#
Art

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.

"Art - Overview" showing 459 items.

Page 2 of 46

## Painting -

*Square Root Of Pi - 0.00001*- Description
- This oil painting on masonite, #91 in the series, uses the same construction as that of painting #52 (see 1979.1093.35). Crockett Johnson's construction leads to a square with side approximately equal to 1.772435, which differs from the square root of pi by less than 0.00001, as the title states. Thus, a square with this side would have an area approximately equal to 3.1415258.

- Unlike painting #52 (1979.1093.35), the circle of this work is divided into four quadrants. Crockett Johnson chose darker shades and lighter tints of pink to illustrate his figure, which appear bold juxtaposed against the black background. The triangle executed in the lightest tint of pink and the shape executed in white with a pink tip adjoin the horizontal line segment that has an approximate length of the square root of pi.

- This painting was completed in 1972, is unsigned, and has a wooden frame accented with chrome. On the back is an inscription, partly obscured, that reads: - 0.00001 (/) Crockett Johnson 1972.

- Location
- Currently not on view

- date made
- 1972

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.60

- catalog number
- 1979.1093.60

- accession number
- 1979.1093

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Squared Rectangle and Euler Line*- Description
- Crockett Johnson had a longstanding interest in squaring figures, that is to say, constructing squares equal in area to other plane figures. Euclid had shown in his
*Elements*(Book II, Proposition 14) how to construct a square equal in area to a given rectangle. Crockett Johnson developed his own construction, one case of which served as the basis of this painting. The rectangle, the square of equal area, and a circle used in the demonstration are shown in various shades of pink.

- Two drawings from Crockett Johnson’s papers illustrate his ideas. The one that relates most closely to this painting is labeled A in his figure. In it, the given rectangle is ABED. The angles at the corner A and D are bisected, and the bisectors extended to meet at point C. The line from corner B through C meets side DE at point X. Line segments CL and XS are constructed parallel to AD. By this construction, the segment DL is half the length of AD. From center X, one may draw a line segment of length DL that intersects CL at point O. The figure and painting then show a circle of radius OX and center O that intersected side AD at V (where OV equals DL and is perpendicular to AD), and side BE at F. The point Y on the circle is on OV extended. As Crockett Johnson states in his notes, XY squared equals the product of AB and AD.

- The Euler line of a triangle includes three points. These are the intersections of the altitudes, of the perpendicular bisectors (lines perpendicular to the sides at their midpoints), and of the medians (lines drawn from a vertex to the midpoint of the opposite side). For an inscribed right triangle, both the perpendicular bisectors and the medians intersect in the center of the inscribing circle, while the altitudes meet at the right angle of the triangle. In the painting there are three right triangles inscribed in the circle. These are triangles XEF, XYF, and VXY in the diagram. The Euler line for the first two triangles is XOF, the Euler line for the third is VOY. The colors of Crockett Johnson's painting draws special attention to XOF, and it is this line he mentions in his figure for the painting.

- The painting is on masonite, and is #94 in the series. It has a blue-black background and a black wooden frame. It is signed on the back: SQUARED RECTANGLE AND EULER LINE (/) Crockett Johnson 1972.

- Location
- Currently not on view

- date made
- 1972

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.62

- catalog number
- 1979.1093.62

- accession number
- 1979.1093

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Velocities and Right Triangles (Galileo)*- 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Heptagon Stated By Seven Toothpicks (Between Parallels)*- Description
- This whimsical painting is part of Crockett Johnson's exploration of ways to represent the sides and angles of a regular heptagon using line segments of equal length. In its mathematics, it follows closely the construction from isosceles triangles within a rhombus used in the painting
*Heptagon from Ten Equal Lines*(#104 in the series - 1979.1093.71). However, both the line segments shown and the appearance of the paintings are quite different.

- Here three pairs of carefully selected equal lines at appropriate equal angles combine with a seventh line of equal length to give a construction of three sides and two angles of a regular heptagon. All but one of the endpoints of the lines lie on a parallelogram (the rhombus mentioned previously), hence the title. The segment of the heptagon is on the right side of the painting. In Crockett Johnson's figure for the work, the segment is lettered BCPE.

- The painting, in oil or acrylic on masonite, is #106 in the series. It has a dark purple background. The pairs of line segments are in turquoise, green, and lavender, with the vertical one in white. This increases the drama of the painting, but obscures the heptagon. There is a wooden frame. The painting is signed on the back: HEPTAGON STATED BY (/) SEVEN TOOTHPICKS (/) (BETWEEN PARALLELS) (/) Crockett Johnson 1973.

- Location
- Currently not on view

- date made
- 1973

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.73

- catalog number
- 1979.1093.73

- accession number
- 1979.1093

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Heptagon from Its Seven Sides*- Description
- Toward the end of his life, Crockett Johnson took up the problem of constructing a regular seven-sided polygon or heptagon. This construction, as Gauss had demonstrated, requires more than a straight edge and compass. Crockett Johnson used compass and a straight edge with a unit length marked on it. Archimedes and Newton had suggested that constructions of this sort could be used to trisect the angle and to find a cube with twice the volume of a given cube, and Crockett Johnson followed their example.

- One may construct a heptagon given an angle of pi divided by seven. If an isosceles triangle with this vertex angle is inscribed in a circle, the base of the triangle will have the length of one side of a regular heptagon inscribed in that circle. According to Crockett Johnson's later account, in the fall of 1973, while having lunch in the city of Syracuse on Sicily during a tour of the Mediterranean, he toyed with seven toothpicks, arranging them in various patterns. Eventually he created an angle with his menu and wine list and arranged the seven toothpicks within the angle in crisscross patterns until his arrangement appeared as is shown in the painting.

- Crockett Johnson realized that the vertex angle of the large isosceles triangle shown is exactly π/7 radians, as desired. The argument suggested by his diagram is more complex than what he later published. The numerical results shown in the figure suggest his willingness to carry out detailed calculations.

*Heptagon from its Seven Sides*, painted in 1973 and #107 in the series, shows a triangle with purple and white sections on a navy blue background. This oil or acrylic painting on masonite is signed on its back : HEPTAGON FROM (/) ITS SEVEN SIDES (/) (Color sketch for larger painting) (/) Crockett Johnson 1973. No larger painting on this pattern is at the Smithsonian.

- Reference: Crockett Johnson, "A Construction for a Regular Heptagon," Mathematical Gazette, 1975, vol. 59, pp. 17–21.

- Location
- Currently not on view

- date made
- 1973

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.74

- catalog number
- 1979.1093.74

- accession number
- 1979.1093

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Heptagon from Ten Equal Lines*- Description
- This is one of a series of paintings in which Crockett Johnson explored ways of constructing the regular heptagon. The construction is his own, and a drawing for it is attached to the back of the painting. By an arrangement of ten equal line segments, he produced three sides and two angles of a regular heptagon. Two sides and one angle are actually shown in the painting.

- Crockett Johnson supposed that four equal isosceles triangles, constructed with six equal line segments, were arranged as shown in his figure to form sides of a rhombus and of a parallelogram within it. Two adjacent sides of the rhombus also served as the long sides of equal triangles oriented in the opposite direction. Finally, a line parallel to one of these sides passed through points of intersection of the sides of triangles.

- More specifically, in the drawing triangles BAF, DAR, DKE, and HBE are arranged within rhombus ABED, and around a central parallelogram. Two other equal triangles DES and BAG are also included. AFand EJ intersect at a point C and EK and BH at a point P. The tenth line, UL parallel to BE, passes through points C and P. Crockett Johnson claimed that BCPE represents three sides of a regular heptagon. His argument appears in his papers. The painting shows only the ten equal lines described in the title.

- The sections of the rhombus are in black, white, and rose, with a purple background. There is a wooden frame painted purple. This oil painting on masonite is #109 in the series. It is marked on the back: HEPTAGON FROM TEN EQUAL LINES (/) Crockett Johnson 1973. Taped to the back is a sheet of paper with an explanation that is entitled: HEPTAGON FROM TEN EQUAL LINES.

- Location
- Currently not on view

- date made
- 1973

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.75

- catalog number
- 1979.1093.75

- accession number
- 1979.1093

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Hippias' Curve*- 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Construction of Heptagon*- 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Painting -

*Construction of the Heptagon*- 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Porter Drawing [from enclosure] [black-and-white cellulose acetate photonegative]

- Summary
- Illustration of a either a cheetah or a leopard. No ink on negative. No visible edge imprint

- Cite as
- Scurlock Studio Records, ca. 1905-1994, Archives Center, National Museum of American History

- Date
- 1930

- 1960

- N.d

- 20th century

- 1930-1960

- photographers
- Scurlock Studio (Washington, D.C.)

- artist
- Porter, James A. (James Amos) 1905-

- film manufacturer
- Eastman Kodak Co

- Local number
- Box 618.04.126

- AC0618.004.0002259.tif (AC Scan)

- 24493 (Scurlock No.)

- Data Source
- Archives Center - NMAH