#
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.

"Science & Mathematics - Overview" showing 1288 items.

Page 2 of 129

## Zeiss Opton Refractometer

- Description (Brief)
- This refractometer was used in Stanley Cohen’s lab at Stanford University in his research on recombinant DNA. Refractometers measure how light changes velocity as it passes through a substance. This change is known as the refractive index and it is dependent on the composition of the substance being measured. In the Cohen lab, this refractometer was one of several techniques used to provide evidence that he and his research team had created a recombinant DNA molecule containing DNA from both a bacterium and a frog.

- To conduct the analysis, Cohen separated out the molecule he assumed to be recombinant DNA and measured its refractive index. The index for the molecule fell between the known values for frog DNA and bacterial DNA, suggesting that the unknown DNA molecule was a mixture of the two.

- For more information on the Cohen/Boyer experiments with recombinant DNA see object 1987.0757.01

- Sources:

- “Section 9.4.2: Buoyant Density Centrifugation.” Smith, H., ed.
*The Molecular Biology of Plant Cells*. Berkeley: University of California Press, 1977. http://ark.cdlib.org/ark:/13030/ft796nb4n2/

- “Louisiana State University Macromolecular Studies Group How-To Guide: ABBE Zeiss Refractometer.” Pitot, Cécile. Accessed December 2012. http://macro.lsu.edu/howto/Abbe_refractometer.pdf

- “Construction of Biologically Functional Bacterial Plasmids In Vitro.” Cohen, Stanley N., Annie C.Y. Chang, Herbert W. Boyer, Robert B. Helling.
*Proceedings of the National Academy of the Sciences*. Vol. 70, No. 11. pp.3240–3244. November 1973.

- “Replication and Transcription of Eukaryotic DNA in Escherichia coli.” Morrow, John F., Stanley N. Cohen, Annie C.Y. Chang, Herbert W. Boyer, Howard M. Goodman, Robert B. Helling.
*Proceedings of the National Academy of the Sciences*. Vol. 71, No. 5. pp.1743–1747. May 1974.

- Accession File

- Location
- Currently not on view

- date made
- 1946-1953

- user
- Cohen, Stanley N.

- maker
- Zeiss

- ID Number
- 1987.0757.28

- catalog number
- 1987.0757.28

- accession number
- 1987.0757

- serial number
- 128646

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

## Agassiz, Peirce, and Patterson

- Description
- Benjamin Peirce, Harvard professor of mathematics and third superintendent of the U.S. Coast Survey, was on good terms with Louis Agassiz, the charismatic Swiss naturalist who taught at Harvard’s Lawrence Scientific School and served as the founding director of Harvard’s Museum of Comparative Zoology. Writing to Agassiz in February 1871, Peirce announced that the Coast Survey was about “to send a new iron steamer round to California” and asked if Agassiz would “go in her, and do deep-sea dredging all the way around?” Since Agassiz had conducted several research projects under the aegis of the Coast Survey, Peirce expected that he would accept this new proposition. The new ship, the first iron-hulled vessel owned by the Survey, was designed to dredge at depths never before reached. Named the
*Hassler*after the first superintendent of the Coast Survey, the ship's maiden voyage would be known as the Hassler Expedition.

- The Coast Survey had the largest budget of any 19th-century American scientific organization, and employed more scientists, both directly and indirectly. But aware of Congressional concerns about how federal funds should be spent, the Survey tended to hide its science behind its more practical activities. Thus while the
*Hassler*sailed from the East Coast where it was built to the Pacific Coast where it would see service, the ship` could transport Agassiz, his wife, and several colleagues and assistants. But Agassiz had to raise the $20,000 needed to preserve the many specimens they hoped to collect and send back to the States for further study. Most of these specimens went to the Museum of Comparative Zoology and the Smithsonian Institution.

- The Hassler left the Boston Navy Yard on Dec. 4, 1871 and made land in San Francisco some nine months later. Despite equipment failure and various delays, much was accomplished on the Expedition. The Coast Survey aimed to discover the origin of the Gulf Stream, determine the greatest depth of the Atlantic, exploring the coasts of Patagonia, chart the dangerous currents in and around the Straits of Magellan, and trace Darwin’s steps in the Galapagos Islands. Agassiz was especially interested in evidence of glacial action in the Southern Hemisphere (which he found), and evidence that might disprove Darwin’s theory of evolution (which he did not).

- The
*Hassler*left the Boston Navy Yard on Dec. 4, 1871 and made land in San Francisco some nine months later. Despite equipment failure and various delays, much was accomplished on the expedition. The Coast Survey aimed to discover the origin of the Gulf Stream, determine the greatest depth of the Atlantic, explore the coasts of Patagonia, chart the dangerous currents in and around the Straits of Magellan, and trace Darwin’s steps in the Galapagos Islands. Agassiz was especially interested in evidence of glacial action in the Southern Hemisphere (which he found), and evidence that might disprove Darwin’s theory of evolution (which he did not).

- This large, carefully posed and somewhat manipulated photograph was made while plans for the expedition were underway. Agassiz is seated at the left of a round table, Peirce stands behind the table, and Carlile Patterson, the Hydrographic Inspector of the Coast Survey (and the man who had planned the internal arrangements of the new ship) sits at right. These men seem to be discussing a chart attached to which an obviously enlarged piece of paper carries the hand-written inscription “Instructions for Expd.” and “To. Prof. L. Agassiz / from Captain C. Patterson / Yours respectfully / Benjamin Peirce / Superintendent.”

- The text at bottom of the photograph reads “Entered according to Act of Congress in the year 1871 by A. SONREL, in the Office of the Librarian of Congress at Washington, D.C.” This refers to the federal copyright act of 1870. That image is now in the Prints and Photographs Division of the Library of Congress. It is identical to our copy, but has an “A. Sonrel” signature in the lower left.

- Antoine Sonrel (d. 1879) was an accomplished scientific illustrator who had worked with Agassiz in Neuchâtel, followed him to the United States, and prepared the lithographic plates for several of his publications. He was also an accomplished photographer who did commercial and scientific work. Several Agassiz cartes-de-visite photographs were taken by in Sonrel’s Boston studio. Another Sonrel photograph dated 1871, probably taken on the same day as our image, shows Agassiz and Peirce, the former seated in a chair, and the latter standing with his right hand on a globe pointing to Boston. And, as our image indicates, Sonrel, like many photographers then as now, enjoyed manipulating images. Another Sonrel photograph shows Agassiz talking to Agassiz across a table. Yet another shows an unidentified man playing chess with himself.

- According to a note on the back of the frame, this photograph was purchased at an auction of the effects Mrs. John Cummings in 1928. The reference is to Mary Phelps Cowles (1839-1927), a woman of culture and wealth who was married to Adino Brackett Hall, a Boston physician, and then John Cummings, a landowner in Woburn, Ma.

- Ref: Christoph Irmscher,
*Louis Agassiz. Creator of American Science*(Boston, 2013).

- David Dobbs,
*Reef Madness: Charles Darwin, Alexander Agassiz, and the Meaning of Coral*(New York, 2005).

- Edward Hogan,
*Of the Human Heart. A Biography of Benjamin Peirce*(Bethlehem, 2008), pp. 270-280.

- Location
- Currently not on view

- date made
- 1871

- depicted (sitter)
- Agassiz, Louis

- ID Number
- 1990.0326.01

- catalog number
- 1990.0326.01

- accession number
- 1990.0326

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

## Sterling 544 Protractor and Drawing Instrument

- Description
- This clear plastic semicircular protractor is contained within an irregularly shaped piece of plastic that features a French curve at the top, two triangles (of 60° and 45°) on the sides, and a 5-1/2" scale along the bottom.

- The scale is divided to 16ths of an inch and is marked by single inches from 1" to 5". The protractor is divided to single degrees and marked by tens from 10° to 90° to 170° and from 170° to 90° to 10°. A semicircular slot separates the protractor from the French curve. Cut-out stencils for six circles range in diameter from 1/8" to 7/16". Also included are two slots for drawing angles of 30° and 45° and templates for an equilateral hexagon and two closed curves. On the curve the object is marked: SP [/] PROTRACTOR – FRENCH CURVE – TRIANGLES – RULER – CIRCLE GAUGES. Between the protractor and scale, the object is marked: MADE IN U.S.A.; 2; STERLING 544. The markings were stamped in black but are wearing off.

- Sterling Plastics was operated by George and Mary Staab in Mountainside, N. J., through the late 1960s. It was a division of Borden Chemical Company in the 1970s and 1980s, during which time this object was called the 7-IN-1 Protractor. For other products of Sterling Plastics, see slide rule 1988.0807.01 and adding machine MA*335327. James J. Williams gave this protractor to the Smithsonian.

- Reference:
*Toxic Substances Control Act: Trademarks and Product Names Reported in Conjunction with the Chemical Substance Initial Inventory*(Washington, D.C.: United States Environmental Protection Agency, 1979), 90.

- Location
- Currently not on view

- date made
- ca 1975

- maker
- Sterling Plastics

- ID Number
- 1998.3104.01

- nonaccession number
- 1998.3104

- catalog number
- 1998.3104.01

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

## Dietzgen Limb Protractor

- Description
- This German silver protractor is in the shape of a quarter-circle. It is divided by half-degrees and marked by tens from 0° to 90°. Flat bars extend on both sides of the protractor. A movable arm extends from the vertex of the quadrant. A tab is cut out from this limb to permit reading the angle markings. The arm is secured by a brass thumbscrew that is near the origin point for the angle markings. The protractor is noticeably rusted and tarnished.

- There is a signature on the bottom edge: E. D. – Co. (/) NEW YORK & CHICAGO. Around 1880, Eugene Dietzgen emigrated from Germany and became a sales distributor for Keuffel & Esser in New York. In 1885, he began to sell mathematical instruments on his own in Chicago. In 1893, his firm started manufacturing instruments under the name Eugene Dietzgen Company. However, this protractor was not advertised in Dietzgen catalogs that were published between 1902 and 1947.

- Leslie Leland Locke (1875–1943) originally owned this protractor. A student at Grove City College, he earned a bachelor's degree in 1896 and a master's degree in 1900. He taught mathematics at Michigan State College, Adelphi College, and Brooklyn College and its Technical High School. He was interested in Peruvian
*quipu*, mysterious and ancient systems of knotted strings used to store and communicate information and data. He donated his collection of early calculating machines to the Smithsonian and his early American textbooks to the University of Michigan.

- Reference: Louis C. Karpinski, "Leslie Leland Locke,"
*Science*n.s., 98, no. 2543 (24 September 1943): 274–275.

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Eugene Dietzgen Company

- ID Number
- 2011.0129.01

- accession number
- 2011.0129

- catalog number
- 2011.0129.01

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

## Model of a Riemann Surface by Richard P. Baker, Baker #405w

- Description
- This geometric model was constructed by Richard P. Baker in about 1930 when he was Associate Professor of Mathematics at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

- The mark "405 w" is carved into one edge of the wooden base of this model and the typed part of a paper label on the base reads: No. 405 z (/) Riemann surface : w
^{2}= z^{3}- z. Someone corrected the error on the label by hand, crossing out the z and inserting a w. Model 405w is listed on page 17 of Baker’s 1931 catalog of models as “w^{2}= z^{3}- z” under the heading*Riemann Surfaces*. This means that the model represents a Riemann surface consisting of pairs of complex numbers, (z,w), for which w^{2}= z^{3}- z. Complex numbers are of the form x + yi for x and y real numbers and i the square root of –1. A complex plane is like the usual real Cartesian plane but with the horizontal axis representing the real part of the number and the vertical axis representing the imaginary part of the number. Riemann surfaces are named after the 19th-century German mathematician Bernhard Riemann.

- Baker explains in his catalog that the w after the number of the model indicates that the metal disks above the wooden base represent copies of a disk in the complex w-plane. These disks are called the sheets of the model. The painted part of the wooden base of the model represents a square in the complex z-plane with the point z = 0 at its center and the real axis along the line between the yellow and light green stripes.

- If w = ±
^{4}√ (4/27) or w = ±i^{4}√ (4/27), the equation w^{2}= z^{3}- z is satisfied by two distinct values of z. For the two real values of w, ±^{4}√ (4/27), z takes the values –1/√3 and 2/√3, and for the two imaginary values of w, ±i^{4}√ (4/27), z takes the values 1/√3 and –2/√3. These four points on the w-plane are called branch points of the model and for all other points on the w-plane the equation w^{2}= z^{3}- z is satisfied by three distinct values of z, each of which produces a different pair on the Riemann surface (if w = 0, the three distinct pairs on the Riemann surface are (0,0) and (±1,0). Thus there are three sheets representing the same disk in the complex w-plane and together they represent part of what is called a branched cover of the complex w-plane. The color of a region on a sheet is chosen with the aim of indicating the stripe on the base in which the z coordinate lies.

- For each sheet, the point at the center is w = 0 and the line lying over the real axis of the base is the real axis of the sheet. The two points marked on the top sheet are the two imaginary branch points, w = ±i
^{4}√ (4/27); the two marked on the bottom sheet are the two real branch points, w = ±^{4}√ (4/27); and all four branch points are marked on the middle sheet.

- The vertical surfaces between the sheets are not part of the Riemann surface but call attention to what are called branch cuts of the model, i.e. curves on a sheet that produce movement to another sheet. This movement occurs when meeting a branch cut while following a path of the inputs of w values into the equation. While the defining equation determines the branch points, the branch cuts are not fixed by the equation but, normally, each branch cut goes through two of the surface’s branch points or runs out to infinity. All of the branch cuts of this model run to infinity and are represented by the horizontal edges of the vertical surfaces.

- There are three other models of Riemann surfaces in the collections that are associated with the equation of this model. One has "405w" carved on the base, Baker's no. 405wn (MA*211257.069), while two have "405z" carved, Baker's no. 405z (MA*211257.070) and Baker's no. 405zn (MA*211257.071). Baker carved a "w" or a "z" to indicate which variable is represented on the sheets of the model and added an n after the w or z to indicate that the sheets of the model are spheres.

- Location
- Currently not on view

- date made
- ca 1915-1935

- maker
- Baker, Richard P.

- ID Number
- MA*211257.068

- accession number
- 211257

- catalog number
- 211257.068

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

## Model of a Riemann Surface by Richard P. Baker, Baker #405wn

- Description
- This geometric model was constructed by Richard P. Baker in about 1930 when he was Associate Professor of Mathematics at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

- The mark "405 w" is carved into one edge of the wooden base of this model and the typed part of a paper label on the base reads: No. 405 zn (/) Riemann surface : w
^{2}= z^{3}- z. The label should have read "405 wn" and someone added a handwritten question mark after the "zn." Model 405wn is listed on page 17 of Baker’s 1931 catalog of models as “w^{2}= z^{3}- z” under the heading*Riemann Surfaces*. This means that the model represents a Riemann surface consisting of pairs of complex numbers, (z,w), for which w^{2}= z^{3}- z. Complex numbers are of the form x + yi for x and y real numbers and i the square root of –1. The spheres of the model are called complex, or Riemann, spheres. They are formed with north and south poles representing ∞ and 0, respectively. The equator represents the points x + yi with x^{2}+ y^{2}= 1. Thus the points ±1 and ±i are equally spaced along the equator. Riemann surfaces and spheres are named after the 19th-century German mathematician Bernhard Riemann.

- Baker explains in his catalog that the wn after the number of the model indicates that the model is made up of spheres representing w-values. These spheres are called the sheets of the model. There is no part of this model in which values of z or pairs (z,w) are represented. However, it is possible that the coloring on this model is related to the painted part of the wooden base of one of three other Baker models of Riemann surfaces that are associated with the equation of this model.

- If w = ±
^{4}√ (4/27) or w = ±i^{4}√ (4/27), the equation w^{2}= z^{3}- z is satisfied by two distinct values of z. For the two real values of w, ±^{4}√ (4/27), z takes the values –1/√3 and 2/√3, and for the two imaginary values of w, ±i^{4}√ (4/27), z takes the values 1/√3 and –2/√3. These four points together with the point z = ∞ are called branch points of the model and for all other points on the w-sphere the equation w^{2}= z^{3}- z is satisfied by three distinct values of z, each of which produces a different pair on the Riemann surface (if w = 0, the three distinct pairs on the Riemann surface are (0,0) and (±1,0)). Thus there are three sheets representing the complex w-sphere and together they represent what is called a branched cover of the complex w-sphere.

- On each of the sheets the equator is a thin circle and there are two great circles through the poles. On one of the great circles the values of w are purely imaginary while on the other they are real. Baker’s usual use of colors implies that the great circles facing the front and back represent imaginary numbers, while those facing the sides represent real numbers. Normally w = ∞ is at the north pole and w = 0 is at the south pole. However, as the four finite branch points of this model lie in the northern hemisphere, it appears that this model has that assignment of values reversed. The great circle facing the front and back has a thick white segment that connects the two imaginary branch points by way of w = ∞ at the south pole, while the other has a thick black segment connecting the two real branch points by way of w = 0 at the north pole. The parts of the great circles that connect two branch points are called branch cuts. This model has three, one is the black arc mentioned above and the others are the two halves of the white arc with ends at an imaginary branch point and infinity. These branch cuts are curves on a sheet that produce movement to another sheet. This movement occurs when meeting a branch cut while following a path of the inputs of w values into the equation.

- There are three other models of Riemann surfaces in the collections that are associated with the equation of this model. One, a model with Baker’s no. 405w (MA*211257.068), has “405w” carved on the base Two others, Baker’s no. 405z (MA*211257.070) and Baker’s no. 405zn (MA*211257.071), both have the mark “405z“ carved on them. Baker carved a "w" or a "z" to indicate which variable is represented on the sheets of the model and added an "n" after the "w" or "z" to indicate that the sheets of the model are spheres.

- Location
- Currently not on view

- date made
- ca 1915-1935

- maker
- Baker, Richard P.

- ID Number
- MA*211257.069

- accession number
- 211257

- catalog number
- 211257.069

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

## Model of a Riemann Surface by Richard P. Baker, Baker #405z

- Description
- This geometric model was constructed by Richard P. Baker in about 1930 when he was Associate Professor of Mathematics at the University of Iowa. Baker believed that models were essential for the teaching of many parts of mathematics and physics, and over one hundred of his models are in the museum collections.

- The mark 405 z is carved into one edge of the wooden base of this model and the typed part of a paper label on the base reads: No. 405 w (/) Riemann surface : w
^{2}= z^{3}- z. Someone corrected the error on the label by hand, crossing out the w and inserting a z. Model 405z is listed on page 17 of Baker’s 1931 catalogue of models as “w^{2}= z^{3}- z” under the heading*Riemann Surfaces*. This means that the model represents a Riemann surface consisting of pairs of complex numbers, (z,w), for which w^{2}= z^{3}- z. Complex numbers are of the form x + yi for x and y real numbers and i the square root of –1. A complex plane is like the usual real Cartesian plane but with the horizontal axis representing the real part of the number and the vertical axis representing the imaginary part of the number. Riemann surfaces are named after the 19th-century German mathematician Bernhard Riemann.

- Baker explains in his catalogue that the z after the number of the model indicates that the metal disks above the wooden base represent copies of a disk in the complex z-plane. These disks are called the sheets of the model. The painted part of the wooden base of the model represents a square in the complex w-plane with the point w = 0 at its center and the real axis along the line between the yellow and dark green stripes.

- If z = 0 or z = ±1, the equation w
^{2}= z^{3}- z is satisfied by only one value of w, i.e., w = 0. These three points on the z-plane are called branch points of the model and for all other points on the z-plane the equation w^{2}= z^{3}- z is satisfied by two distinct values of w, each of which produces a different pair on the Riemann surface (if z = 2, the two distinct pairs on the Riemann surface are (2, ±√6)). Thus there are two sheets representing the same disk in the complex z-plane and together they represent part of what is called a branched cover of the complex z-plane. The color of a region on a sheet is chosen with the aim of indicating the stripe on the base in which the w coordinate lies.

- For each sheet, the center of the disc is the point z = 0 and the solid black line through that point is the real axis. The branch points of this model all lie on the real axis. The point z = –1 is the point inside the green and yellow oval where the real axis meets the small red circle representing the unit circle with center z = 0. The point z = 1 is the other point where the real axis meets the small red circle; it is inside the oval that includes all eight colors used in the model.

- The vertical surfaces between the two sheets are not part of the Riemann surface but call attention to what are called branch cuts of the model, i.e., curves on a sheet that produce movement to another sheet. This movement occurs when meeting a branch cut while following a path of the inputs of z values into the equation. While the defining equation determines the branch points, the branch cuts are not fixed by the equation but, normally, each branch cut goes through two of the surface’s branch points or runs out to infinity. In this model, one of the branch cuts connects z = 0 to z = 1 and the other runs from z = –1 to infinity; they are represented by the horizontal edges of the vertical surfaces.

- There are three other models of Riemann surfaces in the collections that are associated with the equation of this model. One, a model with Baker's number 405zn (MA*211257.071), has "405z" carved on the base. Two others, one with Baker's number 405w (MA*211257.068) and the other with Baker's number 405wn (MA*211257.069) have "405w" carved on the edge of the base. Baker carved a "z" or a "w" to indicate which variable is represented on the sheets of the model and added an "n" after the "z" or "w" to indicate that the sheets of the model are spheres.

- Location
- Currently not on view

- date made
- ca 1915-1935

- maker
- Baker, Richard P.

- ID Number
- MA*211257.070

- accession number
- 211257

- catalog number
- 211257.070

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

## Model of a Riemann Surface by Richard P. Baker, Baker #405zn

- Description

- The mark "405 z" is carved into one edge of the wooden base of this model and the typed part of a paper label on the base reads: No. 405 wn (/) Riemann surface : w
^{2}= z^{3}- z. The label is incorrect and should read "405 zn". Model 405zn is listed on page 17 of Baker’s 1931 catalogue of models as “w^{2}= z^{3}- z” under the heading*Riemann Surfaces*. This means that the model represents a Riemann surface consisting of pairs of complex numbers, (z,w), for which w^{2}= z^{3}- z. Complex numbers are of the form x + yi for x and y real numbers and i the square root of –1. The spheres of the model are called complex, or Riemann, spheres. They are formed with north and south poles representing ∞ and 0, respectively. The equator represents the points x + yi with x^{2 + y}2 = 1. Thus the points ±1 and ±i are equally spaced along the equator. Riemann surfaces and spheres are named after the 19th-century German mathematician Bernhard Riemann.

- Baker explains in his catalog that the zn after the number of the model indicates that the model is made up of spheres representing z-values. These spheres are called the sheets of the model. It appears as if painted part of the wooden base of the model represents the Riemann surface as a torus, i.e., a donut, formed by pasting together the ends of the stripes to form a cylinder and then joining the ends of the cylinder.

- If z = 0 or z = ±1, the equation w
^{2}= z^{3}- z is satisfied by only one value of w, i.e., w = 0. These three points together with the point z = ∞ are called branch points of the model and for all other points on the z-sphere the equation w^{2}= z^{3}- z is satisfied by two distinct values of w, each of which produces a different pair on the Riemann surface (if z = 2, the two distinct pairs on the Riemann surface are (2, ±√6)). Thus there are two sheets representing the complex z-sphere and together they represent what is called a branched cover of the complex z-sphere. The color of a region on a sheet is chosen with the aim of indicating the stripe on the base into which it is mapped.

- On each of the sheets the equator is colored red and there are great circles through the poles that are colored yellow and black. The points on the yellow great circle are purely imaginary while those on the black great circle are real. Thus the real non-zero branch points, z = ±1, lie on the equator and on the black great circle, while the other two branch points are at the north and south poles. The darkened parts of the black great circle are called branch cuts. Assuming the pair (1,0) lies on the Riemann surface along edge shared by the center (yellow and green) stripes on the base and that the pair (–1,0) lies along the edges of the outer stripes on the base, one of the branch cuts runs between join z = 0 and z = 1 and other between z = –1 and z = ∞. These branch cuts are curves on a sheet that produce movement to another sheet. This movement occurs when meeting a branch cut while following a path of the inputs of z values into the equation. Thus one can construct the Riemann surface as a torus by cutting the spheres along the branch cut and sewing the two spheres together along those cuts while matching the four branch points.

- There are three other models of Riemann surfaces in the collections that are associated with the equation of this model. One, with Baker's number 405z (MA*211257.070) has "405z" carved on the base. Two others, Baker's number 405 w (MA*211257.068) and Baker's number 405wn (MA*211257.069) have the mark "405w" on the base. Baker carved a "z" or a "w" to indicate which variable is represented on the sheets of the model and added an "n" after the "z" or "w" to indicate that the sheets of the model are spheres.

- Location
- Currently not on view

- date made
- ca 1915-1935

- maker
- Baker, Richard P.

- ID Number
- MA*211257.071

- accession number
- 211257

- catalog number
- 211257.071

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

## Geometric Model by A. Harry Wheeler, One-Sided Polyhedron

- Description
- In the late 1930s and early 1940s, A. Harry Wheeler took great interest in polyhedra with interpenetrating sides, such as had been discussed by the German mathematician August F. Moebius. In this example, each of the two like-colored quadrilaterals (e.g. the two yellow sides) on the top pass through the model and appear as a white quadrilateral on the bottom. These three figures thus contribute only one side to the polygon.

- A mark on the model reads: 695. This was Wheeler’s number for the model. Models MA*304723.413, MA*304723.397, and MA*304723.398 fit together. Model MA*304723.409 is a compound of four models like MA*304723.413.

- Reference:

- Kurt Reinhardt, “Zu Moebius’ Polyhedertheorie,”
*Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Mathematisch-Physische Classe*, 37, pp. 106-125. Wheeler referred to this article.

- Location
- Currently not on view

- date made
- ca 1940

- maker
- Wheeler, Albert Harry

- ID Number
- MA*304723.413

- accession number
- 304723

- catalog number
- 304723.413

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

## Myoglobin Protein Model

- 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, was the first person to figure 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

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