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: 1960s

Painting - Curve Tangents (Fermat)

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

Camera-ready comic panel, entitled Laugh It Off

Laugh It Off was a comic panel series created by New Yorker cartoonist Sydney "Syd" Hoff (1912-2004) and distributed by King Features Syndicate from 1957 to 1971. The panels often illustrated funny moments or situations people find themselves in on a daily basis.
Description
Laugh It Off was a comic panel series created by New Yorker cartoonist Sydney "Syd" Hoff (1912-2004) and distributed by King Features Syndicate from 1957 to 1971. The panels often illustrated funny moments or situations people find themselves in on a daily basis. In this panel, a boss addresses one of his workers that is putting on his jacket to leave: "I don't mind you leaving early to avoid the traffic rush, Folsom, but it itsn't even noon yet."
Location
Currently not on view
date made
8/10/1966
08/10/1966
graphic artist
Hoff, Syd
publisher
King Features Syndicate
ID Number
GA.22346
catalog number
22346
accession number
277502

Camera-ready comic strip, entitled "Blue Chips".

"Blue Chips", drawn by Morrie Brickman (1917-1994), is based on stock traders and their dealings with the economic uncertainties of the times. This was a precursor to Brickman's most famous cartoon, "The Small Society", which deals with money, politics, and national issues.
Description
"Blue Chips", drawn by Morrie Brickman (1917-1994), is based on stock traders and their dealings with the economic uncertainties of the times. This was a precursor to Brickman's most famous cartoon, "The Small Society", which deals with money, politics, and national issues. In this strip, Pigeon gets advice from his advisor, Bartlett.
Location
Currently not on view
date made
9/24/1966
graphic artist
Brickman, Morrie
publisher
King Features Syndicate
ID Number
GA.22357
catalog number
22357
accession number
277502

Camera-ready comic strip, entitled "All-Stars: Sandy".

Al Liederman (aka Leeds) drew cartoons over a forty-year period, including a stint as assistant artist on Marvel's "Captain America". During his early career and towards the end of his career, Liederman created sports-themed and editorial cartoons, including "Li'l Leaguer".
Description
Al Liederman (aka Leeds) drew cartoons over a forty-year period, including a stint as assistant artist on Marvel's "Captain America". During his early career and towards the end of his career, Liederman created sports-themed and editorial cartoons, including "Li'l Leaguer". In this strip, a baseball player figures out that the base coach is just swatting a bee, not giving a signal to the batter.
Location
Currently not on view
date made
09/03/1966
graphic artist
Liederman, Al
publisher
United Feature Syndicate, Inc.
ID Number
GA.22412
catalog number
22412
accession number
277502

Camera-ready comic art drawing for Judge Parker

This pen-and-ink drawing produced for the Judge Parker comic strip shows Charles holding Casandra Canabar and Randy Parker hostage, telling them to report to the police that the emergency call had been a false alarm.Harold Anthony LeDoux (1926-2015) moved to New York City after W
Description (Brief)
This pen-and-ink drawing produced for the Judge Parker comic strip shows Charles holding Casandra Canabar and Randy Parker hostage, telling them to report to the police that the emergency call had been a false alarm.
Harold Anthony LeDoux (1926-2015) moved to New York City after World War II and began drawing for the Famous Funnies comic books. In 1953 he began assisting Dan Heilman on the comic strip Judge Parker. LeDoux took over the strip after Heilman's death in 1965 and retired in 2006.
Judge Parker (1952- ) was created by psychiatrist and writer Nick Dallis. Dallis invited Dan Heilman, who had previously assisted on Buz Sawyer and Mary Worth,to be the artist for Judge Parker. The title character was a widower with two children, who later married a younger woman. Originally written as an attractive crime-fighting character, Parker had by the 1960s become more conservative and sedate while the younger attorney, Sam Driver, became more central to the cast, along with his client and girlfriend, Abby, and her two children.
Location
Currently not on view
date made
1966-08-21
graphic artist
LeDoux, Harold
publisher
Publishers Newspapers Syndicate, Inc.
ID Number
GA.22570
catalog number
22570
accession number
277502

Camera-ready comic strip, entitled "Debbie Deere".

"Debbie Deere", the first newspaper comic strip created and drawn by Frank Bolle (b. 1924), was published from 1966 to 1969 by McNaught Syndicate. Debbie is a newspaper advice columnist, who is continually involved in the drama of her fans.
Description
"Debbie Deere", the first newspaper comic strip created and drawn by Frank Bolle (b. 1924), was published from 1966 to 1969 by McNaught Syndicate. Debbie is a newspaper advice columnist, who is continually involved in the drama of her fans. Although the strip was short lived, it allowed Bolle to gain recognition as a comic strip artist; he went on to draw five other strips including "Winnie Winkle". In this strip, Mr. Boyd, Debbie's boss, criticizes her writing.
Location
Currently not on view
date made
07/15/1966
graphic artist
Bolle, Frank
publisher
McNaught Syndicate, Inc.
ID Number
GA.22556
catalog number
22556
accession number
277502

The Through Express

Currently not on view
Location
Currently not on view
date made
1969
original artist
Currier & Ives
publisher
Travelers Companies, Inc.
ID Number
2012.3050.05.09
nonaccession number
2012.3050
catalog number
2012.3050.05.09

Camera-ready comic strip, entitled Muggs and Skeeter

Muggs and Skeeter, also published under the title Muggs McGinnis from 1927 until 1936, was created and drawn by Wallace "Wally" Bishop (1906-1982). The strip was distributed by King Features Syndicate from 1927 until 1974.
Description
Muggs and Skeeter, also published under the title Muggs McGinnis from 1927 until 1936, was created and drawn by Wallace "Wally" Bishop (1906-1982). The strip was distributed by King Features Syndicate from 1927 until 1974. The comic strip featured two boys, Muggs and Skeeter, and their adventures in boyhood (and teenage-boyhood). In this strip, Muggs and Skeeter are disappointed because they were not invited to Suzie's party.
Location
Currently not on view
date made
9/7/1966
08/22/1966
graphic artist
Bishop, Wally
publisher
King Features Syndicate
ID Number
GA.22440
catalog number
22440
accession number
277502

Blind Man's Bluff

Currently not on view
Location
Currently not on view
date made
1969
1962
original artist
Palmer, Frances F.
publisher
Travelers Companies, Inc.
ID Number
2012.3050.05.14
nonaccession number
2012.3050
catalog number
2012.3050.05.14

Fiesta

Homer Laughlin China Company, who manufactured the infamous “Fiesta ware” line, began as a partnership between the two Laughlin brothers, Homer and Shakespeare, in 1873.
Description
Homer Laughlin China Company, who manufactured the infamous “Fiesta ware” line, began as a partnership between the two Laughlin brothers, Homer and Shakespeare, in 1873. The company sold primarily Rockingham and yellow ware then later expanded their market to make semi-vitreous dinner, hotel, and toilet wares as well as white granite products. After the Great Depression the market for inexpensive dinner wares increased, and the “Fiesta ware” line was available for purchase in 1936. Designed by Frederick Hurten Rhead, an English potter from Staffordshire, “Fiesta ware” became highly popular for their bright colors, streamlined design, and mix-and-match capabilities for the everyday household. This dinner plate illustrates the original shape of "Fiesta ware," but not the original color. The medium green glaze used on this plate was only manufactured by Homer Laughlin China Company between 1959 and 1969.
Location
Currently not on view
Date made
ca. 1959-69
user
Boughton, George Henry
maker
Homer Laughlin China Co.
ID Number
1999.0136.10
accession number
1999.0136
catalog number
1999.0136.10

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

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

Painting - Homothetic Triangles (Hippocrates of Chios)

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

Enlarged Contact Sheet of Jacqueline Bouvier Kennedy and president-elect John F. Kennedy

Currently not on view
Location
Currently not on view
date made
1961-01-03
depicted
Kennedy, John F.
Kennedy, Jacqueline Bouvier
photographer
Avedon, Richard
maker
Avedon, Richard
ID Number
PG.67.102.058
accession number
270571
catalog number
67.102.58

Camera-ready comic page, entitled Life's Like That

Life’s Like That, created and drawn by Fred Neher (1903-2001), was distributed by Bell-McClure Syndicate and later the United Features Syndicate, from 1934 until 1977. The comic was a gag panel about everyday life.
Description
Life’s Like That, created and drawn by Fred Neher (1903-2001), was distributed by Bell-McClure Syndicate and later the United Features Syndicate, from 1934 until 1977. The comic was a gag panel about everyday life. This comic page features characters such as Golde, Some Punkins and Will-Yum.
Location
Currently not on view
date made
09/04/1966
graphic artist
Neher, Fred
publisher
Bell-McClure Syndicate
ID Number
GA.22423
catalog number
22423
accession number
277502

Camera-ready comic strip, entitled "Donald Duck".

The Walt Disney character Donald Duck debuted in 1934 in a comic strip entitled "Wise Little Hen" which was published in the Silly Symphonies comic strip series.
Description
The Walt Disney character Donald Duck debuted in 1934 in a comic strip entitled "Wise Little Hen" which was published in the Silly Symphonies comic strip series. Donald debuted in his own "Donald Duck" black and white daily comic strip on Febuary 7, 1938 and in 1939 he had his own Sunday color comic strip. Al Taliaferro (1905-1969) drew the majority of the strips until the late 1960s, which were distributed by King Features Syndicate. In this strip, Donald attempts to karate chop a board to impress his nephews Huey, Dewey, and Louie. However, he ends up with a big splinter in his hand.
Location
Currently not on view
date made
08/11/1966
graphic artist
Disney, Walt
publisher
Walt Disney Productions
graphic artist
Taliaferro, Al
author
Karp, Bob
ID Number
GA.22409
catalog number
22409
accession number
277502

Painting - Rectangles of Equal Area (Pythagoras)

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

Camera-ready comic strip, entitled Little Lulu

Little Lulu, created in 1935 by Marjorie Henderson "Marge" Buell, started as a comic to replace Carl Anderson's Henry comic in The Saturday Evening Post. The daily comic strip was syndicated from 1950 until 1969, drawn by several different artists.
Description
Little Lulu, created in 1935 by Marjorie Henderson "Marge" Buell, started as a comic to replace Carl Anderson's Henry comic in The Saturday Evening Post. The daily comic strip was syndicated from 1950 until 1969, drawn by several different artists. The comic strip features the title character, a precocious and often bad-tempered little girl, Lulu, and her interactions with her family and others around her. In this strip, Tubby ate the dinner Lulu had made for her dog Mops.
Location
Currently not on view
date made
08/26/1966
graphic artist
Buell, Marge
ID Number
GA.22638
catalog number
22638
accession number
277502

Lily Lake

Currently not on view
Location
Currently not on view
date made
1969
original artist
Currier & Ives
publisher
Travelers Companies, Inc.
ID Number
2012.3050.05.05
nonaccession number
2012.3050
catalog number
2012.3050.05.05

Painting - Bouquet of Triangle Theorems (Euclid)

The mathematician Euclid lived around 300 BC, probably in Alexandria in what is now Egypt. Like most western scholars of his day, he wrote in Greek. Euclid prepared an introduction to mathematics known as The Elements.
Description
The mathematician Euclid lived around 300 BC, probably in Alexandria in what is now Egypt. Like most western scholars of his day, he wrote in Greek. Euclid prepared an introduction to mathematics known as The Elements. It was an eminently successful text, to the extent that most of the works he drew on are now lost. Translations of parts of The Elements were used in geometry teaching well into the nineteenth century in both Europe and the United States.
Euclid and other Greek geometers sought to prove theorems from basic definitions, postulates, and previously proven theorems. The book examined properties of triangles, circles, and more complex geometric figures. Euclid's emphasis on axiomatic structure became characteristic of much later mathematics, even though some of his postulates and proofs proved inadequate.
To honor Euclid's work, Crockett Johnson presented not a single mathematical result, but what he called a bouquet of triangular theorems. He did not state precisely which theorems relating to triangles he intended to illustrate in his painting, and preliminary drawings apparently have not survived. At the time, he was studying and carefully annotating Nathan A. Court's book College Geometry (1964). Court presents several theorems relating to lines through the midpoints of the side of a triangle that are suggested in the painting. The midpoints of the sides of the large triangle in the painting are joined to form a smaller one. According to Euclid, a line through two midpoints of sides of a triangle is parallel to the third side. Thus the construction creates a triangle similar to the initial triangle, with one fourth the area (both the height and the base of the initial triangle are halved). In the painting, triangles of this smaller size tile the plane. All three of the lines joining midpoints create triangles of this small size, and the large triangle at the center has an area four times as great.
The painting also suggests properties of the medians of the large triangle, that is to say, the lines joining each midpoint to the opposite vertex. The three medians meet in a point (point G in the figure from Court). It is not difficult to show that point G divides each median into two line segments, one twice as long as the other.
To focus attention on the large triangle, Crockett Johnson executed it in shades of white against a background of smaller dark black and gray triangles.
Bouquet of Triangle Theorems apparently is the artist's own construction. It was painted in oil or acrylic and is #26 in the series. It was completed in 1966 and is signed: CJ66. It is signed on the back: Crockett Johnson 1966 (/) BOUQUET OF TRIANGLE THEOREMS (/) (EUCLID).
Reference: Nathan A. Court, College Geometry, (1964 printing), p. 65. The figure on this page is not annotated.
Location
Currently not on view
date made
1966
referenced
Euclid
painter
Johnson, Crockett
ID Number
1979.1093.19
catalog number
1979.1093.19
accession number
1979.1093

Camera-ready comic art drawing for Lolly

This pen-and-ink drawing produced for the Lolly comic strip shows the title character, who has taken a job as a secretary, making an initial spelling mistake in a letter she has prepared for her boss.Per Ruse "Pete" Hansen (1920-1994) was born in Denmark and moved to the United S
Description (Brief)
This pen-and-ink drawing produced for the Lolly comic strip shows the title character, who has taken a job as a secretary, making an initial spelling mistake in a letter she has prepared for her boss.
Per Ruse "Pete" Hansen (1920-1994) was born in Denmark and moved to the United States as a child. He began his comic art career as an artist at Disney Animation Studios in 1938. In the early 1950s, after leaving Disney, he began working on Flapdoodles and later, between 1955 and 1983, Lolly, Hansen’s best known strip. In the 1980s, after returning to Disney, Hansen wrote for their foreign publication strips.
Lolly (1955-1983) was a newspaper comic strip about a young, single woman who supported herself, her grandmother, and her younger brother, Pepper. The strip stood out in the 1950s because it featured a young girl as the family’s breadwinner. The strip appeared as a comic book series in the 1950s and 1960s.
Location
Currently not on view
date made
1966-07-11
graphic artist
Hansen, Pete
publisher
Tribune Printing Company
ID Number
GA.22538
catalog number
22538
accession number
277502

Camera-ready comic strip, entitled "Kerry Drake".

"Kerry Drake", created by Alfred Andriola (1912-1983) and [unofficially] ghostwritten by Allen Saunders, was distributed by Publishers-Hall Syndicate from 1943 to 1983. The strip features Kerry Drake, a criminal investigator and policeman.
Description
"Kerry Drake", created by Alfred Andriola (1912-1983) and [unofficially] ghostwritten by Allen Saunders, was distributed by Publishers-Hall Syndicate from 1943 to 1983. The strip features Kerry Drake, a criminal investigator and policeman. Drake used new crime analysis tools to solve complex cases, which gained the strip popular readership. In this strip, Drake and Johnny investigate a home that has been burglarized.
Location
Currently not on view
date made
7/24/1966
maker
James, Alfred
publisher
King Features Syndicate
ID Number
GA.22599
catalog number
22599
accession number
277502

Winter Morning in the Country

Currently not on view
Location
Currently not on view
date made
1969
1962
original artist
Palmer, Frances F.
publisher
Travelers Companies, Inc.
ID Number
2012.3050.05.13
nonaccession number
2012.3050
catalog number
2012.3050.05.13

Camera-ready comic strip, entitled Louie

Louie was created and drawn by British cartoonist Harry Hanan (d. 1982) from 1947 until 1976, distributed by The Post-Hall Syndicate and The Chicago Tribune Syndicate. The strip features a soft-spoken, often silent husband and his misadventures with his wife and others.
Description
Louie was created and drawn by British cartoonist Harry Hanan (d. 1982) from 1947 until 1976, distributed by The Post-Hall Syndicate and The Chicago Tribune Syndicate. The strip features a soft-spoken, often silent husband and his misadventures with his wife and others. In this strip, Louie drops a book at the library and is yelled at by the librarian.
Location
Currently not on view
date made
8/8/1966
08/08/1966
graphic artist
Hanan, Harry
publisher
News Syndicate Co., Inc.
ID Number
GA.22534
catalog number
22534
accession number
277502

Painting - Squared Circle

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

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