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: 1970s

Painting - Law of Motion (Galileo)

Crockett Johnson based this painting on the discussion of motion along inclined planes by Galileo Galilee in his Dialogues Concerning Two New Sciences (1638).
Description
Crockett Johnson based this painting on the discussion of motion along inclined planes by Galileo Galilee in his Dialogues Concerning Two New Sciences (1638). Here Galileo showed that if from a fixed point straight lines be extended indefinitely downwards and a point be imagined to move along each line at a constant speed, all starting from the fixed point at the same time and moving with equal speeds, the locus of the moving points will be an expanding circle.
This painting shows four superimposed circles in various shades of gray, white and black. These circles all have a common point at the center top, and differ in radius. They are shaded into several regions which are divided by lines originating at the common point. The work has an orange background and a black wooden frame. It is probably based on a drawing in E. G. Valens, The Attractive Universe (1969). This volume is in Crockett Johnson's library, annotated on the page indicated.
The painting is #71 in the series. It is signed: CJ70.
References: Galileo Galilee, Dialog Concerning Two New Sciences, Third Day (Figure 59 in the Dover edition).
E. G. Valens, The Attractive Universe: Gravity and the Shape of Space, Cleveland and New York: World Publishing Company, 1969, p. 135.
Location
Currently not on view
date made
1970
referenced
Galilei, Galileo
painter
Johnson, Crockett
ID Number
1979.1093.46
catalog number
1979.1093.46
accession number
1979.1093

Painting - Golden Rectangle

Crockett Johnson annotated several diagrams in his copy of Valens’s book The Number of Things, and used a few of them as the basis of paintings. This is one example.
Description
Crockett Johnson annotated several diagrams in his copy of Valens’s book The Number of Things, and used a few of them as the basis of paintings. This is one example. It shows three golden rectangles, the curves from a compass used to construct the rectangles, and a section of a five-pointed Pythagorean star.
Euclid showed in his Elements that it is possible to divide a line segment into two smaller segments wherein the ratio of the whole length to the longer part equals the ratio of the longer part to the smaller. He used this theorem in his construction of a regular pentagon. This ratio came to be called the “golden ratio.”
A golden rectangle is a rectangle whose sides adhere to the golden ratio (in modern terms, the ratio of its length to its width equals (1 + √(5) ) /2, or about 1.62). The golden rectangle is described as the rectangle whose proportions are most pleasing to the eye.
This painting shows the relationship between a golden rectangle and a five-pointed Pythagorean star by constructing the star from the rectangle. It follows a diagram on the top of page 131 in Evans G. Valens, The Number of Things. This diagram is annotated. Valens describes a geometrical solution to the two expressions f x f = e x c and f = e - c, and associates it with the Pythagoreans. The right triangle on the upper part of Valens's drawing, with the short side and part of the hypotenuse equal to f, is shown facing to the left in the painting. It can be constructed from a square with side equal to the shorter side of the rectangle. Two of the smaller rectangles in the painting are also golden rectangles. Crockett Johnson also includes in the background the star shown by Valens and related lines.
This painting on masonite, #64 in the series, dates from 1970 and is signed: CJ70. It also is marked on the back: ”GOLDEN RECTANGLE (/) Crockett Johnson 1970. It is executed in two hues of gold to emphasize individual sections. While this method creates a detailed and organized contrast, it disguises the three rectangles and the star. Compare paintings 1979.1093.33 (#46) and 1979.1093.70 (#103).
Reference: Evans G. Valens, The Number of Things (1964), p. 131.
Location
Currently not on view
date made
1970
painter
Johnson, Crockett
ID Number
1979.1093.39
accession number
1979.1093
catalog number
1979.1093.39

Painting - Aligned Triangles (Desargues)

In the 17th century, the French engineer and architect Girard Desargues (1591–1661) explored interconnections between extensions of the lines within a pencil of three line segments (a pencil of line segments consists of several line segments originating at a common point).
Description
In the 17th century, the French engineer and architect Girard Desargues (1591–1661) explored interconnections between extensions of the lines within a pencil of three line segments (a pencil of line segments consists of several line segments originating at a common point). His theorems, as published in his own extremely obscure work and also by his contemporary, Abraham Bosse, were extended in the 19th century, and proved of fundamental importance to projective geometry.
Crockett Johnson's library contains discussions of Desargues' theorem by H. S. M. Coxeter, N. A. Court, Heinrich Dorrie, and William M. Ivins. This painting most resembles a figure from Coxeter, although the diagram is not annotated. Suppose that the vertices of two triangles (PQR and P'Q'R' in Figure 1.5B from Coxeter) lie on a pencil of three line segments emanating from the point O. Suppose that similarly situated sides of the two triangles can be extended to meet in the three points denoted by A, C and B in the figure. According to Desargues' theorem, A, C, and B are collinear.
In the painting, the two concurrent triangles are shown in shades of gray and black, while the top of the pencil of three lines is in shades of gold. Extensions of the sides and their points of intersection are clearly shown. Both the figure and the background of the painting are divided by the line joining the points of intersection
The painting is #63 in the series. It is painted in oil or acrylic on masonite, and has a brown wooden frame. The painting is signed: CJ70.
References:
Newman, J. R., The World of Mathematics, p. 133. Figure annotated.
Court, N. A., College Geometry (1952), pp. 163–5. The figure is not annotated.
Coxeter, H. S. M., The Real Projective Plane, (1955 edition), p. 7. The figure resembles the painting but is not annotated.
Dorrie, Heinrich, 100 Great Problems of Elementary Mathematics: Their History and Solution (1965), p. 267. There is an annotated figure here for another theorem of Desargues, the theorem of involution.
Field, J. V., The Invention of Infinity: Mathematics and Art in the Renaissance (1997), pp. 190–206.
Ivins, William M. Jr., Art & Geometry: A Study in Space Intuitions (1946), pp. 87–94.
Location
Currently not on view
date made
1970
referenced
Desargues, Girard
painter
Johnson, Crockett
ID Number
1979.1093.38
accession number
1979.1093
catalog number
1979.1093.38

Painting - Nine-Point Circle

Although 18th- and 19th-century mathematicians were much interested in analysis and algebra, they continued to explore geometrical constructions. In 1765, the eminent Swiss-born mathematician Leonhard Euler showed that nine points constructed from a triangle lie on a circle.
Description
Although 18th- and 19th-century mathematicians were much interested in analysis and algebra, they continued to explore geometrical constructions. In 1765, the eminent Swiss-born mathematician Leonhard Euler showed that nine points constructed from a triangle lie on a circle. This circle would come to be called the Feuerbach circle after Karl Wilhelm Feuerbach, a professor at the gymnasium in Erlangen, Germany. In 1822, he published a paper explaining and proving the theorem.
It seems likely that the direct inspiration for this painting was a figure in H. S. M. Coxeter’s The Real Projective Plane (1955). A diagram on p. 143 of this book shows a triangle with its respective nine points. In his copy of the book, Crockett Johnson connected the points himself, thereby completing the circle (see the annotated figure). In addition, Johnson also annotated a figure in Nathan A. Court’s College Geometry (1964 printing), p. 103. Crockett Johnson's painting does not directly imitate either drawing, but it is evident that he studied each figure in creating his own construction.
The first three points of the nine-point circle are the midpoints of the sides of triangle QRP (points L, M, and N in the annotated drawing). The second three points are the bases of the altitudes of the triangle (points A, B, C). These altitudes meet at a point (S). The midpoints of the lines joining the vertices of the triangle to the intersection of the altitudes create the last three points that indicate the nine-point circle (L’, M’, N’).
The segments of the triangle that are not part of the circle are colored in shades of blue and gray. Those segments that are part of the circle are white and various shades of pink and yellow. The painting has a background defined by two shades of gray.
This oil painting on masonite, #75 in the series, dates from 1970, is signed in the upper left corner : CJ70. It is inscribed on the back: NINE-POINT CIRCLE (/) Crockett Johnson 1970. There is a metal frame.
Location
Currently not on view
date made
1970
painter
Johnson, Crockett
ID Number
1979.1093.49
catalog number
1979.1093.49
accession number
1979.1093

Painting - Velocities and Right Triangles (Galileo)

This is the third painting by Crockett Johnson to represent the motion of bodies released from rest from a common point and moving along different inclined planes.
Description
This is the third painting by Crockett Johnson to represent the motion of bodies released from rest from a common point and moving along different inclined planes. In the Dialogues Concerning Two New Sciences (1638), Galileo argued that the points reached by the balls at a given time would lie on a circle. Two such circles and three inclined planes, as well as a vertical line of direct fall, are indicated in the painting. One circle has half the diameter of the other. Crockett Johnson also joins the base of points on the inclined planes to the base of the diameters of the circles, forming two sets of right triangles.
This oil painting on masonite is #96 in the series. It has a black background and a wooden and metal frame. It is signed on the back: VELOCITIES AND RIGHT TRIANGLES (GALILEO) (/) Crockett Johnson 1972. Compare to paintings #42 (1979.1093.30) and #71 (1979.1093.46), as well as the figure from Valens, The Attractive Universe: Gravity and the Shape of Space (1969), p. 135.
Location
Currently not on view
date made
1972
referenced
Galilei, Galileo
painter
Johnson, Crockett
ID Number
1979.1093.64
catalog number
1979.1093.64
accession number
1979.1093

Painting - Rotated Triangle and Reflections

Plane figures of the same size and shape can be moved about in several ways and preserve their size and form.
Description
Plane figures of the same size and shape can be moved about in several ways and preserve their size and form. Such congruent transformations, as they are called, are combinations of rotations about a point or a line, reflections about a line, or translations in which the figure moves about the plane but the directions of the sides is unchanged.
This painting, which closely follows a diagram from a book by H. S. M. Coxeter, illustrates two properties of congruent transformations. First, a transformation in which only one point remains unchanged is a rotation. In the figure, the triangle PQR passes through a congruent transformation into the triangle PQ'R'. Suppose that the transformation consisted of a reflection. Then triangle PQR could be rotated about the line m to another triangle, PRR[1]. However, these two triangles have a line, and not simply a point, in common. Coxeter went on to argue that any congruent transformation can be constructed as the product of reflections, the number of which can be reduced to three.
In the painting, as in the diagram, there are three congruent triangles. One light blue and gray triangle rotates into another light blue triangle above it to the right (the axis of rotation is perpendicular to the painting). The blue and blue-gray triangle is a rotation of the first triangle about the axis m, and a reflection of the other. The background is in two shades of gray, divided by this line of rotation.
The painting is #73 in the series and signed: CJ70. It has a metal frame.
Reference: H. S. M. Coxeter, The Real Projective Plane, p. 153.
Location
Currently not on view
date made
1970
painter
Johnson, Crockett
ID Number
1979.1093.47
catalog number
1979.1093.47
accession number
1979.1093

Painting - Doubled Cube (Newton)

Two paintings in the Crockett Johnson collection concern the ancient problem of doubling the volume of a given cube, or the Problem of Delos.
Description
Two paintings in the Crockett Johnson collection concern the ancient problem of doubling the volume of a given cube, or the Problem of Delos. Crockett Johnson wrote of this problem: "Plutarch mentions it, crediting as his source a now lost version of the legend written by the third century BC Alexandrian Greek astronomer Eratosthenes, who first measured the size of the Earth. Suffering from plague, Athens sent a delegation to Delos, Apollo’s birthplace, to consult its oracle. The oracle’s instruction to the Athenians, to double the size of their cubical altar stone, presented an impossible problem . . . . It could not be done with the compass and an unmarked straightedge."
(p. 99).
Crockett Johnson's paintings follow a construction proposed by the eminent English mathematician Isaac Newton. As Lucasian professor of mathematics at Cambridge University, Newton was required to deposit copies of his lectures in the university library. In 1683, after he had taught a course in algebra for 11 years, he finally deposited the notes for it. After Newton left Cambridge in 1696, his successor, William Whiston, arranged to have the lectures published in a book with the short title Arithmetica Universalis. Latin editions of the book appeared in 1707, 1722, 1732, and 1761; and English translations in 1720, 1728, and 1769.
In an appendix to this book, Newton discussed ways of finding the roots of numbers through geometric constructions. One problem was that of finding two mean proportions between given numbers. One case of this problem gives the cube root of a number. [Suppose the numbers are a and b and the proportionals x and y. Then a / x = x / y = y /b). Squaring the first and last term, a² / x² = y² / b². But, from the first equation, one also has x = y² / b. By substitution, a² / x² = x / b, or x³ = a² b. If a is 1, x is the cube root of b, as desired.]
Newton and Crockett Johnson represented the quantities involved as lengths of the sides of triangles. Newton’s figure is #99 in his Arithmetica Universalis. Crockett Johnson's figure is differently lettered, and the mirror image of that of Newton.
Following the artist's notation (figure 1979.3083.04.05), suppose AB = 1, bisect it at M, and construct an equilateral triangle MBX on MB. Draw AX and MX extended. Using a marked straightedge, construct line segment BZY, intersecting AX at Z and MX at Y in such a way that XY = AM = MB = 1/2. Then the distance BZ will have a length of one half the cube root of 2, that is to say the length of the side of a cube of side 1/2.
A proof of Newton’s construction is given in Dorrie. Crockett Johnson's copy of a drawing in this volume is annotated. The duplication of the cube also was discussed in at least two other books in Crockett Johnson's library. One is a copy of the 1764 edition of an English translation of the Arithmetica Universalis, which Crockett Johnson purchased in January of 1972. The second is W. W. Rouse Ball’s Mathematical Recreations and Essays, which also discusses Newton's solution.
Crockett Johnson's painting emphasized doubled lines in the construction, building on the theme of the painting. His diagram for the painting is oriented differently from the painting itself.
This oil painting on masonite is #85 in the series. It depicts overlapping blue, pink and gray circular segments in two adjacent rectangles. These rectangles are divided by various lines into gray and black sections. A lighter gray border goes around the edge. There is a metal and wooden frame. The painting is unsigned. For a mathematically related painting, see #56 (1979.1093.36).
References: Crockett Johnson, "On the Mathematics of Geometry in My Abstract Paintings," Leonardo 5 (1972): pp. 98–100. This specific painting is not discussed in the article.
Heinrich Dorrie, trans. David Antin, 100 Great Problems of Elementary Mathematics: Their History and Solution (1965) p. 171. The figure on this page, figure 27, is annotated.
Isaac Newton, Universal Arithmetick, (1769), esp. pp. 486–87, figure 99. This volume was in Crockett Johnson's library. It is not annotated.
W. W. Rouse Ball, rev. H. S. M. Coxeter, Mathematical Essays and Recreations, (1962 printing), pp. 327–33. This is a slightly different construction. The volume was in Crockett Johnson's library.
Isaac Newton, The Mathematical Works of Isaac Newton, assembled by Derek T. Whiteside, vol. 2, (1967). This includes a reprint of the 1728 English translation of the Arithmetica Universalis.
Location
Currently not on view
date made
ca 1970
referenced
Newton, Isaac
painter
Johnson, Crockett
ID Number
1979.1093.55
catalog number
1979.1093.55
accession number
1979.1093

Painting -Hippias' Curve

This painting is a construction of Crockett Johnson, relating to a curve attributed to the ancient Greek mathematician Hippias. This was one of the first curves, other than the straight line and the circle, to be studied by mathematicians.
Description
This painting is a construction of Crockett Johnson, relating to a curve attributed to the ancient Greek mathematician Hippias. This was one of the first curves, other than the straight line and the circle, to be studied by mathematicians. None of Hippias's original writings survive, and the curve is relatively little known today. Crockett Johnson may well have followed the description of the curve given by Petr Beckmann in his book The History of Pi (1970). Crockett Johnson's copy of Beckmann’s book has some light pencil marks on his illustration of the theorem on page 39 (see figure).
Hippias envisioned a curve generated by two motions. In Crockett Johnson's own drawing, a line segment equal to OB is supposed to move uniformly leftward across the page, generating a series of equally spaced vertical line segments. OB also rotates uniformly about the point O, forming the circular arc BQA. The points of intersection of the vertical lines and the arc are points on Hippias's curve. Assuming that the radius OK has a length equal to the square root of pi, the square AOB (the surface of the painting) has area equal to pi. Moreover, the height of triangle ASO, OS, is √(4 / pi), so that the area of triangle ASO is 1.
The painting has a gray border and a wood and metal frame. The sections of the square and of the regions under Hippias's curve are painted in various pastel shades, ordered after the order of a color wheel.
This oil painting is #114 in the series. It is signed on the back: HIPPIAS' CURVE (/) SQUARE AREA = (/) TRIANGLE " = 1 = [ . .] (/) Crockett Johnson 1973.
Location
Currently not on view
date made
1973
referenced
Hippias
painter
Johnson, Crockett
ID Number
1979.1093.76
accession number
1979.1093
catalog number
1979.1093.76

Documentation on the Standard Trigonometric Program for the Wang 700B Electronic Calculator

Wang Laboratories not only sold desktop electronic calculators but also pre-recorded tape cassettes that included useful programs. This reference manual with its yellow cover describes use of the standard trigonometric package program.
Description
Wang Laboratories not only sold desktop electronic calculators but also pre-recorded tape cassettes that included useful programs. This reference manual with its yellow cover describes use of the standard trigonometric package program. The package included programs for converting between degrees and radians, finding standard trigonometric, inverse trigonometirc, hyperbolic trigonometric, and inverse hyperbolic trigonometric functions.
For a related object, see 1983.0171.01.
Location
Currently not on view
date made
1970
maker
Wang Laboratories
ID Number
1983.0171.05
catalog number
1983.0171.05
accession number
1983.0171

Gino’s Pocket Counter

This small and very simple key-driven adding machine has three white plastic keys and a plastic frame. A window below the first key is marked cents. Pushing the plastic key above it rotates a disc below with the digits 0 to 9 on it by one unit.
Description
This small and very simple key-driven adding machine has three white plastic keys and a plastic frame. A window below the first key is marked cents. Pushing the plastic key above it rotates a disc below with the digits 0 to 9 on it by one unit. The window below the second key is marked dimes. Pushing this key rotates a disc similarly marked. The third window is marked dollars. There is a carry from the first column to the second and from the second to the third. Pushing the key above it rotates a disc marked from 0 to 19. Repeatedly pushing another white key on the right side zeroes the instrument.
The instrument is marked: Gino’s {/} FREEDOM OF CHOICE. It is also marked: JAPAN. It is also marked: POCKET COUNTER.
Judy Wallace, the mother of the donor, used it in and around Cockeysville, Md., in grocery stores during the 1970s.
date made
ca 1975
ID Number
2009.0180.09
catalog number
2009.0180.09
accession number
2009.0180

Polycube Puzzle Known as Kolor Kraze

This thirteen-piece puzzle has twelve brightly colored plastic pieces that consist of two small cubes of different colors and one that consists of three small cubes. The small cubes come in nine colors, three of each color. They can be arranged as 3 x 3 x 3 cube.
Description
This thirteen-piece puzzle has twelve brightly colored plastic pieces that consist of two small cubes of different colors and one that consists of three small cubes. The small cubes come in nine colors, three of each color. They can be arranged as 3 x 3 x 3 cube. The goal of the puzzle is to have all nine colors showing on each face of the cube. This example of the puzzle is in a transparent plastic box which is too large for it. The box has no lid.
The shape and number of the pieces in puzzles 2012.0091.06 and 2012.0091.07 are the same, although the coloring is different.
The size, colors and arrangement of the puzzle corresponds to that of the Kolor Kraze puzzle copyrighted in 1970 by House of Games Corporation in Don Mills, Ontario, Canada.
Reference:
Jerry Slocum and Jack Botermans, Puzzles Old and New: How to Make and Solve Them, Seattle: University of Washington Press, 1986, p. 43.
Location
Currently not on view
date made
ca 1970
maker
House of Games Ltd.
ID Number
2012.0091.07
accession number
2012.0091
catalog number
2012.0091.07

Control Data Corporation Flowcharting Template Form 10124300

This clear plastic flowcharting template has spaces representing twenty-four flowcharting symbols, labeled appropriately. It fits in a blue paper envelope which explains the meaning of the symbols. A mark on the front of the template reads: CONTROL DATA (/) CORPORATION.
Description
This clear plastic flowcharting template has spaces representing twenty-four flowcharting symbols, labeled appropriately. It fits in a blue paper envelope which explains the meaning of the symbols. A mark on the front of the template reads: CONTROL DATA (/) CORPORATION. A mark on the envelope reads: FLOWCHART TEMPLATE (/) Form 10124300 (/) The symbols shown on this jacket conform to (/) American National Standard X3.5 – 1970 . . . . This final mark gives a rough date for the object.
Location
Currently not on view
date made
ca 1970
maker
Control Data
ID Number
2012.3058.01
nonaccession number
2012.3058
catalog number
2012.3058.01

Polycube Puzzle, SOMA Cube

The SOMA cube is a three-dimensional arrangement puzzle devised in 1936 by the Danish poet and puzzler Peter Hein (1905-1996) while he was a student listening to a lecture on quantum mechanics by Werner Heisenberg.
Description
The SOMA cube is a three-dimensional arrangement puzzle devised in 1936 by the Danish poet and puzzler Peter Hein (1905-1996) while he was a student listening to a lecture on quantum mechanics by Werner Heisenberg. The seven pieces represent all the ways three or four cubes can be arranged, other than in a straight line. In addition to forming a cube, the pieces can form in a wide array of other surfaces. According to Slocum and Bosterman, the name SOMA is taken from a drug envisioned in Aldous Huxley’s book Brave New World. The drug SOMA induced a dreamlike trance.
This example of the puzzle is made from light blue plastic. It closely resembles one sold by Parker Brothers from the late 1960s.
References:
Martin Gardner, The Colossal Book of Mathematics, New York and London: W.W. Norton & Company, 2001, pp. 398-408. Gardner first wrote a column about the puzzle in 1958.
Martin Gardner, Knotted Doughnuts and Other Mathematical Entertainments, New York: W. H. Freeman and Company, 1986, pp. 28-43.
[Advertisement], The Washington Post, Washington, D.C., November 30,1969, p. 214. The puzzle by Parker Bothers sold for $1.57.
Jerry Slocum and Jack Botermans, Puzzles Old and New: How to Make and Solve Them, Seattle: University of Washington Press, 1986, pp. 40-41.
Location
Currently not on view
date made
ca 1970
maker
Parker Brothers
ID Number
2012.0091.04
accession number
2012.0091
catalog number
2012.0091.04

Electrophoresis Tank, Model LT48-A

Carl Woese, a microbiologist and evolutionary biologist, used this electrophoresis tank in pioneering research on the evolution of bacteria.
Description (Brief)
Carl Woese, a microbiologist and evolutionary biologist, used this electrophoresis tank in pioneering research on the evolution of bacteria. His work established that evolutionary relationships between organisms could be found using genetic differences, not just morphology (the way they look).
Woese made his career at the University of Illinois at Urbana-Champaign where early on he searched for a way to classify species of bacteria. In the early 1960s, scientists developed evolutionary trees mainly by comparing species' morphological differences. Simple, single-celled organisms like bacteria, however, lack the complex morphology necessary for this kind of comparison.
A biophysicist by training, Woese looked to differences in the chemical makeup of bacteria to help classify them. Woese chose ribosomal RNA (rRNA) as his molecule of comparison, specifically a section of the rRNA called the 16S portion. Ribosomal RNA made a good target molecule for several reasons. Most importantly, its sequence (the order of its individual molecules) tends to be highly conserved. This means that there is not a wide variety of changes over time or between species, so there are a smaller number of differences to compare between organisms. What’s more, all living things contain rRNA, therefore it can be used to compare any two species. Finally, it’s relatively easy to extract from cells.
Woese's team for the project included Ralph S. Wolfe, George E. Fox, William E. Balch, Kenneth R. Luehrsen, and Linda J. Magrum. In the lab, they cut the rRNA into small fragments and sequenced the shorter fragments. Next, they searched for differences in the sequences between bacterial species. Part of this work entailed separating fragments from one another according to their electrical charges. The task was completed using this electrophoresis tank. The team’s findings suggested that comparing molecular differences between species was indeed an effective way to discern evolutionary relationships. What’s more, they discovered that some of the bacterial species were so distinct from others that they necessitated a new branch on the tree of life—“Archaea.” At the time, scientists divided life between just two branches—prokaryotes and eukaryotes.
At first the larger scientific community was skeptical of the Archaea addition. With time and growing evidence through the 1980s, however, they accepted Woese’s findings. Today, genetic and molecular comparisons between species are the primary tool for figuring out evolutionary relationships.
Sources:
Collections Committee Memo, Accession File 2013.0281, National Museum of American History.
Virginia Morell, “Microbiology's Scarred Revolutionary,” Science 276, no. 5313 (1997): 699–702.
Norman R. Pace, Jan Sapp, and Nigel Goldenfeld, “Phylogeny and beyond: Scientific, historical, and conceptual significance of the first tree of life,” Proceedings of the National Academy of Sciences 109, no. 4 (2012): 1011–18.
Exhibition Booklet, Uncovering Life’s Third Domain: The Discovery of the Archaea, The Institute for Genomic Biology and the Spurlock Museum, University of Illinois at Urbana-Champaign.
Carl Woese et al., “A Comparison of the 16S Ribosomal RNAs from Mesophilic and Thermophilic Bacilli: Some Modifications in the Sanger Method for RNA Sequencing,” Journal of Molecular Evolution 7, no. 3 (1976): 197–213.
Location
Currently not on view
date used
1966-1976
ID Number
2013.0281.01
catalog number
2013.0281.01
accession number
2013.0281
model number
Model LT48-A
serial number
48A-74-100-LT

Ricoh Duplex Slide Rule Sold by Staedtler-Mars (944-24)

Numerous slide rule manufacturers also sold rules made by other companies.
Description
Numerous slide rule manufacturers also sold rules made by other companies. For instance, the German pencil-manufacturer Staedtler, which used the trade name Mars for slide rules, marketed this ten-inch bamboo rule coated with white plastic and held together with metal L-shaped endpieces. Staedtler's own rules had distinctive light blue slides, but this rule is entirely white. It was made as model 151 between about 1960 and 1972 by the Japanese firm known as San-Ai Measuring Instruments and then as Ricoh Measuring Instruments. Several companies besides Staedtler sold these rules, including Lutz.
On one side, the base has LL/1, LL/2, LL/3, DF, D, LL3, LL2, and LL1 scales, with CF, CIF, CI, and C scales on the slide. The right end of each scale identifies the meaning of the letters, i.e., the C and D scales are marked with an x. The right end of the slide has the company logo of a Greek soldier's head and is marked: STAEDTLER (/) MARS (/) 944 24. On the other side, the base has LL/0, L, K, A, D, DI, P, and LL0 scales, with B, S, ST, T, and C scales on the slide. The indicator is clear plastic with white plastic edges. The bottom edge of the rule is marked: JAPAN.
The rule fits in a brown leather case with a loop for attaching to a belt. The flap is marked: STAEDTLER (/) MARS. The back bottom of the case is marked: JAPAN. A blue and white cardboard box is marked on the end: STAEDTLER MARS (/) 1 BAMBOO SLIDE RULE 944 24 (/) Duplex Log Log 10". See 2009.0019.02.01 for instructions. Compare to 1986.0790.04.
The mathematician and theoretical computer scientist Harley Flanders received this instrument as a gift, but he never used it.
References: "A Modern Brand Rich in Tradition," Staedtler, http://www.staedtler.com/brand_with_tradition_gb.Staedtler?ActiveID=3049; David A. Davis, "Relay/Ricoh Archive," http://www.oocities.org/usra482b/page3.html; Peter M. Hopp, Slide Rules: Their History, Models, and Makers (Mendham, N.J.: Astragal Press, 1999), 213.
Location
Currently not on view
date made
1960-1972
maker
Ricoh Measuring Instruments
ID Number
2009.0019.02
accession number
2009.0019
catalog number
2009.0019.02

Beat the Elf, Polycube Puzzle

The thirteen pieces of this plastic polycube consist of twelve small double cubes and a triple cube (three cubes in a row). Eleven pieces have one yellow and one black cube. One piece consists of two black cubes. The final piece has one black and two yellow cubes.
Description
The thirteen pieces of this plastic polycube consist of twelve small double cubes and a triple cube (three cubes in a row). Eleven pieces have one yellow and one black cube. One piece consists of two black cubes. The final piece has one black and two yellow cubes. The goal of the puzzle is to arrange the pieces into a 3x3x3 cube, with no face of the cube representing a winning game of tic-tac-toe.
The puzzle fits in a transparent plastic box which is shorter than it and has no lid.
The shape and number of the pieces in puzzles 2012.0091.06 and 2012.0091.07 are the same, although the coloring is different.
References:
Jerry Slocum and Jack Botermans, The Book of Ingenious and Diabolical Puzzles, New York: Times Books, 1994, pp. 36-37.
Location
Currently not on view
date made
ca 1975
maker
House of Games Ltd.
ID Number
2012.0091.06
accession number
2012.0091
catalog number
2012.0091.06

Digital Educational Services Flowcharting Template

This clear plastic rectangular template has thirty-one flowcharting symbols arranged in four rows. In addition a scale of tenths of inches across the top is numbered to 90. A "card count" scale along the right side is numbered from 100 to 700.
Description
This clear plastic rectangular template has thirty-one flowcharting symbols arranged in four rows. In addition a scale of tenths of inches across the top is numbered to 90. A "card count" scale along the right side is numbered from 100 to 700. A scale of sixths of an inch, numbered from 1 to 30, is along the left side. Along the bottom is a scale of millimeters numbered from 0 to 250.
The template fits in a tan paper sleeve that explains the meaning of the symbols. The front of the sleeve has an address label directed from Digital Equipment Corporation to Mr. David Studebaker, Marketing Director, Digital Systems House, Batavia, IL.
According to the donor: "I was a minor partner in Digital Systems House from July 1976 through March 1984. We became a Digital Equipment Corporation reseller in 1977 or 1978. I became Sales & Marketing Director in about 1978 through about 1981 or 1982."
Reference:
Electronic message, August 22, 2014.
Location
Currently not on view
date made
ca 1970
1978-1982
maker
Digital Equipment Corporation
ID Number
2014.3067.10
nonaccession number
2014.3067
catalog number
2014.3067.10

Coin-Operated Arcade Game, Piano Playing Duck

This carnival game consists of a wooden crate painted blue, gold, and yellow with a metal mesh window on the right front and a cash box left of it. A cord extends from the back. Two metal handles for carrying the object are on both the right and left sides.
Description
This carnival game consists of a wooden crate painted blue, gold, and yellow with a metal mesh window on the right front and a cash box left of it. A cord extends from the back. Two metal handles for carrying the object are on both the right and left sides. Opening a door on the left side reveals two metal boxes. The back one has various electrical cords and a rotary switch. The front one appears to have held food.
A door on the back opens into the main compartment. It has a floor partly covered with mesh, as well as a toy piano with a lamp on it. The left side of the compartment has a dispenser for food.
A mark on the cash box reads: PIANO DUCK (/) TYPE D.
The piano-playing duck was manufactured by the firm of Animal Behavior Enterprises, a company established in the late 1940s by students of the behavioral psychologist B.F. Skinner. In use, it included not only the crate, piano, and lamp, but a duck or chicken. The staff of ABE trained the duck to turn on the lamp and then play “several rippling cadenzas” before the lamp went off to signal the end of the performance. This example of the game was displayed in Massachusetts, first at the Aquarium of Cape Cod (also called Aqua Circus and ZooQuarium) in West Yarmouth and then at a private animal preserve / rehabilitation center in Westport. The Westport concern was operated by Damase (Jiggs) Giguere.
For a related object, see 2004.0075.01. For related documentation see 2015.3170.
Location
Currently not on view
date made
ca 1975
maker
Animal Behavior Enterprises, Inc.
ID Number
2015.0290.01
catalog number
2015.0290.01
accession number
2015.0290

Lasico L30-A Electronic Polar Compensating Planimeter Prototype

This metal prototype for an electronic polar planimeter has an adjustable 12" tracer arm with lens. The top of the arm is divided to millimeters and numbered from 10 to 24 centimeters. The bottom is marked with a serial number: 45254.
Description
This metal prototype for an electronic polar planimeter has an adjustable 12" tracer arm with lens. The top of the arm is divided to millimeters and numbered from 10 to 24 centimeters. The bottom is marked with a serial number: 45254. The arm slides into a painted metal holder for an electronic measuring unit with a plug. The holder has a vernier for the scale on the tracer arm and is marked: LASICO. The plug attaches to a Series 40 processor with a digital screen for displaying the measurement and a knob for setting the instrument to OFF, A, ACCU, or B. An AC adapter by Calrad, a Taiwanese company, powers the processor.
An adjustable 10" pole arm fits into the holder at one end and a rectangular painted metal pole weight at the other end. The weight is marked: LASICO (/) U.S.A. The arm is divided to millimeters and numbered by tens from 30 to 60 millimeters. The adjusting part of the arm is marked: LASICO. An additional tracer arm with a point instead of a lens has serial number: 45275. A business card for the designer, who also donated the instrument, an extra lens, and two plastic washers for the lens are inside a black plastic case lined with foam.
Maximilian Berktold (b. 1929) immigrated from Kempten-Allgäu, West Germany, in 1950 and almost immediately began working for the Los Angeles Scientific Instrument Company. He oversaw design and production of the firm's planimeters, integrators, pantographs, and various optical instruments until Lasico closed in 2008. He developed this prototype around 1970 from the company's model L30 mechanical planimeter, but the final version was sold as model series 40 and 50. These devices cost several hundred dollars.
An 18-page booklet, "LASICO Instruction Manual [for] Digital Compensating Polar Planimeters," was received with the instrument. It contains the calibration settings for a model L50-E, serial number 65879. For company history, see 2011.0043.01.
This instrument reached the Smithsonian if 2011.
Reference: Accession file.
Location
Currently not on view
date made
1970
maker
Los Angeles Scientific Instrument Company
ID Number
2011.0043.03
accession number
2011.0043
catalog number
2011.0043.03

Electrophoresis Tank, Model LT48-A

Carl Woese, a microbiologist and evolutionary biologist, used this electrophoresis tank in pioneering research on the evolution of bacteria.
Description (Brief)
Carl Woese, a microbiologist and evolutionary biologist, used this electrophoresis tank in pioneering research on the evolution of bacteria. His work established that evolutionary relationships between organisms could be found using genetic differences, not just morphology (the way they look).
Woese made his career at the University of Illinois at Urbana-Champaign where early on he searched for a way to classify species of bacteria. In the early 1960s, scientists developed evolutionary trees mainly by comparing species' morphological differences. Simple, single-celled organisms like bacteria, however, lack the complex morphology necessary for this kind of comparison.
A biophysicist by training, Woese looked to differences in the chemical makeup of bacteria to help classify them. Woese chose ribosomal RNA (rRNA) as his molecule of comparison, specifically a section of the rRNA called the 16S portion. Ribosomal RNA made a good target molecule for several reasons. Most importantly, its sequence (the order of its individual molecules) tends to be highly conserved. This means that there is not a wide variety of changes over time or between species, so there are a smaller number of differences to compare between organisms. What’s more, all living things contain rRNA, therefore it can be used to compare any two species. Finally, it’s relatively easy to extract from cells.
Woese's team for the project included Ralph S. Wolfe, George E. Fox, William E. Balch, Kenneth R. Luehrsen, and Linda J. Magrum. In the lab, they cut the rRNA into small fragments and sequenced the shorter fragments. Next, they searched for differences in the sequences between bacterial species. Part of this work entailed separating fragments from one another according to their electrical charges. The task was completed using this electrophoresis tank. The team’s findings suggested that comparing molecular differences between species was indeed an effective way to discern evolutionary relationships. What’s more, they discovered that some of the bacterial species were so distinct from others that they necessitated a new branch on the tree of life—“Archaea.” At the time, scientists divided life between just two branches—prokaryotes and eukaryotes.
At first the larger scientific community was skeptical of the Archaea addition. With time and growing evidence through the 1980s, however, they accepted Woese’s findings. Today, genetic and molecular comparisons between species are the primary tool for figuring out evolutionary relationships.
Sources:
Collections Committee Memo, Accession File 2013.0281, National Museum of American History.
Virginia Morell, “Microbiology's Scarred Revolutionary,” Science 276, no. 5313 (1997): 699–702.
Norman R. Pace, Jan Sapp, and Nigel Goldenfeld, “Phylogeny and beyond: Scientific, historical, and conceptual significance of the first tree of life,” Proceedings of the National Academy of Sciences 109, no. 4 (2012): 1011–18.
Exhibition Booklet, Uncovering Life’s Third Domain: The Discovery of the Archaea, The Institute for Genomic Biology and the Spurlock Museum, University of Illinois at Urbana-Champaign.
Carl Woese et al., “A Comparison of the 16S Ribosomal RNAs from Mesophilic and Thermophilic Bacilli: Some Modifications in the Sanger Method for RNA Sequencing,” Journal of Molecular Evolution 7, no. 3 (1976): 197–213.
Location
Currently not on view
date used
1966-1976
maker
Savant Instruments, Inc.
ID Number
2013.0281.02
catalog number
2013.0281.02
accession number
2013.0281
model number
Model LT20-A

Documentation, Letters and Drawings of Crockett Johnson Sent to Milton Rosenau

Between 1968 and 1975, the artist and author Crockett Johnson (1906-1975) sent a variety of mathematical inquiries to his Connecticut acquaintance Milton (Mickey) Rosenau. The questions relate to Crockett Johnson's mathematical paintings and drawings for them.
Description
Between 1968 and 1975, the artist and author Crockett Johnson (1906-1975) sent a variety of mathematical inquiries to his Connecticut acquaintance Milton (Mickey) Rosenau. The questions relate to Crockett Johnson's mathematical paintings and drawings for them. Rosenau's replies apparently do not survive.
For related transactions, see the collection of Crockett Johnson's mathematical paintings (transaction 1979.1093), related nonaccessioned correspondence and drawings of Crockett Johnson (transaction 1979.3083), and correspondence received from Harley Flanders (transaction 2009.3005).
Location
Currently not on view
date made
1968-1975
maker
Johnson, Crockett
ID Number
2012.3120.01
nonaccession number
2012.3120
catalog number
2012.3120.01

Puzzle, Instant Insanity

This puzzle consists of four plastic cubes with differently colored faces. The goal is to arrange the cubes so that the four square faces in each long row of are of four different colors.The general form of this puzzle dates to the early twentieth century.
Description
This puzzle consists of four plastic cubes with differently colored faces. The goal is to arrange the cubes so that the four square faces in each long row of are of four different colors.
The general form of this puzzle dates to the early twentieth century. California computer programmer Franz O. Armbruster (1929-2013) developed this version. Parker Brothers offered it from the mid-1960s as Instant Insanity, Millions of copies sold.
References:
{Advertisement}, Los Angeles Times, Los Angeles, Calif. Feb 1, 1968: 15. The toy cost 87 cents.
Erik D. Demaine, Martin L. Demaine, and Tom Rodgers, A Lifetime of Puzzles, CRC Press, 2008, pp. 157-175.
Jerry Slocum and Jack Botermans, Puzzles Old and New: How to Make and Solve Them, Seattle: University of Washington Press, 1986, p. 38.
Location
Currently not on view
date made
ca 1980
ca 1970
ca 1968
maker
Parker Brothers
ID Number
2012.0091.02
accession number
2012.0091
catalog number
2012.0091.02

A Group of Six Polycube Puzzles, Known as Impuzzables

Each of these six colorful plastic puzzles is made up of groups of small cubes that can be arranged into a larger cube. The puzzles fit into clear plastic boxes.
Description
Each of these six colorful plastic puzzles is made up of groups of small cubes that can be arranged into a larger cube. The puzzles fit into clear plastic boxes. The objects have been assigned the following subindex numbers:
2012.0091.01.01 - brown
2012.0091.01.02 - green
2012.0091.01.03 - blue
2012.0091.01.04 - yellow
2012.0091.01.05 - red
2012.0091.01.06 - orange.
All six puzzles have the mark: MADE IN HONGKONG
The puzzles belonged to Rebecca Coven, the mother of the donor, who was a mathematics teacher in Brooklyn, New York. The donor dated the objects to about 1975. A mark on one of them gives the copyright date 1969.
According to Martin Gardner, Lakeside Industries, a division of Leisure Dynamics of Minneapolis, sold this series of six polycube puzzles from 1969. The puzzles ranged in difficulty from the easiest (yellow) to the hardest (blue). California game inventor Gerard D’Arcey designed the puzzles. Recent websites list a similar set of puzzles, although the colors are different.
Single examples of this puzzle (with six different versions available) were advertised as on sale in 1970 for forty-nine cents each. A 1982 advertisement lists individual puzzles at $1.99, reduced from a regular price of $2.99.
References:
[Advertisement], The Hartford Courant, November 12, 1970, p. 27.
[Advertisement}, The Chicago Tribune, February 24, 1982, p. C8.
Kevin Holmes and Rik Van Grol, A Compendium of Cube-Assembly Puzzles Using Polycube Shapes, Suffolk, England: Trench Puzzles, 2002.
Martin Gardner, Knotted Doughnuts and Other Mathematical Entertainments, New York: W. H. Freeman, 1986, p. 41.
Location
Currently not on view
date made
ca 1975
ID Number
2012.0091.01
accession number
2012.0091
catalog number
2012.0091.01

Teacher’s Number Line

From the time of Descartes (1596–1650), mathematicians have described positive and negative integers as evenly spaced points on a line, now called the number line, that extends infinitely in both directions.
Description
From the time of Descartes (1596–1650), mathematicians have described positive and negative integers as evenly spaced points on a line, now called the number line, that extends infinitely in both directions. This usage had made it into some school textbooks by the early 20th century. Particularly at the time of the development of the New Math in the 1950s and 1960s, number lines became part of the school classroom. This example of a number line was developed by Loraine McMillan and sold by Houghton Mifflin Company to accompany the 1972 edition of the textbook Modern School Mathematics. McMillan also prepared the leaflet describing how the number line should be used, as well as a that sold separately.
The teacher's number line consists of eleven cards. Ten of these can be placed end to end to show a number line with the integers from 0 to 100 written in red. The eleventh card is divided into segments but has no numbers marked on it. Each card, unfolded, measures 89 cm. w. x 11 cm. d. The cards were coated with clear plastic so that teachers could mark them with crayons or felt tip markers. The teacher’s guide is printed on blue paper. A mark on it reads: Teacher’s number line; teacher’s guide(/) by (/) Loraine McMillan. Another mark on it reads: houghton (/) mifflin (/) company. A third mark reads: 1972 .
This example appears unused. It was received in 2012, and had been the property of Harvard University mathematician Andrew Gleason.
References:
P. A. Kidwell, A. Ackerberg-Hastings, and D. L. Roberts, Tools of American Mathematics Teaching, Baltimore: Johns Hopkins University Press (2008), pp. 202-203.
Max Beberman and Bruce Meserve, “The Concept of a Literal Number Symbol,” Mathematics Teacher; 48, 1955, pp. 198–202.
Location
Currently not on view
date made
1972
maker
Houghton Mifflin Company
ID Number
2012.0064.01
accession number
2012.0064
catalog number
2012.0064.01

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