#
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 3509 items.

Page 1 of 351

## Misc 1941[from enclosure] [black-and-white cellulose acetate photonegative]

- Summary
- Display of illustrations, small statues and small objects. "Agfa Safety Film" edge imprint.

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

- Date
- 1941

- 1940-1950

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

- film manufacturer
- Agfa

- Local number
- Box 618.04.122

- AC0618.004.0002129.tif (AC Scan)

- No Scurlock number

- Data Source
- Archives Center - NMAH

## [Costumed figure with pictures. Stereo photonegative.]

- Notes
- Currently stored in box 1.1.31 [161].

- Orig. no. 330-B.

- Date
- 1900

- 1910

- 1900-1910

- publisher
- Underwood & Underwood

- H.C. White Co

- Local number
- RSN 5780

- Data Source
- Archives Center - NMAH

## [Seated figure wearing strange costume. Stereo photonegative.]

- Notes
- Currently stored in box 1.1.31 [161].

- Orig. no. 331-B.

- Summary
- The setting includes paintings or other artworks.

- Date
- 1900

- 1910

- 1900-1910

- publisher
- Underwood & Underwood

- H.C. White Co

- Local number
- RSN 5781

- Data Source
- Archives Center - NMAH

## Relief Map of Palestine by Pal. Ex. Soc. (vertical scale 3-1/2 times greater than the horizontal). [Active no. 3186 : interpositive.]

- Notes
- Currently stored in box 3.2.8 [54]

- Orig. no. 0594.

- Date
- 1900

- 1910

- 1900-1910

- publisher
- Underwood & Underwood

- Local number
- RSN 20368

- Data Source
- Archives Center - NMAH

## [Art in New York; interior view.] 25 interpositive

- Notes
- Currently stored in box 1.2.16 [17].

- Date
- 1900-1910

- publisher
- Underwood & Underwood

- H.C. White Co

- Local number
- RSN 8130

- Video number 07294

- Data Source
- Archives Center - NMAH

## Painting -

*Proof of the Pythagorean Theorem (Euclid)*- Description
- The Pythagorean theorem states that in any right triangle, the square of the side opposite the right angle (the hypotenuse), is equal to the sum of the squares of the other two sides. This painting depicts the “windmill” figure found in Proposition 47 of Book I of Euclid’s
*Elements*. Although the method of the proof depicted was written about 300 BC and is credited to Euclid, the theorem is named for Pythagoras, who lived 250 years earlier. It was known to the Babylonians centuries before then. However, knowing a theorem is different from demonstrating it, and the first surviving demonstration of this theorem is found in Euclid’s*Elements*.

- Crockett Johnson based his painting on a diagram in Ivor Thomas’s article on Greek mathematics in
*The World of Mathematics*, edited by James R. Newman (1956), p. 191. The proof is based on a comparison of areas. Euclid constructed a square on the hypotenuse BΓ of the right triangle ABΓ. The altitude of this triangle originating at right angle A is extended across this square. Euclid also constructed squares on the two shorter sides of the right triangle. He showed that the square on side AB was of equal area to the rectangle of sides BΔ and Δ;Λ. Similarly, the area of the square on side AΓ was of equal area to the rectangle of sides EΓ and EΛ. But then the square of the hypotenuse of the right triangle equals the sum of the squares of the shorter sides, as desired.

- Crockett Johnson executed the right triangle in the neutral, yet highly contrasting, hues of white and black. Each square area that rests on the sides of the triangle is painted with a combination of one primary color and black. This draws the viewer’s attention to the areas that complete Euclid’s proof of the Pythagorean theorem.

*Proof of the Pythagorean Theorem*, painting #2 in the series, is one of Crockett Johnson’s earliest geometric paintings. It was completed in 1965 and is marked: CJ65. It also is signed on the back: Crockett Johnson 1965 (/) PROOF OF THE PYTHAGOREAN THEOREM (/) (EUCLID).

- Location
- Currently not on view

- date made
- 1965

- referenced
- Euclid

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.01

- catalog number
- 1979.1093.01

- accession number
- 1979.1093

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

## Painting -

*Reciprocation*- Description
- In this oil or acrylic painting on masonite, Crockett Johnson illustrates a theorem presented by the Greek mathematician Pappus of Alexandria (3rd century AD). Suppose that one chooses three points on each of two line straight segments that do not intersect. Join each point to the two more distant points on the other lines. These lines meet in three points, which, according to the theorem, are themselves on a straight line.

- The inspiration for this painting probably came from a figure in the article "The Great Mathematicians" by Herbert W. Turnbull found in the artist's copy of James R. Newman's
*The World of Mathematics*(p. 112). This figure is annotated. It shows points A, B, and C on one line segment and D, E, and F on another line segment. Line segments AE and DB, AF and DC, and BF and EC intersect at 3 points (X, Y, and Z respectively), which are collinear. Turnbull's figure and Johnson's painting include nine points and nine lines that are arranged such that three of the points lie on each line and three of the lines lie on each point. If the words "point" and "line" are interchanged in the preceding sentence, its meaning holds true. This is the "reciprocation," or principle of duality, to which the painting's title refers.

- Crockett Johnson chose a brown and green color scheme for this painting. The main figure, which is executed in seven tints and shades of brown, contains twelve triangles and two quadrilaterals. The background, which is divided by the line that contains the points X, Y, and Z, is executed in two shades of green. This color choice highlights Pappus' s theorem by dramatizing the line created by the points of intersection of AE and DB, AF and DC, and BC and EC. There wooden frame painted black.

*Reciprocation*is painting #6 in this series of mathematical paintings. It was completed in 1965 and is signed: CJ65.

- Location
- Currently not on view

- date made
- 1965

- referenced
- Pappus

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.02

- catalog number
- 1979.1093.02

- accession number
- 1979.1093

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

## Painting -

*Perspective (Alberti)*- Description
- Artists used methods of projecting lines developed by the Italian humanist Leon Battista Alberti and his successors to create a sense of perspective in their paintings. In contrast, Crockett Johnson made these methods the subject of his painting. He followed a diagram in William M. Ivins Jr.,
*Art & Geometry: A Study in Space Intuitions*(1964 edition), p. 76. The figure in Crockett Johnson’s copy of the book is annotated. This painting has a triangle in the center that is divided by a diagonal line, with the left half painted a darker shade than the right. Inside the triangle is one large quadrilateral that is divided into four rows of quadrilaterals that are painted various shades of red, purple, blue, and white.

- To represent three-dimensional objects on a two-dimensional canvas, an artist must render forms and figures in proper linear perspective. In 1435 Alberti wrote a treatise entitled
*De Pictura*(*On Painting*) in which he outlined a process for creating an effective painting through the use of one-point perspective. Investigation of the mathematical concepts underlying the rules of perspective led to the development of a branch of mathematics called projective geometry.

- Alberti’s method (as modified by Pelerin in the early 17th century) and Crockett Johnson’s painting begin with the selection of a vanishing point (point C in the figure from Ivins). The eye of the viewer is assumed to be across from and on the same level as C. The eye looks through the vertical painting at a picture that appears to continue behind the canvas. To portray on the canvas what the eye sees, the artist locates point A on the horizon (the horizontal through C). The artist then draws the diagonal from A to the lower right-hand corner of the painting (point I). The separation of the angle ICH into smaller, equal angles creates lines that delineate parallel lines in the picture plane. The horizontal lines that create small quadrilaterals, and thus the checkerboard effect, are determined by the intersections of the lines from C with the diagonals FH and EI.

- This painting, #7 in the series, dates from 1966. It is signed: CJ66. It is marked on the back: Crockett Johnson 1966 (/) PERSPECTIVE (ALBERTI). It is of acrylic or oil paint on masonite, and has a wooden frame.

- Location
- Currently not on view

- date made
- 1966

- referenced
- Alberti, Leon Battista

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.03

- catalog number
- 1979.1093.03

- accession number
- 1979.1093

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

## Painting -

*Squares of a 3-4-5 Triangle in Scalene Perspective (Dürer)*- Description
- This painting, while similar in subject to the painting entitled
*Perspective (Alberti)*, depicts three planes perpendicular to the canvas. These three planes provide a detailed, three-dimensional view of space through the use of perspective. Three vanishing points are implied (though not shown) in the painting, one in each of the three planes.

- The painting shows a 3-4-5 triangle surrounded by squares proportional in number to the square of the side. That is, the horizontal plane contains nine squares, the vertical plane contains sixteen squares, and the oblique plane, which represents the hypotenuse of the 3-4-5 triangle, contains twenty-five squares. This explains the extension of the vertical and oblique planes and reminds the viewer of the Pythagorean theorem. Thus, Crockett Johnson has cleverly shown the illustration of two of his other paintings;
*Squares of a 3-4-5 Triangle (Pythagoras)*and*Proof of the Pythagorean Theorem (Euclid)*, in perspective; hence the title of the painting.

- The title of this painting points to the role of the German artist Albrecht Dürer (1471–1528) in creating ways of representing three-dimensional figures in a plane. Dürer is particularly remembered for a posthumously published treatise on human proportion. In his book entitled
*The Life and Art of Albrecht Dürer*, art historian Erwin Panofsky explains that the work of Dürer with perspective demonstrated that the field was not just an element of painting and architecture, but an important branch of mathematics.

- This construction may well have originated with Crockett Johnson. The oil painting was completed in 1965 and is signed: CJ65. It is #8 in his series of mathematical paintings.

- Location
- Currently not on view

- date made
- 1965

- referenced
- Duerer, Albrecht

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.04

- catalog number
- 1979.1093.04

- accession number
- 1979.1093

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

## Painting -

*Mystic Hexagon (Pascal)*- Description
- This painting is based on a theorem generalized by the French mathematician Blaise Pascal in 1640, when he was sixteen years old. When the opposite sides of a irregular hexagon inscribed in a circle are extended, they meet in three points. Pappus, writing in the 4th century AD, had shown in his
*Mathematical Collections*that these three points lie on the same line. In the painting, the circle and cream-colored hexagon are at the center, with the sectors associated with different pairs of lines shown in green, blue and gray. The three points of intersection are along the top; the line that would join them is not shown. Pascal generalized the theorem to include hexagons inscribed in any conic section, not just a circle. Hence the figure came to be known as "Pascal’s hexagon" or, to use Pascal’s terminology, the "mystic hexagon." Pascal’s work in this area is known primarily from notes on his manuscripts taken by the German mathematician Gottfried Leibniz after his death.

- There is a discussion of Pascal’s hexagon in an article by Morris Kline on projective geometry published in James R. Newman's
*World of Mathematics*(1956). A figure shown on page 629 of this work may have been the basis of Crockett Johnson's painting, although it is not annotated in his copy of the book.

- The oil or acrylic painting on masonite is signed on the bottom right: CJ65. It is marked on the back: Crockett Johnson (/) "Mystic" Hexagon (/) (Pascal). It is #10 in the series.

- References: Carl Boyer and Uta Merzbach,
*A History of Mathematics*(1991), pp. 359–62.

- Florian Cajori,
*A History of Elementary Mathematics*(1897), 255–56.

- Morris Bishop,
*Pascal: The Life of a Genius*(1964), pp. 11, 81–7.

- Location
- Currently not on view

- date made
- 1965

- referenced
- Pascal, Blaise

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.05

- catalog number
- 1979.1093.05

- accession number
- 1979.1093

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