Science & Mathematics

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

The Belgian physicist Joseph Plateau (1801–1883) performed a sequence of experiments using soap bubbles. One investigation led him to show that when two soap bubbles join, the two exterior surfaces and the interface between the two bubbles will all be spherical segments.
Description
The Belgian physicist Joseph Plateau (1801–1883) performed a sequence of experiments using soap bubbles. One investigation led him to show that when two soap bubbles join, the two exterior surfaces and the interface between the two bubbles will all be spherical segments. Furthermore, the angles between these surfaces will be 120 degrees.
Crockett Johnson's painting illustrates this phenomenon. It also displays Plateau's study of the situation that arises when three soap bubbles meet. Plateau discovered that when three bubbles join, the centers of curvature (marked by double circles in the figure) of the three overlapping surfaces are collinear.
This painting was most likely inspired by a figure located in an article by C. Vernon Boys entitled "The Soap-bubble." James R. Newman included this essay in his book entitled The World of Mathematics (p. 900). Crockett Johnson had this publication in his personal library, and the figure in his copy is annotated.
The artist chose several pastel shades to illustrate his painting. This created a wide range of shades and tints that allows the painting to appear three-dimensional. Crockett Johnson chose to depict each sphere in its entirety, rather than showing just the exterior surfaces as Boys did. This helps the viewer visualize Plateau's experiment.
This painting was executed in oil on masonite and has a wood and chrome frame. It is #23 in the series. It was completed in 1966 and is signed: CJ66. It is marked on the back: Crockett Johnson 1966 (/) GEOMETRY OF A TRIPLE BUBBLE (/) (PLATEAU).
Location
Currently not on view
date made
1966
referenced
Plateau, Joseph
painter
Johnson, Crockett
ID Number
1979.1093.17
catalog number
1979.1093.17
accession number
1979.1093
Ira Freeman was a professor of physics at Rutgers University, and Mae Freeman an active author of beginner's books on a variety of topics.
Description
Ira Freeman was a professor of physics at Rutgers University, and Mae Freeman an active author of beginner's books on a variety of topics. Before 1957 the couple had collaborated on such popular science books as Fun With Chemistry (1944) and Fun With Astronomy (1953).
With the launch of Sputnik , the Freemans began writing books related to space travel. You Will go to the Moon and The Sun, the Moon and the Stars were both published in 1959. They also began to write scientific books for use in the home. Fun With Science (1958) was quickly followed by Fun With Scientific Experiments (1960).
Fun With Scientific Experiments was supplemented with the "Ed-U-Cards of Science."
Location
Currently not on view
Date made
1960
maker
Random House, Inc.
ID Number
2007.0041.02
catalog number
2007.0041.02
accession number
2007.0041
Those making mathematical instruments for surveying, navigation, or the classroom have long been interested in creating equal divisions of the circle. Ancient geometers knew how to divide a circle into 2, 3, or 5 parts, and as well as into multiples of these numbers.
Description
Those making mathematical instruments for surveying, navigation, or the classroom have long been interested in creating equal divisions of the circle. Ancient geometers knew how to divide a circle into 2, 3, or 5 parts, and as well as into multiples of these numbers. For them to draw polygons with other numbers of sides required more than a straightedge and compass.
In 1796, as an undergraduate at the University of Göttingen, Friedrich Gauss proposed a theorem severely limiting the number of regular polygons that could be constructed using ruler and compass alone. He also found a way of constructing the 17-gon.
Crockett Johnson, who himself would develop a great interest in constructing regular polygons, drew this painting to illustrate Gauss's discovery. His painting follows a somewhat later solution to the problem presented by Karl von Staudt in 1842, modified by Heinrich Schroeter in 1872, and then published by the eminent mathematician Felix Klein. Klein's detailed account was in Crockett Johnson's library, and a figure from it is heavily annotated.
This oil painting on masonite is #70 in the series. It is signed: CJ69. The back is marked: SEVENTEEN SIDES (GAUSS) (/) Crockett Johnson 1969. The painting has a black background and a wood and metal frame. There are two adjacent purple triangles in the center, with a white circle inscribed in them. The triangles have various dark gray regions, and the circle has various light gray regions and one dark gray segment. The length of the top edge of this segment is the chord of the circle corresponding to length of the side of an inscribed 17-sided regular polygon.
Reference: Felix Klein, Famous Problems of Elementary Geometry (1956), pp. 16–41, esp. 41.
Location
Currently not on view
date made
1969
referenced
Gauss, Carl Friedrich
painter
Johnson, Crockett
ID Number
1979.1093.45
accession number
1979.1093
catalog number
1979.1093.45
In the 17th century, the natural philosophers Isaac Newton and Gottfried Liebniz developed much of the general theory of the relationship between variable mathematical quantities and their rates of change (differential calculus), as well as the connection between rates of change
Description
In the 17th century, the natural philosophers Isaac Newton and Gottfried Liebniz developed much of the general theory of the relationship between variable mathematical quantities and their rates of change (differential calculus), as well as the connection between rates of change and variable quantities (integral calculus).
Newton called these rates of change "fluxions." This painting is based on a diagram from an article by H. W. Turnbull in Newman's The World of Mathematics. Here Turnbull described the change in the variable quantity y (OM) in terms of another variable quantity, x (ON). The resulting curve is represented by APT.
Crockett Johnson's painting is based loosely on these mathematical ideas. He inverted the figure from Turnbull. In his words: "The painting is an inversion of the usual textbook depiction of the method, which is one of bringing together a fixed part and a ‘moving’ part of a problem on a cartesian chart, upon which a curve then can be plotted toward ultimate solution."
The arc at the center of this painting is a circular, with a tangent line below it. The region between the arc and the tangent is painted white. Part of the tangent line is the hypotenuse of a right triangle which lies below it and is painted black. The rest of the lower part of the painting is dark purple. Above the arc is a dark purple area, above this a gray region. The painting has a wood and metal frame.
This oil painting on pressed wood is #20 in the series. It is unsigned, but inscribed on the back: Crockett Johnson 1966 (/) FLUXIONS (NEWTON).
References: James R. Newman, The World of Mathematics (1956), p. 143. This volume was in the library of Crockett Johnson. The figure on this page is annotated.
Crockett Johnson, "On the Mathematics of Geometry in My Abstract Paintings," Leonardo, 5 (1972): pp. 97–8.
Location
Currently not on view
date made
1966
referenced
Newton, Isaac
painter
Johnson, Crockett
ID Number
1979.1093.14
catalog number
1979.1093.14
accession number
1979.1093
Mathematicians have explored the properties of polyhedra since ancient times, but it was the Swiss scholar Leonhard Euler (1707–1783) who proved the formula V-E+F = 2. That is, for a simple convex polyhedron (e.g.
Description
Mathematicians have explored the properties of polyhedra since ancient times, but it was the Swiss scholar Leonhard Euler (1707–1783) who proved the formula V-E+F = 2. That is, for a simple convex polyhedron (e.g. one with no holes, so that it can be deformed into a sphere) the number of vertices minus the number of edges plus the number of faces is two. An equivalent formula had been presented by Descartes in an unpublished treatise on polyhedra. However, this formula was first proved and published by Euler in 1751 and bears his name.
Crockett Johnson's painting echoes a figure from a presentation of Euler's formula found in Richard Courant and Herbert Robbins's article “Topology,” which is in James R. Newman's The World the Mathematics (1956), p. 584. This book was in the artist’s library, but the figure that relates to this painting is not annotated.
To understand the painting we must understand the mathematical argument. It starts with a hexahedron, a simple, six-sided, box-shaped object. First, one face of the hexahedron is removed, and the figure is stretched so that it lies flat (imagine that the hexahedron is made of a malleable substance so that it can be stretched). While stretching the figure can change the length of the edges and the area and shape of the faces, it will not change the number of vertices, edges, or faces.
For the "stretched" figure, V-E+F = 8 - 12 + 5 = 1, so that, if the removed face is counted, the result is V-E+F = 2 for the original polyhedron. The next step is to triangulate each face (this is indicated by the diagonal lines in the third figure). If, in triangle ABC [C is not shown in Newman, though it is referred to], edge AC is removed, the number of edges and the number of faces are both reduced by one, so V-E+F is unchanged. This is done for each outer triangle.
Next, if edges DF and EF are removed from triangle DEF, then one face, one vertex, and two edges are removed as well, and V-E+F is unchanged. Again, this is done for each outer triangle. This yields a rectangle from which a right triangle is removed. Again, this will leave V-E+F unchanged. This last step will also yield a figure for which V-E+F = 3-3+1. As previously stated, if we count the removed face from the initial step, then V-E+F = 2 for the given polyhedron.
The “triangulated” diagram was the one Crockett Johnson chose to paint. Each segment of the painting is given its own color so as to indicate each step of the proof. Crockett Johnson executed the two right triangles that form the center rectangle in the most contrasting hues. This draws the viewer’s eyes to this section and thus emphasizes the finale of Euler's proof. This approach to the proof of Euler's polyhedral formula was pioneered by the French mathematician Augustin Louis Cauchy in 1813.
This oil painting on masonite is #39 in the series. It was completed in 1966 and is signed: CJ66. It is inscribed on the back: Crockett Johnson 1966 (/) POLYHEDRON FORMULA (EULER). It has a wood and chrome frame.
Reference:
David Richeson, “The Polyhedral Formula,” in Leonhard Euler: Life, Work and Legacy, editors R. E. Bradley and C. E. Sandifer (2007), pp. 431–34.
Location
Currently not on view
date made
1966
referenced
Euler, Leonhard
painter
Johnson, Crockett
ID Number
1979.1093.27
catalog number
1979.1093.27
accession number
1979.1093
Professor Jonathan Wittenberg used this model of sperm whale myoglobin structure as a teaching tool at the Albert Einstein College of Medicine at Yeshiva University in the Bronx.
Description (Brief)
Professor Jonathan Wittenberg used this model of sperm whale myoglobin structure as a teaching tool at the Albert Einstein College of Medicine at Yeshiva University in the Bronx. It was used beginning in the mid-1960s as part of his class on cell function, which would later come to be known as molecular biology. Wittenberg purchased the model from A. A. Barker, an employee of Cambridge University Engineering Laboratories, who fabricated the models for sale to interested scientists starting in May 1966 under the supervision of John Kendrew.
Between the years 1957 and 1959, John Kendrew, a British biochemist, figured out the complete structure of a protein. For his breakthrough he won the 1962 Nobel Prize for Chemistry, an award he shared with his co-contributor Max Perutz.
Proteins are large molecules used for a vast variety of tasks in the body. Knowing their structure is a key part of understanding how they function, as structure determines the way in which proteins interact with other molecules and can give clues to their purpose in the body.
Kendrew uncovered the structure of myoglobin using a method known as X-ray crystallography, a technique where crystals of a substance—in this case myoglobin—are grown and then bombarded with X-rays. The rays bounce off the atoms in the crystal at an angle and hit a photographic plate. By studying these angles, scientists can pinpoint the average location of single atoms within the protein molecule and piece this data together to figure out the complete structure of the protein.
Interestingly, Kendrew had a hard time getting enough crystals of myoglobin to work with until someone was kind enough to give him a slab of sperm whale meat. Myoglobin’s purpose in the body is to store oxygen in the muscles until needed. Sperm whales, as aquatic mammals, have to be very efficient at storing oxygen for their muscles during deep sea dives, which means they require a lot of myoglobin. Until the gift of the sperm whale meat, Kendrew couldn’t isolate enough myoglobin to grow crystals of sufficient size for his research.
Sources:
Accession file
“History of Visualization of Biological Macromolecules: A. A. Barker’s Models of Myoglobin.” Eric Francouer, University of Massachusetts-Amherst. http://www.umass.edu/molvis/francoeur/barker/barker.html
The Eighth Day of Creation: The Makers of the Revolution in Biology. Horace Freeland Judson. Cold Spring Harbor Laboratory Press: 1996.
Location
Currently not on view
date made
1965
ID Number
2009.0111.01
accession number
2009.0111
catalog number
2009.0111.01
This globe is 6 inches in diameter, with the moon's major known topographical features painted on in shades of gray, green, and black.
Description
This globe is 6 inches in diameter, with the moon's major known topographical features painted on in shades of gray, green, and black. A 60-degree-wide area on the far side of the moon is left blank on this globe, as these features were unknown at the time the globe was printed.
With the globe came an eight page booklet The Story of the Moon, written by Robert I. Johnson.
Location
Currently not on view
Date made
ca 1963
date received
1965 or 1966
maker
Replogle Globes
ID Number
PH.326612
accession number
268427
catalog number
326612
This moon globe is 6 inches in diameter, with topographical features painted in shades of white, gray and tan. Three lunar landings are located and labeled.
Description
This moon globe is 6 inches in diameter, with topographical features painted in shades of white, gray and tan. Three lunar landings are located and labeled. One is the U.S.S.R.'s LUNIK 2, dated 9/12/59, and described as "First unmanned spacecraft to reach the moon." The second is the RANGER 4, dated 4/26/62, and described as "First U.S. unmanned spacecraft to reach the Moon." And there is the site of the U.S. APOLLO 11, dated 7/20/69, and described as "First manned spacecraft landing."
With the globe came a twelve-page booklet written by Robert I. Johnson, and titled The Story of the Moon. The cover shows a view of the moon composed from satellite photographs and carries the notation: "This book dedicated to the Flight of Apollo 8."
Location
Currently not on view
Date made
ca 1969
maker
Replogle Globes, Inc.
ID Number
1990.0015.02
accession number
1990.0015
catalog number
1990.0015.02
Classical Greek mathematicians were able to square all convex polygons. That is, given any polygon, they could produce a square of equal area in a finite number of steps using only a compass and a straight edge. Figures with curved sides proved more difficult.
Description
Classical Greek mathematicians were able to square all convex polygons. That is, given any polygon, they could produce a square of equal area in a finite number of steps using only a compass and a straight edge. Figures with curved sides proved more difficult. However, as this painting suggests, the mathematician Hippocrates of Chios (5th century BC) squared a lune, a figure bounded by arcs of two circle with different radii (lunes resemble quarter moons, hence the name). Finding the area of a lune in terms of a square might seem more difficult than squaring a circle, but the latter problem would prove intractable.
The painting follows annotated figures in Evans G. Valens's The Number of Things (1964), p.103, which was part of Crockett Johnson's mathematical library. It corresponds to an early diagram in Valens's discussion of squaring the circle. According to Valens, Hippocrates began by arguing that the areas of similar segments of different circles are in the same ratio as the squares of their bases. Suppose an isosceles right triangle is inscribed in a semicircle of diameter c. Construct smaller semicircles of diameter a and b on the sides of the inscribed triangle. As the square of a plus the square of b equals the square of c, the area of the two smaller semicircles equals that of the large one. The proof goes on to consider the area of the two crescents and the triangle.
Although Valens called the crescent moon shape a crescent, Crockett Johnson used the term lune. This probably indicates that he also read Herbert Westren Turnball “The Great Mathematicians” in The World of Mathematics, edited by James R. Newman (1956), where the term lune is used. Also, on page page 91 of Turnball’s article there is a diagram on which the painting could have been based.
In this version of Squared Lunes Crockett Johnson uses brown, black, red, and white against a gray background. This oil painting is #67 in the series, and the first in the series with the title "Squared Lunes." It was completed in 1968 and is signed: CJ68. It is inscribed on the back: SQUARED LUNES (/) (HIIPPOCRATES OF CHIOS) (/) Crockett Johnson 1968. A related painting is #68 (1979.1093.43).
Location
Currently not on view
date made
1968
referenced
Hippocrates of Chios
painter
Johnson, Crockett
ID Number
1979.1093.42
accession number
1979.1093
catalog number
1979.1093.42
Some of Crockett Johnson's paintings reflect relatively recent research. Mathematicians had long been interested in the distribution of prime numbers.
Description
Some of Crockett Johnson's paintings reflect relatively recent research. Mathematicians had long been interested in the distribution of prime numbers. At a meeting in the early 1960s, physicist Stanislaw Ulam of the Los Alamos Scientific Laboratory in New Mexico passed the time by jotting down numbers in grid. One was at the center, the digits from 2 to 9 around it to form a square, the digits from 10 to 25 around this, and the spiral continued outward.
Circling the prime numbers, Ulam was surprised to discover that they tended to lie on lines. He and several colleagues programmed the MANIAC computer to compute and plot a much larger number spiral, and published the result in the American Mathematical Monthly in 1964. News of the event also created sufficient stir for Scientific American to feature their image on its March 1964 cover. Martin Gardner wrote a related column in that issue entitled “The Remarkable Lore of the Prime Numbers.”
The painting is #77 in the series. It is unsigned and undated, and has a wooden frame painted white.
Location
Currently not on view
date made
ca 1965
painter
Johnson, Crockett
ID Number
1979.1093.51
catalog number
1979.1093.51
accession number
1979.1093
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.
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
Crockett Johnson much enjoyed constructing square roots of numbers geometrically. He offered the following account of this painting, as well as the figure shown: "Let AN and BN be 1.
Description
Crockett Johnson much enjoyed constructing square roots of numbers geometrically. He offered the following account of this painting, as well as the figure shown: "Let AN and BN be 1. Then the diagonal AB is the square root of 2, because it is the hypotenuse of a right triangle with sides of length √1 and √1. The large right triangle √1 plus √2 adds up to a hypotenuse of √3. The compass traces pronounce a statement and also declare its proof. The square root of 2 is 1.4142 . . . and the square root of 3 is 1.7321 . . . Their decimals run on and on but as produced by the compass and blind straightedge both numbers are quite as finite as 1. The triangle embodies three dimensions of the cube. CB is any edge, AB is a face diagonal, and AC is an internal diagonal." Crockett-Johnson described the source of the painting as "Artist's Construction, or Anybody's."
The triangle with three sides equal to the lengths of interest is painted white. Remaining segments of the construction are in dark gray and purple, with a black background. The painting has a brown wooden frame.
The painting is #66 in the series and is signed: CJ69. For a related painting, see #45 (1979.1093.32).
Reference: "Geometric Geometric [sic] Paintings by Crockett Johnson" NMAH Collections.
Location
Currently not on view
date made
1969
painter
Johnson, Crockett
ID Number
1979.1093.41
accession number
1979.1093
catalog number
1979.1093.41
Most geometric surfaces have a distinct inside and outside. This painting shows one that doesn’t. Take a strip of material, give it a half-twist, and attach the ends together. The result is a band with only one surface and one edge.
Description
Most geometric surfaces have a distinct inside and outside. This painting shows one that doesn’t. Take a strip of material, give it a half-twist, and attach the ends together. The result is a band with only one surface and one edge. Mathematicians began to explore such surfaces in the nineteenth century. In 1858 German astronomer and mathematician August Ferdinand Möbius (1790–1868), who had studied theoretical astronomy under Carl Friedrich Gauss at the University of Goettingen, discovered the one-sided surface shown in the painting. It has come to be known by his name. As often happens in the history of mathematics, another scholar, Johann Benedict Listing, had found the same result a few months earlier. Listing did not publish his work until 1861.
If one attaches the ends of a strip of paper without a half twist, the resulting figure is a cylinder. The cylinder has two sides such that one can paint the outside surface red and the inside surface green. If you try to paint the outside surface of a Möbius band red you will paint the entire band red without crossing an edge. Similarly, if you try to paint the inside surface of a Möbius band green you will paint the entire surface green. A cylinder has an upper edge and a lower edge. However, if you start at a point on the edge of a Möbius band you will trace out its entire edge and return to the point at which you began. Since Möbius's time, mathematicians have discovered and explored many other one-sided surfaces.
This painting, #34 in the series, was executed in oil on masonite and is signed: CJ65. The strip is shown in three shades of gray based on the figure’s position. The shades of gray, especially the lightest shade, are striking against the rose-colored background, and this contrast allows the viewer to focus on the properties of the Möbius band. The painting has a wooden frame.
Crockett Johnson's painting is similar to illustrations in James R. Newman's The World of Mathematics (1956), p. 596. However, the figures are not annotated in the artist's copy of the book.
Location
Currently not on view
date made
1965
referenced
Moebius, August Ferdinand
painter
Johnson, Crockett
ID Number
1979.1093.23
catalog number
1979.1093.23
accession number
1979.1093
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
This is an experimental ruby laser made in 1963 at Ohio State University.
Description
This is an experimental ruby laser made in 1963 at Ohio State University. Edward Damon, a researcher at the University’s Antenna Laboratory, made this and several other lasers during his investigation of Theodore Maiman’s ruby laser experiments of three years earlier.
In addition to replicating Maiman's 1960 experiments, Damon wished to explore variations of the ruby laser. Unlike Maiman's laser, this laser does not use a spiral flashlamp to energize the ruby crystal. Instead, Damon placed three linear flashlamps parallel to the rod-shaped laser crystal. Firing these lamps simultaneously provided energy to the crystal. The laser also demonstrates a water cooling technique still used in some lasers today.
Location
Currently not on view
date made
1963
ID Number
2009.0228.02
accession number
2009.0228
catalog number
2009.0228.02
This piece is a further example of Crockett Johnson's exploration of Kepler’s first two laws of planetary motion. The ellipse represents the path of a planet, and the white sections represent equal areas swept out in equal times.
Description
This piece is a further example of Crockett Johnson's exploration of Kepler’s first two laws of planetary motion. The ellipse represents the path of a planet, and the white sections represent equal areas swept out in equal times. This work, a silk screen inked on paper board, is signed: CJ66. It is #76 in the series, and it echoes painting #22 (1979.1093.16) and painting #99 (1979.1093.66).
Location
Currently not on view
date made
1966
referenced
Kepler, Johannes
painter
Johnson, Crockett
ID Number
1979.1093.50
catalog number
1979.1093.50
accession number
1979.1093
Currently not on view
Location
Currently not on view
date made
1968
maker
Bausch & Lomb Optical Company
ID Number
MG.M-12196
accession number
272522
catalog number
M-12196
Working at the Lamont Geological Observatory, a Columbia University facility in Palisades, N.Y., Frank Press and his mentor, Maurice Ewing, developed seismometers that responded to surface waves of long-period and small-amplitude, whether caused by explosions or by earthquakes.
Description
Working at the Lamont Geological Observatory, a Columbia University facility in Palisades, N.Y., Frank Press and his mentor, Maurice Ewing, developed seismometers that responded to surface waves of long-period and small-amplitude, whether caused by explosions or by earthquakes. The first long-period vertical seismometer at Lamont came to public attention in early 1953 with news that it had recorded waves from a large earthquake that had recently occurred at Kamchatka, in the Soviet Union. A painting of a subsequent but similar Lamont instrument appeared on the cover of Scientific American in March 1959.
This example was made for the World Wide Standard Seismological Network. Established in 1961, the WWSSN was designed to detect underground nuclear tests and generate valuable information about the earth’s interior and its dynamic processes. The WWSSN was a key component of VELA Uniform, a Cold War project that was funded by the Advanced Research Projects Agency (ARPA), a branch of the Department of Defense. It was managed by the U.S. Coast and Geodetic Survey and then by the U.S. Geological Survey. That agency transferred this instrument to the Smithsonian in 1999.
Each of the 120 WWSSN stations had an instrument of this sort. This example was used in Junction City, Tex. It would have been linked to a matched galvanometer (such as 1999.0275.09) and a photographic drum recorder (such as 1999.0275.10). The “Sprengnether Instrument Co.” signature refers to a small shop in St. Louis, Mo., that specialized in seismological apparatus.
Like other long-period vertical seismometers developed at Lamont, this one was built around a “zero-length spring” of the sort that had been proposed in 1934 by Lucien LaCoste, a graduate student in physics at the University of Texas, and later incorporated into the gravity meters manufactured by LaCoste & Romberg.
Ref: United States Coast and Geodetic Survey, Instrumentation of the World-Wide Seismograph System, Model 10700 (Washington, D.C., 1962)
Ta-Liang Teng, “Seismic Instrumentation,” in Methods of Experimental Physics, vol. 24 part B, Geophysics (1987), pp. 56-58.
Location
Currently not on view
date made
1961-1962
maker
W. F. Sprengnether Instrument Co.
ID Number
1999.0275.03
catalog number
1999.0275.03
accession number
1999.0275
This multipore filter multiplater was designed and used in the National Institute of Health lab of Dr.
Description (Brief)
This multipore filter multiplater was designed and used in the National Institute of Health lab of Dr. Marshall Nirenberg, a scientist who won the 1968 Nobel Prize in Physiology or Medicine for his work in helping to “crack the genetic code,” or to understand the way DNA codes for the amino acids that are linked to build proteins.
Part of Dr. Nirenberg's research involved making radioactively-labeled proteins. To analyze the proteins, Nirenberg had to separate them from the solution in which they were suspended. The first step in this process was to add trichloroacetic acid, which caused the proteins to form a solid, clumping together into a mass known as a precipitate. Next, the precipitate had to be separated from the rest of the solution. Originally separation was done by differential centrifugation, but that process was very time-consuming. Eventually, Nirenberg decided to try washing the precipitate over millipore filters under suction. The solution was pored over a millipore filter, trapping the precipitate but letting the solution drain through. Suction sped up the draining process. The first device he designed only was capable of handling one sample at a time, but later Philip Leder, who was then working with Dr. Nirenberg, designed this device to run large batches of the process. The mulitiple pores allowed suction to be applied to 45 samples at once.
The instrument was made in the NIH Instrument Fabrication section and was dubbed the "multi-plater" by Dr. Nirenberg. Compared to the centrifuge, it saved immense amounts of time, allowing the researchers to increase their output by more than five-fold.
The device has a four-legged steel base with tube connections for suction. The top portion, made of plastic, is in two parts and clamps onto the base. The bottom plastic part contains the 45 millipore filters. The top portion, which fits over it, has 45 holes connecting to the filters into which the precipitate is placed and then stoppered.
To learn more about Dr. Nirenberg’s efforts to crack the genetic code please see his jar of oligonucleotides, object number 2001.0023.02.
Location
Currently not on view
date made
1963
maker
NIH Instrument Fabrication Section
ID Number
2001.0023.08
accession number
2001.0023
catalog number
2001.0023.08
This is an experimental ruby laser made in 1963 at Ohio State University.
Description
This is an experimental ruby laser made in 1963 at Ohio State University. Edward Damon, a researcher at the University’s Antenna Laboratory, made this and several other lasers during his investigation of Theodore Maiman’s successful ruby laser experiments of three years earlier.
An important part of science consists of replicating the experiments conducted by other researchers and confirming their results. Like Maiman's 1960 laser, Damon's 1963 laser used a photographer's helical flashlamp to energize the ruby crystal. It demonstrated the use of mirrors external to the ruby rod instead of mirrors deposited in the crystal itself. The mirrors are on adjustable mounts that allowed Damon to make a variety of experiments with this unit.
Location
Currently not on view
date made
1963
maker
Ohio State University
ID Number
2009.0228.01
accession number
2009.0228
catalog number
2009.0228.01
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.
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.
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. However, he may have been influenced by Figure 1 (p. 604) and Figure 3 (p. 608) in Panofsky’s article on Dürer as a Mathematician in The World of Mathematics, edited by James R. Newman (1956). Johnson did not annotate either of these diagrams. 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
In ancient times, the Greek mathematician Apollonius of Perga (about 240–190 BC) made extensive studies of conic sections, the curves formed when a plane slices a cone.
Description
In ancient times, the Greek mathematician Apollonius of Perga (about 240–190 BC) made extensive studies of conic sections, the curves formed when a plane slices a cone. Many centuries later, the French mathematician and philosopher René Descartes (1596–1650) showed how the curves studied by Apollonius might be related to points on a straight line. In particular, he introduced an equation in two variables expressing points on the curve in terms of points on the line. An article by H. W. Turnbull entitled "The Great Mathematicians" found in The World of Mathematics by James R. Newman discussed the interconnections between Apollonius and Descartes, and apparently was the basis of this painting. The copy of this book in Crockett Johnson's library is very faintly annotated on this page. Turnbull shows variable length ON, with corresponding points P on the curve.
The analytic approach to geometry taken by Descartes would be greatly refined and extended in the course of the seventeenth century.
Johnson executed his painting in white, purple, and gray. Each section is painted its own shade. This not only dramatizes the coordinate plane but highlights the curve that extends from the middle of the left edge to the top right corner of the painting.
Conic Curve, an oil or acrylic painting on masonite, is #11 in the series. It was completed in 1966 and is signed: CJ66. It is marked on the back: Crockett Johnson 1966 (/) CONIC CURVE (APOLLONIUS). It has a wooden frame.
Location
Currently not on view
date made
1966
referenced
Apollonius of Perga
painter
Johnson, Crockett
ID Number
1979.1093.06
catalog number
1979.1093.06
accession number
1979.1093
The Greek mathematician Aristotle, who lived from about 384 BC through 322 BC, believed that heavy bodies moved naturally downward, while lighter substances such as air naturally ascended.
Description
The Greek mathematician Aristotle, who lived from about 384 BC through 322 BC, believed that heavy bodies moved naturally downward, while lighter substances such as air naturally ascended. Other forms of terrestrial motion required a sustaining force, which was not expressed mathematically. The Italian Galileo Galilei (1564–1642) challenged Aristotle. He held that motion was persistent and would continue until acted upon by an opposing, outside force.
In a book entitled Dialogues Concerning the Two Chief World Systems, Galileo presented his ideas in a dispute between three men: Salviati, Sagredo, and Simplicio. Salviati, a spokesman for Galileo, explained his revolutionary ideas, one of which is illustrated by a diagram that was the basis for this painting. This image can be found in Crockett Johnson's copy of The World of Mathematics, a book by James R. Newman. It is probable that this image served as inspiration for this painting, although Johnson did not annotate this diagram.
In Galileo's Dialogues, Salviati argued that if a lead weight is suspended by a thread from point A (see figure) and is released from point C, it will swing to point D, which is located at the same height as the initial point C. Furthermore, Salviati stated that if a nail is placed at point E so that the thread will snag on it, then the weight will swing from point C to point B and then up to point G, which is also located at the same height as the initial point C. The same occurs if a nail is placed at point F below the line segment CD.
The painting is executed in purple that progresses from light tints to darker shades right to left. This gives the figure a sense of motion akin to that of a pendulum. The background is washed in gray and black. The line created by the initial and final height of the weight divides the background.
Pendulum Momentum, a work in oil on masonite, is painting #13 in the Crockett Johnson series. It was executed in 1966 and is signed: CJ66. There is a wooden frame painted black.
Location
Currently not on view
date made
1966
referenced
Galilei, Galileo
painter
Johnson, Crockett
ID Number
1979.1093.08
catalog number
1979.1093.08
accession number
1979.1093
This work illustrates two laws of planetary motion proposed by the German mathematician Johannes Kepler (1571–1630) in his book Astronomia Nova (New Astronomy) of 1609. Kepler argued that planets move about the sun in elliptical orbits, with the sun at one focus of the ellipse.
Description
This work illustrates two laws of planetary motion proposed by the German mathematician Johannes Kepler (1571–1630) in his book Astronomia Nova (New Astronomy) of 1609. Kepler argued that planets move about the sun in elliptical orbits, with the sun at one focus of the ellipse. He also claimed that a planet moves about the sun in such a way that a line drawn from the planet to the sun sweeps out equal areas in equal times. The ellipse in the work represents the path of a planet and the white sections equal areas. The extraordinary contrast between the deep blue and white colors dramatize this phenomenon.
This oil painting on masonite has a wooden frame. It is signed: CJ65. It also is marked on the back: Crockett Johnson 1965 (/) LAW OF ORBITING VELOCITY (/) (KEPLER). It is #22 in the series. The work follows an annotated diagram from Crockett Johnson’s copy of Newman's The World of Mathematics (1956), p. 231. Compare to paintings #76 (1979.1093.50) and #99 (1979.1093.66).
Reference: Arthur Koestler, The Watershed (1960).
Location
Currently not on view
date made
1965
referenced
Kepler, Johannes
painter
Johnson, Crockett
ID Number
1979.1093.16
catalog number
1979.1093.16
accession number
1979.1093

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