Art

Panorama of the Army of the Cumberland

The National Museum of American History is not an art museum. But works of art fill its collections and testify to the vital place of art in everyday American life. The ceramics collections hold hundreds of examples of American and European art glass and pottery. Fashion sketches, illustrations, and prints are part of the costume collections. Donations from ethnic and cultural communities include many homemade religious ornaments, paintings, and figures. The Harry T Peters "America on Stone" collection alone comprises some 1,700 color prints of scenes from the 1800s. The National Quilt Collection is art on fabric. And the tools of artists and artisans are part of the Museum's collections, too, in the form of printing plates, woodblock tools, photographic equipment, and potters' stamps, kilns, and wheels.

Date: 1970s

Little Jimmy Dickens

Known for his strong voice and small physical stature, Jimmy Dickens (b.1920) gained national fame in 1949 and 1950 with a string of novelty and "heart" songs, including "Take an Old Cold Tater (and Wait)" and "I'm Little but I'm Loud."Currently not on view
Description
Known for his strong voice and small physical stature, Jimmy Dickens (b.1920) gained national fame in 1949 and 1950 with a string of novelty and "heart" songs, including "Take an Old Cold Tater (and Wait)" and "I'm Little but I'm Loud."
Location
Currently not on view
negative
1974
print
2003
maker
Horenstein, Henry
ID Number
2003.0169.071
accession number
2003.0169
catalog number
2003.0169.071

House Band

The house band at Tootsie's Orchid Lounge played for tips and the hope that they might be heard by Tootsie's record producing patrons.Currently not on view
Description
The house band at Tootsie's Orchid Lounge played for tips and the hope that they might be heard by Tootsie's record producing patrons.
Location
Currently not on view
negative
1974
print
2003
maker
Horenstein, Henry
ID Number
2003.0169.108
catalog number
2003.0169.108
accession number
2003.0169

Painting - Square Root of Pi

This oil painting is an original construction of Crockett Johnson. Since there are no notes on this construction, there is no way to tell what, if any, geometrical statement Johnson was representing in this painting.
Description
This oil painting is an original construction of Crockett Johnson. Since there are no notes on this construction, there is no way to tell what, if any, geometrical statement Johnson was representing in this painting. It may be the case that he merely thought of a more artistic way to portray the rectangles with area the square root of pi that appear in notes used for another painting, “Pi Squared and its Square Root” (1979.1093.54).
This painting has at its center a circle with center O and area pi. Also in the painting there are two rectangles, each of area the square root of pi, that share a diagonal that is the diameter of the circle with one end at point E. The purple rectangle in the painting has sides CE and EX and the white rectangle has sides DE and EF. The square in the painting is congruent to the square BDXA so it also has area pi, but it has been translated so its center is the same as the center of the circle, i.e. at O.
This is one of two paintings in the collection with this same title referring to the area the rectangles shown in the paintings. The geometry of the two is identical (see painting #100 - 1979.1093.67) but the dimensions and colors are different. The method of the color scheme of this painting, #89 in the series, is similar to painting #100 because, like the electric blue rectangle in the other painting, the white color of the rectangle against the purple background creates a dramatic contrast that highlights a rectangle with area the title of the painting.
This painting was executed in oil on masonite and has a black wooden frame. It is unsigned and undated.
Location
Currently not on view
date made
1970-1975
painter
Johnson, Crockett
ID Number
1979.1093.58
catalog number
1979.1093.58
accession number
1979.1093

Herb Vegetable Sauce

Currently not on view
Location
Currently not on view
date made
1968-1970
author
Waters, Alice
ID Number
2016.0085.11
accession number
2016.0085
catalog number
2016.0085.11

Painting -Construction of Heptagon

This painting represents one of Crockett Johnson's early constructions of a heptagon. It shows a large purple circle, a pink triangle superimposed, and two smaller circles. Crockett Johnson's diagram for the painting is shown.
Description
This painting represents one of Crockett Johnson's early constructions of a heptagon. It shows a large purple circle, a pink triangle superimposed, and two smaller circles. Crockett Johnson's diagram for the painting is shown. Two equal circles are constructed, with the center of the first on the second and conversely (circles with centers C and D in the diagram), and a line segment drawn that includes their points of intersection. Then, in Crockett Johnson's words, "Against a straight edge controlling their alignment the sought points B, U, and E, are determined by the adjustment of compass arcs BC from U and EC from B. Angles FBC, CBD, DBE, and BAF are π/ 7." Detailed examination of the triangles in the drawing shows that this is indeed the case.
The colors of the painting highlight the circles, lines, and arcs central to the construction, and the largest of the resulting isosceles triangles with vertex angle π/7 is shown in bold shades of pink. The short line called CF in the drawing (as well as line segments CD and DE, which are not shown), is the length of the side of a heptagon inscribed in a circle centered at B with radius BF.
The oil on masonite work is #116 in the series. It has a gray background and a wood and metal frame. It is inscribed on the back: CONSTRUCTION OF HEPTAGON (/) . . .(8) (/) Crockett Johnson 1973.
Location
Currently not on view
date made
1973
painter
Johnson, Crockett
ID Number
1979.1093.78
accession number
1979.1093
catalog number
1979.1093.78

Painting - Construction of a Heptagon

This is one of three very similar Crockett Johnson paintings closely related to the construction of a side of an inscribed regular heptagon which the artist published in The Mathematical Gazette in 1975.
Description
This is one of three very similar Crockett Johnson paintings closely related to the construction of a side of an inscribed regular heptagon which the artist published in The Mathematical Gazette in 1975. The paper presents a way of producing an isosceles triangle with angles in the ratio 3:3:1, so that the smallest angle in the triangle is π / 7. This angle is then inscribed in a large circle, and intercepts an arc length of π/7. A central angle of the same circle intercepts twice the angle, that is to say 2π/7, and the corresponding chord the side of an inscribed heptagon.
Crockett Johnson described the construction of his isosceles triangle in the diagram shown. The horizontal line segment below the circle on the painting corresponds to unit length BF in the figure, and the largest triangle in the painting is triangle is ABF in the figure, with vertex angle equal to one seventh of pi. This angle is inscribed in the large circular arc KDC. The side of the heptagon is the chord KC.
This version of Crockett Johnson's construction of a heptagon is #115 in the series. It has a dark blue background and a wood and metal frame. The painting is an oil or acrylic on masonite. The work is unsigned. See also #108 (335571) and #117 (1979.1093.79).
References: Crockett Johnson, “A Construction for a Regular Heptagon,” Mathematical Gazette, 1975, vol. 59, pp. 17–21.
Location
Currently not on view
date made
ca 1975
painter
Johnson, Crockett
ID Number
1979.1093.77
accession number
1979.1093
catalog number
1979.1093.77

Painting - Construction of Heptagon

Three very similar paintings in the Crockett Johnson collection are closely related to the the construction of a side of an inscribed regular a heptagon which he published in The Mathematical Gazette in 1975.
Description
Three very similar paintings in the Crockett Johnson collection are closely related to the the construction of a side of an inscribed regular a heptagon which he published in The Mathematical Gazette in 1975. The paper presents a way of producing an isosceles triangle with angles in the ratio 3:3:1, so that the smallest angle in the triangle is π/ 7. This angle is then inscribed in a large circle, and intercepts an arc length of π/7. A central angle of the same circle intercepts twice the angle, that is to say 2π/7, and the corresponding chord the side of an inscribed heptagon. Crockett Johnson described the construction of his isosceles triangle in the diagram reproduced. The horizontal line segment below the circle on the painting corresponds to unit length BF in the figure, and the triangle is ABF. Three of the four light-colored sections of the painting highlight important points in the construction. The critical steps are drawing a perpendicular bisector to the line segment BF, marking off an arc of radius equal to the √(2) with center F, and measuring the unit length AO along a marked straightedge that passes through B and intersects the perpendicular bisector at A. Finally, one finds the side of the regular inscribed heptagon.
Construction of Heptagon is #117 in the series. The oil painting on masonite is in shades of purple, cream, turquoise, and black. It has a black wood and metal frame. The work is unsigned. The surface appears damaged, perhaps from water. See also #115 (1979.1093.77) and #108 (335571).
Reference: Crockett Johnson, “A Construction for a Regular Heptagon,” Mathematical Gazette, 1975, vol. 59, pp. 17–21.
Location
Currently not on view
date made
ca 1975
painter
Johnson, Crockett
ID Number
1979.1093.79
accession number
1979.1093
catalog number
1979.1093.79

Painting - Construction of the Heptagon

Three very similar paintings in the Crockett Johnson collection are closely related to the construction of a side of an inscribed regular a heptagon which he published in The Mathematical Gazette in 1975.
Description
Three very similar paintings in the Crockett Johnson collection are closely related to the construction of a side of an inscribed regular a heptagon which he published in The Mathematical Gazette in 1975. The paper presents a way of producing an isosceles triangle with angles in the ratio 3:3:1, so that the smallest angle in the triangle is π/7. This angle is then inscribed in a large circle, and intercepts an arc length of π/7. A central angle of the same circle intercepts twice the angle, that is to say 2π/7, and the corresponding chord the side of an inscribed heptagon.
Crockett Johnson described the construction of his isosceles triangle in the diagram shown in the image. The horizontal line segment below the circle on the painting corresponds to unit length BF in the figure, and the triangle is ABF. The light colors of the painting highlight important points in the construction - marking off an arc of radius equal to the square root of 2 with center F, measuring the unit length AO along a marked straight edge that passes through B and ends at point A on the perpendicular bisector, and finding the side of the regular inscribed heptagon.
This version of the construction of a heptagon is #108 in the series. The oil painting on masonite with chrome frame was completed in 1975 and is unsigned. It is marked on the back: Construction of the Heptagon (/) Crockett Johnson 1975. See also paintings #115 (1979.1093.77) and #117 (1979.1093.79) in the series.
Reference: Crockett Johnson, "A Construction for a Regular Heptagon," Mathematical Gazette, 1975, vol. 59, pp.17–21.
Location
Currently not on view
date made
1975
painter
Johnson, Crockett
ID Number
MA.335571
accession number
322732
catalog number
335571

Women Artists Speak to Government

A 1979 poster, "Women Artists Speak to Government"Currently not on view
Description
A 1979 poster, "Women Artists Speak to Government"
Location
Currently not on view
date made
1979
associated date
January 28, 1979
ID Number
1982.3014.07

Women Artists Speak to Government

A 1979 poster, "Women Artists Speak to Government"Currently not on view
Description
A 1979 poster, "Women Artists Speak to Government"
Location
Currently not on view
date made
1979
associated date
January 28, 1979
ID Number
1982.3014.06

Women Artists Speak to Government

A 1979 poster, "Women Artists Speak to Government"Currently not on view
Description
A 1979 poster, "Women Artists Speak to Government"
Location
Currently not on view
date made
1979
associated date
January 28, 1979
ID Number
1982.3014.01

Predictions for the Year 2070 A.D.

Watercolor drawing by Rube Goldberg for the single cell cartoon Predictions for the Year 2070 A.D., 1970.Considered to be Rube's last cartoon, this watercolor drawing looks humorously at problems with politics, women's liberation, scientific invention and the generation gap, and
Description
Watercolor drawing by Rube Goldberg for the single cell cartoon Predictions for the Year 2070 A.D., 1970.
Considered to be Rube's last cartoon, this watercolor drawing looks humorously at problems with politics, women's liberation, scientific invention and the generation gap, and the potential for those issues to continue for at least one hundred years.
Rube Goldberg (1883-1970) was best known for the invention comic art series The Inventions of Professor Lucifer Gorgonzola Butts that he created for local and national newspapers between 1914 and the 1964. In a career that spanned more than half a century, he created some 50,000 individual and series cartoons. His subjects included American politics, sports, and everyday, timeless concerns. As he said in 1940, "Humor comes from everyday situations, because nothing is as funny as real life."
His best-remembered invention comic series looks at everyday life and our love-hate relationship with technology. The series reminds us of the disquieting feelings we have when using new mechanical devices that offer progress while taking away the comfort of an acquired skill or an older way of performing a task. The automobile, the airplane, the telephone, and the radio, among other conveniences, had not been invented when Rube Goldberg was born in 1883. They were world-wide and life-changing innovations by the 1920s, to which everyone was becoming accustomed. The inventions promised hours of entertainment and freedom, but at the same time created fear and feelings of loss of human importance.
Along with the more common fear that the new technologies would take the place of manual labor and human intelligence, Rube Goldberg also came to believe that individualism was disappearing. The more we gave in to the use of innovations and commodities, he felt, the less room there was for our individual perceptions, concerns, and activities. In 1921, for example, he declared that the telephone had "superseded the dog as man's best friend."
Another of Rube Goldberg's continuing themes touched on the humor of man's situation, even to his last cartoons; that nothing really changes no matter how persistent we are, and that man has a "capacity for exerting maximum effort to accomplish minimum results."
Location
Currently not on view
Date made
1970
original artist
Goldberg, Rube
Goldberg, Rube
ID Number
GA.23483
catalog number
GA*23483
accession number
1972.299186

Alarm Clock

Alarm Clock by Rube Goldberg, circa 1970.
Description
Alarm Clock by Rube Goldberg, circa 1970. This non-working, sculpted model signed by Rube Goldberg was crafted [during the 1960s] to replicate a cartoon from the series The Inventions of Professor Lucifer Gorgonzola Butts that he drew for between 1914 and 1964.
Inscription: At 6 a.m. garbage man picks up ashcan, causing mule to kick over statue of Indian warrior. Arrow punctures bucket and ice cubes fall on false teeth, causing them to chatter and nip elephant's tail. Elephant raises his trunk in pain, pressing lever which starts toy maestro to lead quartet in sad song. Sentimental girl breaks down and cries into flower pot, causing flower to grow and tickle man's feet. He rocks with laughter, starting machine that rings gong and slides sleeper out of bed into slippers on wheels, which propel him into bathroom where cold shower really wakes him up.
Location
Currently not on view
Date made
circa 1970
depicted
Butts, Lucifer Gorgonzola
original artist
Goldberg, Rube
ID Number
GA.23502
accession number
1972.289709
catalog number
GA*23502
accession number
289709

On the Beach

"On the Beach" is a black and white linoleum block print by Margaret Taylor Goss Burroughs (1915-2010).
Description
"On the Beach" is a black and white linoleum block print by Margaret Taylor Goss Burroughs (1915-2010). Burroughs produced prints at the School of the Art Institute of Chicago, where she completed her master's degree in 1948 and later enrolled as a senior citizen in order to gain access to their printing presses. Those prints were mainly lithographs, etchings, and silkscreens. She designed "On the Beach" in the 1950s after seeing a family group on a beach in Montego Bay, Jamaica. This impression was printed in September 1977, and the linoleum printing block is also in the Museum's collection.
Beyond her work as an artist, Burroughs also was an educator, writer, and activist. During the 1930s Burroughs worked for the Works Progress Administration Federal Arts Project in Chicago. Her family had moved to Chicago from Louisiana as part of the "Great Migration," the relocation of African Americans to the north. In 1941 she helped found the WPA/FAP-sponsored South Side Community Art Center in the predominantly black South Side neighborhood. In 1961 she and her husband founded Chicago's Ebony Museum of History and Art, now called the DuSable Museum of African American History. She served as director for both institutions.
Location
Currently not on view
date printed
1977
date made
1950
graphic artist
Burroughs, Margaret
printer
Freedenfeld, Robin
publisher
Pebbleford Editions, Ltd.
Great American Picture Company
maker
Burroughs, Margaret
ID Number
GA.24878.02
catalog number
24878.02
accession number
1978.0811

Women Artists Speak to Government

A 1979 poster, "Women Artists Speak to Government"Currently not on view
Description
A 1979 poster, "Women Artists Speak to Government"
Location
Currently not on view
date made
1979
associated date
January 24, 1979
ID Number
1982.3014.02

Women Artists Speak to Government

A 1979 poster, "Women Artists Speak to Government"Currently not on view
Description
A 1979 poster, "Women Artists Speak to Government"
Location
Currently not on view
date made
1979
associated date
January 28, 1979
ID Number
1982.3014.08

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

Book, A History of Pi

his volume is Petr Beckman, A History of Pi, Colarado: Golem Press, 1970. It is from the library of the painter Crockett Johnson. A figure on page 39 of this book relates to a painting of Crockett Johnson entitled Hippias' Curve.
Description
his volume is Petr Beckman, A History of Pi, Colarado: Golem Press, 1970. It is from the library of the painter Crockett Johnson. A figure on page 39 of this book relates to a painting of Crockett Johnson entitled Hippias' Curve. The painting has museum catalog number 1979.1093.76 and image number 2008-2517.
Location
Currently not on view
date made
1970
maker
Beckman, Petr
ID Number
1979.3083.06.06
catalog number
1979.3083.06.06
nonaccession number
1979.3083

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

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