1141.01, 1977.1141.02, 1977.1141.03, 1977.1141.05, 1977.1141.08, 1977.1141.09, 1977.1141.10, 1977.1141.11, 1977.1141.12, 1977.1141.18, 1977.1141.19, 1977.1141.20, 1977.1141.21, 1977.1141.22, 1977.1141.23, 1977.1141.24, and 1977.1141.30.
Location
Currently not on view
date attributed by donor
1969
maker
Felsenthal
ID Number
1977.1141.39
accession number
1977.1141
catalog number
336423

Perrygraf Clipper Cargo Dimensional Weight Computer Circular Slide Chart

This instrument consists of two pieces of blue and white rectangular cardboard, riveted together at the corners. It is marked with a circular logarithmic scale of weight in pounds that ranges from 1 to 250. Inside this is a scale of lengths from 50" to 10".
Description
This instrument consists of two pieces of blue and white rectangular cardboard, riveted together at the corners. It is marked with a circular logarithmic scale of weight in pounds that ranges from 1 to 250. Inside this is a scale of lengths from 50" to 10". A white disc attached below that scale has a scale of heights from 5" to 30" and a scale of widths from 30" to 6". A paper indicator is attached on top of the disc. It contains a scale of densities in cubic inches per pound from 300 to 200 and three steps of instructions. This slide chart is marked: CLIPPER CARGO (/) DIMENSIONAL WEIGHT COMPUTER. It performs the same function as 1996.3029.01.
Unlike the other object, a rectangular piece of white cardboard slides inside the instrument to also permit readings of conversions from kilograms to pounds on the front and readings of pounds to kilograms on the back. This part of the chart is marked: WEIGHT CONVERTER. The bottom of the chart is marked: PAN AMERICAN, with LEADERS IN AIR CARGO on the front and SPACE CAN BE RESERVED on the back. The back also has an advertisement: CLIPPER CARGO (/) Reduces Pilferage (/) Reduces Damage (/) Reduces Inventory (/) Extends your working capital!
The lower left corner of the front is marked: Slide-Chart Copr. 1957, (/) PERRYGRAF Corp., Maywood, Ill. The lower right corner is marked: *T.M. Reg. U. S. Pat. Off. Perrygraf was a very successful producer of promotional slide charts. In 1968, the company was sold to Nashua Corporation and moved to Los Angeles, Calif.
Reference: Walter Shawlee II, "The Wonderful World of Slide Charts, Wheel Charts, and Perrygrafs," Sphere Research Corp., http://sphere.bc.ca/test/perrygraf.html.
Location
Currently not on view
date made
1957-1968
maker
Perry Graf Corporation
ID Number
1996.3029.02
nonaccession number
1996.3029
catalog number
1996.3029.02

Head Piece from Maiman Laser

This object may be the first laser. It was made by Theodore Maiman and his assistant Irnee D'Haenens at Hughes Aircraft Company in May 1960.In 1959 Maiman attended a technical conference on the subject of lasers.
Description
This object may be the first laser. It was made by Theodore Maiman and his assistant Irnee D'Haenens at Hughes Aircraft Company in May 1960.
In 1959 Maiman attended a technical conference on the subject of lasers. Maiman heard several speakers state that ruby was unsuitable for a laser but grew troubled by some of the numbers they cited. When he returned to his lab at Hughes he began experimenting. By May 1960 he and D'Haenens constructed several small metal cylinders. Each contained a photographer's spiral-shaped, xenon flashlamp that surrounded a small cylindrical crystal of synthetic ruby. When they fired the flashlamp, the burst of light stimulated the ruby crystal to emit a tightly focused pulse of light--the first operating laser.
Hughes Aircraft donated this and several other pieces of Maiman's apparatus to the Smithsonian in 1970. The crystal mounted inside this unit is from a 1961 experiment. While the donation records indicate that this is the first laser, Maiman wrote that he received the first laser as a gift when he left the company in April 1961. Several experimental models were made during the research, a common practice. So we may never know which unit actually generated the first laser light.
Location
Currently not on view
Date made
1960
associated date
1960
maker
Maiman, Theodore H.
Hughes Aircraft Company
ID Number
EM.330050
accession number
288813
catalog number
330050

Monroe Model CSAE-10 Calculating Machine

This full-keyboard, electric non-printing modified stepped drum calculating machine has a dark gray steel frame, a light gray keyboard and carriage, and ten columns of oblong plastic keys in two shades of gray. At the bottom of each column is a key for clearing it.
Description
This full-keyboard, electric non-printing modified stepped drum calculating machine has a dark gray steel frame, a light gray keyboard and carriage, and ten columns of oblong plastic keys in two shades of gray. At the bottom of each column is a key for clearing it. Between the columns of keys and under the keyboard are metal rods, painted red on one side and the same gray as the keyboard on the other. They turn to serve as decimal markers.
To the right of the number keys are subtraction and addition bars, two carriage shift keys, and a multiplier key. Below these are two buttons, one of which is depressed when entries are repeated and the other depressed for non-repeating entries. This section also has a multiply/divide lever. Below these are three other function keys and a gray clear-keyboard key. Beneath the number keys are five additional function keys.
In back of the keyboard is a carriage with ten dials to show a number set up for multiplication, 20 dials to show the result, and a row of ten dials that serves as a revolution counter. Sliding decimal markers are provided. A two-pronged gray electrical cord attaches to the back.
An incomplete mark on the left side reads: omatic. A mark on the front reads: Classmate. Another mark there reads: li. A paper sticker glued to the bottom of the machine reads: MONROE INTERNATIONAL CORPORATION [/] A DIVISION OF LITTON INDUSTRIES [/] ORANGE, NEW JERSEY. A list of 28 patents on this sticker ranges from number 2,473,422 (1949) to D-192,457 (1962). A metal tag attached to the bottom of the machine reads: MODEL CSAE-10 [/] SERIAL B066597. Scratched on the frame at the back are the initials: EHS.
This is a relatively late mechanical calculating machine, produced by Monroe after it became a division of Litton Industries in 1958. The rough date is based on the patent date.
Location
Currently not on view
date made
ca 1966
maker
Monroe International Corporation, a Division of Litton Business Systems
ID Number
1987.0182.01
maker number
MODEL CSAE-10 B066597
accession number
1987.0182
catalog number
1987.0182.01

Burroughs Simplex P601

This full-keyboard printing adding machine has a gray metal case and the following columns of square tan and brown keys starting from the left:1. column of 12 month keys2. two columns of number keys, ranging from 1 to 93. column of keys with abbreviated financial terms4.
Description
This full-keyboard printing adding machine has a gray metal case and the following columns of square tan and brown keys starting from the left:
1. column of 12 month keys
2. two columns of number keys, ranging from 1 to 9
3. column of keys with abbreviated financial terms
4. nine columns of number keys, each column ranging from 1 to 9.
5. two columns of function keys.
The carriage and electrical cord are missing. The 14 type bars include one for months, two for digits, one for the type of transaction, nine for the result, and one for special characters (indicating sum, subtotal, etc.)
A red tag attached to the object reads: PATENT DEPT. (/) #263. The machine is marked across the front above the keyboard: Burroughs. It is marked on the bottom: A7075. It is marked on the back on the inside of the case: 397.
This object was model #263 in the collection of the Patent Division of Burroughs Corporation.
Location
Currently not on view
date made
1950-1960
maker
Burroughs Adding Machine Company
ID Number
1982.0794.64
catalog number
1982.0794.64
accession number
1982.0794

Programmer, Peptide Synthesizer

Proteins, which are among the most diverse and important molecules in the natural world, are built from long chains of smaller molecules known as amino acids. In the early 1960s, scientists synthesized proteins by assembling amino acids into chains one by one.
Description (Brief)
Proteins, which are among the most diverse and important molecules in the natural world, are built from long chains of smaller molecules known as amino acids. In the early 1960s, scientists synthesized proteins by assembling amino acids into chains one by one. The time-consuming reaction required crystallization and purification of the product after each addition of an amino acid “link” to the protein chain.
In 1963 Bruce Merrifield, a biochemist at Rockefeller University in New York, described a new method for making short-chain proteins from scratch. His reaction, known as solid phase peptide synthesis, eliminated the need to crystalize and purify the product. This breakthrough greatly increased yields and opened the door for scientists to synthesize a wider variety of proteins. Merrifield’s work won him the 1984 Nobel Prize in Chemistry. Much of today’s industrial production of complex organic molecules still relies on Merrifield’s original reaction.
In 1965 Merrifield and his partners, John Stewart and Nils Jernberg, built a machine that automated the chemical reaction. Their peptide synthesizer, consisting of a programmer and a reaction vessel, was the first protein-making machine. This object is the original programmer.
Location
Currently not on view
date made
1965-1966
ID Number
1988.0492.01
catalog number
1988.0492.01
accession number
1988.0492
patent number
3531258

Experimental Ruby Laser

This is an experimental ruby laser made in 1963 at Ohio State University.
Description
This is an experimental ruby laser made in 1963 at Ohio State University. Edward Damon, a researcher at the University’s Antenna Laboratory, made this and several other lasers during his investigation of Theodore Maiman’s ruby laser experiments of three years earlier.
In addition to replicating Maiman's 1960 experiments, Damon wished to explore variations of the ruby laser. Unlike Maiman's laser, this laser does not use a spiral flashlamp to energize the ruby crystal. Instead, Damon placed three linear flashlamps parallel to the rod-shaped laser crystal. Firing these lamps simultaneously provided energy to the crystal. The laser also demonstrates a water cooling technique still used in some lasers today.
Location
Currently not on view
date made
1963
ID Number
2009.0228.02
accession number
2009.0228
catalog number
2009.0228.02

Wave guide with ruby crystal

This is an experimental device made by Theodore Maiman at Hughes Aircraft in late 1959 or early 1960 as part of the series of experiments leading up to the demonstration of the first laser in May 1960.
Description
This is an experimental device made by Theodore Maiman at Hughes Aircraft in late 1959 or early 1960 as part of the series of experiments leading up to the demonstration of the first laser in May 1960. This object features a cube-shaped ruby crystal mounted at one end of a microwave wave-guide. Maiman sought to test the response of the synthetic ruby crystal to microwave stimulation. Other researchers claimed that ruby would be a poor material to use in a laser. Maiman thought otherwise.
After Charles Townes invented the microwave-emitting maser in 1954, researchers began trying to move to the higher energy levels of infrared and visible light. They referred to such devices as "optical masers," and only later did people adopt Gordon Gould's term, "laser." This experimental piece clearly shows the influence of microwave technology. The metal tube is not a stand but rather a hollow guide that channels microwaves to the ruby crystal. The results of this and other experiments led Maiman to ultimately choose a cylinder of ruby rather than a cube for his laser.
Location
Currently not on view
date made
1959
associated date
1960
associated user
unknown
associated institution
Hughes Research Laboratories
maker
Maiman, Theodore H.
Hughes Aircraft Company
ID Number
EM.330052
accession number
288813
catalog number
330052

IBM X-20-8020 Flowcharting Template

This rectangular blue-green flowcharting templatet has a scale of inches divided to tenths at the top and a scale of inches divided to eighths at the bottom. Twenty-five holes representing various logical operations are cut in the plastic.
Description
This rectangular blue-green flowcharting templatet has a scale of inches divided to tenths at the top and a scale of inches divided to eighths at the bottom. Twenty-five holes representing various logical operations are cut in the plastic. A white paper sleeve has definitions of the symbols on it. The device is meant for use in conjunction with a worksheet with IBM number X20-8021. A mark on the object reads: IBM FLOWCHARTING TEMPLATE FORM X20-8020. A mark on the envelope reads in part: Have you considered using IBM’s System/360 Flowchart (/) Program? The IBM System/360 was announced in 1964 and sold from 1965. The donor of this template, Terry M. Sachs, was trained to program the IBM System/360.
Reference:
IBM, IBM Data Processing Techniques - Flowcharting Techniques, White Plains, NY: IBM, ca 1963.
Location
Currently not on view
date made
ca 1965
maker
IBM
ID Number
1995.3023.01
nonaccession number
1995.3023
catalog number
1995.3023.01

Painting - Polar Line of a Point and a Circle (Apollonius)

In 1966, Crockett Johnson carefully read Nathan A. Court's book College Geometry, selecting diagrams that he thought would be suitable for paintings. In the chapter on harmonic division, he annotated several figures that relate to this painting.
Description
In 1966, Crockett Johnson carefully read Nathan A. Court's book College Geometry, selecting diagrams that he thought would be suitable for paintings. In the chapter on harmonic division, he annotated several figures that relate to this painting. The work shows two orthoganol circles, that is to say two circles in which the square of the line of centers equals the sum of the squares of the radii. A right triangle formed by the line of centers and two radii that intersect is shown. The small right triangle in light purple in the painting is this triangle.
Crockett Johnson's painting combines a drawing of this triangle with a more complex figure used in a discussion of further properties of lines drawn in orthoganal circles. In particular, suppose that one draws a line segment from a point outside a circle that intersects it in two points, and selects a fourth point on the line that divides the segment harmonically. For a single exterior point, all these such points lie on a single line, perpendicular to the line of centers of the two circles, which is called the polar line.
The painting is #38 in the series. It has a background in two shades of cream, and a light tan wooden frame. It shows two circles that overlap slightly and have various sections. The circles are in shades of blue, purple and cream. The painting is signed: CJ66.
References: Nathan A. Court, College Geometry (1964 printing), p. 175–78. This volume was in Crockett Johnson's library.
T. L. Heath, ed., Apollonius of Perga: Treatise on Conic Sections (1961 reprint). This volume was not in Crockett Johnson's library.
Location
Currently not on view
date made
1966
referenced
Apollonius of Perga
painter
Johnson, Crockett
ID Number
1979.1093.26
catalog number
1979.1093.26
accession number
1979.1093

Painting - Homothetic Triangles (Hippocrates of Chios)

Two polygons are said to be homothetic if they are similar and their corresponding sides are parallel.
Description
Two polygons are said to be homothetic if they are similar and their corresponding sides are parallel. If two polygons are homothetic, then the lines joining their corresponding vertices meet at a point.
The diagram on which this painting is based is intended to illustrate the homothetic nature of two polygons ABCDE . . . and A'B'C'D'E' . . . From the title, it appears that Crockett Johnson wished to call attention of homothetic triangular pairs ABS and A'B'S, BCS and B'C'S, CDS and C'D'S, DES and D'E'S, etc. The painting follows a diagram that appears in Nathan A. Court's College Geometry (1964 printing). Court's diagram suggests how one constructs a polygon homothetic to a given polygon. Hippocrates of Chios, the foremost mathematician of the fifth century BC, knew of similarity properties, but there is no evidence that he dealt with the concept of homothecy.
To illustrate his figure, the artist chose four colors; red, yellow, teal, and purple. He used one tint and one shade of each of these four colors. The larger polygon is painted in tints while the smaller polygon is painted in shades. The progression of the colors follows the order of the color wheel, and the black background enhances the vibrancy of the painting.
Homothetic Triangles, painting #17 in the Crockett Johnson series, is painted in oil on masonite. The work was completed in 1966 and is signed: CJ66. It is inscribed on the back: Crockett Johnson 1966 (/) HOMOTHETIC TRIANGLES (/) (HIPPOCRATES OF CHIOS). It has a black wooden frame.
References: Court, Nathan A., College Geometry, (1964 printing), 38-9.
van der Waarden, B. L., Science Awakening (1954 printing), 131-136.
Location
Currently not on view
date made
1966
referenced
Hippocrates of Chios
painter
Johnson, Crockett
ID Number
1979.1093.11
catalog number
1979.1093.11
accession number
1979.1093

Painting - Rectangles of Equal Area (Pythagoras)

Crockett Johnson used a wide range of geometrical constructions as the basis for his paintings.
Description
Crockett Johnson used a wide range of geometrical constructions as the basis for his paintings. This painting is based on a method of constructing a rectangle equal in area to a given rectangle, given one side of the rectangle to be constructed.
In the painting, suppose that the cream-colored rectangle on the bottom left is given, as well as a line segment extending from the upper right corner of it. Construct the small triangle on the upper left. Draw the three horizontal lines shown, as well as the diagonal of the rectangle constructed. Extend this diagonal until it meets the bottom line, creating another triangle. The length of the base of this triangle will be the side of the rectangle desired. This rectangle is on the upper right in the painting.
This construction has been associated with the ancient Pythagoreans. Crockett Johnson may well have learned it from Evans G. Valens, The Number of Things. The drawing on page 121 of this book is annotated, although the annotations are faint.
The oil painting is #48 in the series. It has a black background and a black wooden frame, with the two equal triangles in light shades. The painting is signed on the front: CJ69. It is signed on the back: RECTANGLES OF EQUAL AREA (/) (PYTHAGORAS) (/) Crockett Johnson 1969.
Location
Currently not on view
date made
1969
referenced
Pythagoras
painter
Johnson, Crockett
ID Number
1979.1093.34
catalog number
1979.1093.34
accession number
1979.1093

Keuffel & Esser 4071-3 Polyphase Decitrig Duplex Slide Rule

This ten-inch mahogany duplex linear slide rule is almost completely coated with white celluloid. The frameless glass indicator has plastic edges. On one side, the base has K and A scales at the top and D and DI scales at the bottom. The slide has B, T, SRT, and S scales.
Description
This ten-inch mahogany duplex linear slide rule is almost completely coated with white celluloid. The frameless glass indicator has plastic edges. On one side, the base has K and A scales at the top and D and DI scales at the bottom. The slide has B, T, SRT, and S scales. Divisions of angles are indicated in decimal fractions. The left side of the slide is marked with the serial number 330508, with the number 508 printed on the left side of both parts of the base.
The other side of the rule has a DF scale on the top of the base and D and L scales on the bottom of the base. The slide has CF, CIF, CI, and C scales. The top of the base is marked in red: KEUFFEL & ESSER CO.; PATS. 2,500,460 2,168,056 2,170,144 PAT PEND.; MADE IN U.S.A. The right side of the slide is marked with the K&E logo, a copyright sign, and the model number, 4071-3. The instrument fits in an orange leather case with the K&E logo on the flap. Inside the flap is written in ink: H. R. L. (/) JULY '62.
Keuffel & Esser Company of New York sold this model from 1939 to 1967. The combination of scales on this example was sold beginning in 1955, and the model was renumbered in 1962 to 68-1502. Thus, the rule was probably manufactured between 1955 and 1962. The serial number is consistent with this dating.
The donor, Alfred E. Brown, was a research chemist for Celanese Corporation, which partnered with K&E in the 1960s to produce a special version of the 68-1555 slide rule (see 1993.0357.01). However, it is not known how this rule came into Brown's possession.
References: Clark McCoy, "Collection of Pages from K&E Catalogs for the 4071-3 Family of Slide Rules," http://www.mccoys-kecatalogs.com/KEModels/ke4071family.htm; Carl M. Bernegau, "Slide Rule" (U.S. Patent 2,168,056 issued August 1, 1939); Lyman M. Kells, Willis F. Kern, and James R. Bland, "Slide Rule" (U.S. Patent 2,170,144 issued August 22, 1939); Herschel Hunt, "Slide Rule" (U.S. Patent 2,500,460 issued March 14, 1950); Walter Shawlee II, Ted Hume, and Paul Ross, "Keuffel & Esser Co. Slide Rules," Sphere Research Corporation, http://www.sphere.bc.ca/test/ke-sliderule.html; "Alfred E. Brown Chemist," The Washington Post, March 19, 2004, http://www.washingtonpost.com/wp-dyn/articles/A9676-2004Mar19_2.html.
Location
Currently not on view
date made
1955-1962
date received
1993
maker
Keuffel & Esser Co.
ID Number
1993.0482.01
accession number
1993.0482
catalog number
1993.0482.01

Pickett N901-ES Simplex Slide Rule

This aluminum slide rule is coated in "Eye Saver" yellow, as denoted by the model number. It is held together with aluminum braces; the indicator is nylon (also denoted by the model number) with three metal screws.
Description
This aluminum slide rule is coated in "Eye Saver" yellow, as denoted by the model number. It is held together with aluminum braces; the indicator is nylon (also denoted by the model number) with three metal screws. The front of the rule has A, D, and L scales, with B, CI, and C scales on the slide. The scales are about ten inches long. The slide and the top of the rule are both marked: MODEL N901-ES (/) SIMPLEX (/) MATH RULE. The other end of the slide bears the Pickett logo and the mark: MADE IN U.S.A.
The back of the rule has X and D* scales, with Y and C* scales on the slide. The top of the rule is marked: PICKETT, INC.; MODEL N901-ES; SIMPLEX MATH RULE. The bottom of the rule is marked: COPYRIGHT 1965; PICKETT, INC. SANTA BARBARA. CALIF.; MADE IN U.S.A.
The rule fits in a black leather sheath. The sheath was received in a green, white, and black cardboard box. One end of the box is marked: PickETT (/) 901-ES (/) ELEMENTARY MATH. It also is marked: about this rule: (/) 10 scales are keyed to (/) new math. Aids under- (/) standing of addition, (/) subtraction, multiplica- (/) tion, division and Base 10 (/) relationships. Grade 3 up. The inside of the box top flips up for display. The box slides into a green, white, and black cardboard cover. The top and sides of the box cover are each marked: PickETT; ALL METAL (/) SLIDE (/) RULE.
The box also contains a yellow paper slide rule guarantee and registration card. The object's serial number is A1216143. A 48-page instruction manual by Maurice L. Hartung is stored separately (1995.0126.02.01).
The X and Y scales were used for addition and subtraction and were unique to Pickett. Donor Lawrence J. Kamm conjectured that Hartung, a mathematics professor at the University of Chicago, recommended they be added to this product. According to Kamm, Hartung encouraged company cofounder Ross Pickett to market its slide rules only to schoolchildren. In order to provide scientists and engineers with access to rules such as the Decimal Keeper (1995.0126.01), Kamm opened a mail-order business that distributed Pickett's products.
References: Peter M. Hopp, Slide Rules: Their History, Models, and Makers (Mendham, N.J.: The Astragal Press, 1999), 209–210; Maurice L. Hartung, Complete, Semi-Programmed Teaching Instructions for the Use of Elementary Simplex Math Slide Rule (Santa Barbara, Calif.: Pickett, Inc., 1965); accession file; International Slide Rule Museum, "Pickett," http://sliderulemuseum.com/Pickett.htm.
Location
Currently not on view
date made
after 1965
date received
1995
maker
Pickett & Eckel, Incorporated
ID Number
1995.0126.02
accession number
1995.0126
catalog number
1995.0126.02

Structural Arithmetic I, Workbook for Stern Teaching Apparatus

Documentation received with Catherine Stern's apparatus for teaching arithmetic suggests how her ideas changed over time. This colorful publication from 1965 describes a relatively late version of her teaching apparatus, as sold by Houghton Mifflin.
Description
Documentation received with Catherine Stern's apparatus for teaching arithmetic suggests how her ideas changed over time. This colorful publication from 1965 describes a relatively late version of her teaching apparatus, as sold by Houghton Mifflin. Some exercises in the workbook have been completed. Stern's coauthors were Margaret B. Stern and Toni S. Gould.
For Stern's apparatus, see 2005.0229.01 and 2005.0229.02. For closely related books, see 2005.3100.06 and 2005.3100.08.
Location
Currently not on view
date made
1965
maker
Stern, Catherine
Stern, Margaret B.
Gould, Toni S.
ID Number
2005.3100.04
catalog number
2005.3100.04
nonaccession number
2005.3100

Painting - Bouquet of Triangle Theorems (Euclid)

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.
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

Faber-Castell 111/54 Linear Slide Rule

This white plastic German slide rule has a clear plastic cursor. Scales 25 cm. long are on the front of the base of the rule and on both sides of the slide. The slides on the rule are K, A, B, P, S, and T.
Description
This white plastic German slide rule has a clear plastic cursor. Scales 25 cm. long are on the front of the base of the rule and on both sides of the slide. The slides on the rule are K, A, B, P, S, and T. Those on the slide are B, BI, CI and C on the front and LL1, LL2, and LL3 on the back. The beveled top edge has a scale of equal parts divided to tenths of a centimeter, 27 centimeters long. The front of the instrument has an L scale. The back has a set of tables of use in mathematics, mechanics, and electronics.
The scale fits in a plastic case that is transparent on top and green on the bottom. Also included is a manual by Faber-Castell entitled "Anleitung Castell Praezisions-Rechenstaebe fuer Maschinen und Elektro-Ingenieure." This manual describes the Castell models 1/54, 4/54, 67/54 b, 67/54 R, 111/54, and 111/54 A. The only three of these with scales 25 cm. long are the 1/54, the 111/54, and the 111/54 A. None of the rules described in the booklet has a BI scale.
Location
Currently not on view
date made
ca 1965
ID Number
2014.0136.02
accession number
2014.0136
catalog number
2014.0136.02

Concise Model 28 Circular Slide Rule

This white plastic circular slide rule was made by Concise Company, Ltd., of Tokyo, Japan, for Pan American Airlines. The base has a D scale, and there are C, CI, A, and K scales on a disc that rotates atop the base. A clear plastic indicator is pivoted at the center.
Description
This white plastic circular slide rule was made by Concise Company, Ltd., of Tokyo, Japan, for Pan American Airlines. The base has a D scale, and there are C, CI, A, and K scales on a disc that rotates atop the base. A clear plastic indicator is pivoted at the center. The center of the rotating disc is marked: CIRCULAR CONCISE SLIDE RULE (/) NO. 28 (/) MADE IN JAPAN.
The back of the object is light blue with a white logo of a globe and is marked: WORLD'S LARGEST AIR CARGO CARRIER (/) PAN AM (/) WORLD'S MOST EXPERIENCED AIRLINE. The instrument was received with a clear plastic sleeve, a black vinyl case, and an undated instruction manual. The case is marked: Concise (/) No. 28. In 1963, the rule was advertised as "a revolutionary new design concept."
Concise has specialized in circular slide rules, particularly for promotional distribution by other companies, since its founding in 1949. The company operated under the name Concise Co., Ltd., which appears on the instruction manual, from 1959 to 1966, hence the rough date assigned this slide rule. The donor, industrial engineer Richard Freeze, reported that he received the item as a promotional item distributed at a conference. For other Pan American promotional slide rules, see 1996.3029.01 and 1996.3029.02. For other slide rules by Concise, see 1985.0636.02, 1996.0141.01, and 2006.0173.01.
References: "Concise Corporate History," http://www.concise.co.jp/eng0731/history.html; Peter M. Hopp, Slide Rules: Their History, Models, and Makers (Mendham, N.J.: Astragal Press, 1999), 105; advertisement, Civil Engineering 33 (February 1963): 84; accession file.
Location
Currently not on view
date made
1959-1966
distributor
Pan American Airlines
maker
Concise
ID Number
2003.0012.01
accession number
2003.0012
catalog number
2003.0012.01

Painting - Squared Circle

This oil painting on pressed wood, #52 in the series, shows an original construction of Crockett Johnson. He executed this work in 1968, three years after he began creating mathematical paintings.
Description
This oil painting on pressed wood, #52 in the series, shows an original construction of Crockett Johnson. He executed this work in 1968, three years after he began creating mathematical paintings. It is evident that the artist was very proud of this construction because he drew four paintings dealing with the problem of squaring the circle. The construction was part of Crockett Johnson's first original mathematical work, published in The Mathematical Gazette in early 1970. A diagram relating to the painting was published there.
To "square a circle," mathematically speaking, is to construct a square whose area is equal to that of a given circle using only a straightedge (an unmarked ruler) and a compass. It is an ancient problem dating from the time of Euclid and is one of three problems that eluded Greek geometers and continued to elude mathematicians for 2,000 years. In 1880, the German mathematician Ferdinand von Lindermann showed that squaring a circle in this way is impossible - pi is a transcendental number. Because this proof is complicated and difficult to understand, the problem of squaring a circle continues to attract amateur mathematicians like Crockett Johnson. Although he ultimately understood that the circle cannot be squared with a straightedge and compass, he managed to construct an approximate squaring.
Crockett Johnson began his construction with a circle of radius one. In this circle he inscribed a square. Therefore, in the figure, AO=OB=1 and OC=BC=√(2) / 2. AC=AO+OC=1 + √(2) / 2 and AB=√(AC² + BC²) which equals the square root of the quantity (2+√(2)). Crockett Johnson let N be the midpoint of OT and constructed KN parallel to AC. K is thus the midpoint of AB, and KN=AO - (AC)/2=1/2 - √(2) / 4. Next, he let P be the midpoint of OG, and he drew KP, which intersects AO at X. Crockett Johnson then computed NP=NO+OP=(√(2))/4+(1/2). Triangle POX is similar to triangle PNK, so XO/OP=KN/NP. From this equality it follows that XO=(3-2√(2))/2.
Also, AX=AO-XO=(2√(2)-1)/2 and XC=XO+OC=(3-√(2))/2. Crockett Johnson continued his approximation by constructing XY parallel to AB. It is evident that triangle XYC is similar to triangle ABC, and so XY/XC=AB/AC. This implies that XY=[√((2+√(2)) × (8-5√(2))]/2. Finally he constructed XZ=XY and computed AZ=AX+XZ=[2√(2)-1+(√(2+√(2)) × (8-5√(2))]/2 which approximately equals 1.7724386. Crockett Johnson knew that the square root of pi approximately equals 1.772454, and thus AZ is approximately equal to √(Π) - 0.000019. Knowing this value, he constructed a square with each side equal to AZ. The area of this square is (AZ)² = 3.1415258. This differs from the area of the circle by less than 0.0001. Thus, Crockett Johnson approximately squared the circle.
The painting is signed: CJ68. It is marked on the back: SQUARED CIRCLE* (/) Crockett Johnson 1968 (/) FLAT OIL ON PRESSED WOOD) (/) MATHEMATICALLY (/) DEMONSTRATED (/) TO √π + 0.000000001. It has a white wooden frame. Compare to painting #91 (1979.1093.60).
References: Crockett Johnson, “On the Mathematics of Geometry in My Abstract Paintings,” Leonardo 5 (1972): p. 98.
C. Johnson, “A Geometrical look at √π," Mathematical Gazette, 54 (1970): p. 59–60. the figure is from p. 59.
Location
Currently not on view
date made
1968
painter
Johnson, Crockett
ID Number
1979.1093.35
catalog number
1979.1093.35
accession number
1979.1093

Painting - Transversals (Ceva)

A transversal is a line that intersects a system of other lines or line segments. Here Crockett Johnson explores the properties of certain transversals of the sides of a triangle.
Description
A transversal is a line that intersects a system of other lines or line segments. Here Crockett Johnson explores the properties of certain transversals of the sides of a triangle. The Italian mathematician Giovanni Ceva showed in 1678 that lines drawn from a point to the vertices of a triangle divide the edges of the triangle into six segments such that the product of the length of three nonconsecutive segments equals the product of the remaining three segments.
This painting shows a triangle (in white), lines drawn from a point inside the triangle to the three vertices, and a line drawn from a point outside the triangle (toward the bottom of the painting) to the three vertices. Segments of the sides of the triangle to be multiplied together are of like color. Crockett Johnson's painting combines two diagrams on page 159 of Nathan Court's College Geometry (1964 printing). These diagrams are annotated in his copy of the volume. Several of the triangles adjacent to the central triangle were used by Court in his proof of Ceva's theorem.
The painting is #31 in the series. It is signed: CJ66. There is a wooden frame painted off-white.
Location
Currently not on view
date made
1966
referenced
Ceva, Giovanni
painter
Johnson, Crockett
ID Number
1979.1093.22
catalog number
1979.1093.22
accession number
1979.1093

Keuffel and Esser Deci-Lon Slide Rule

This Keuffel and Esser Deci-Lon slide rule is a model 68 1100 with 10-inch 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.
Description
This Keuffel and Esser Deci-Lon slide rule is a model 68 1100 with 10-inch 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: Ln-3, Ln-2, Ln-1, Ln-0, 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 left-side 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.mccoys-kecatalogs.com/KECatalogs/1962/1962kecatp10.htm
http://www.mccoys-kecatalogs.com/KECatalogs/1967/1967kecatp12.htm
http://www.sliderules.info/collection/10inch/020/1025-decilon.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

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