Science & Mathematics - Overview
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 6 items.
Flexible Polyhedron
- Description
- The mathematician Leonard Euler once wrote,"A closed spatial figure allows no changes, as long as it is not ripped apart." Proving the "rigidity" of polyhedra was another matter. In 1813, Augustin-Louis Cauchy showed that a convex polyhedral surface is rigid if its flat polygonal faces are held rigid. In 1974, Herman Gluck proved that almost all triangulated spherical surfaces were rigid. However, in 1977 Robert Connelly of Cornell University found a counterexample, that is to say a flexible polyhedron. He built this model of such a surface some years later. It is made of cardboard and held together with duct tape. Two cutout plastic windows allow the viewer to observe changes when the polyhedron is flexed. The top section has 12 large faces and a six-faced appendage. The bottom section has 12 corresponding faces but no appendage.
- Location
- Currently not on view
- date made
- 1985
- maker
- Connelly, Robert
- ID Number
- 1990.0492.01
- accession number
- 1990.0492
- catalog number
- 1990.0492.01
- Data Source
- National Museum of American History, Kenneth E. Behring Center
Crocheted Model of the Hyperbolic Plane
- Description
- This model of the hyperbolic plane was crocheted by the Latvian-born mathematician Daina Taimina in about 2002. Although called a model of a plane, it is not flat like a Euclidean plane and its lines are not straight. However, lines on any plane, Euclidean or hyperbolic, are still the shortest paths along the plane connecting two points.
- The distinguishing difference between a hyperbolic plane and a Euclidean plane is that on a hyperbolic plane there are infinitely many lines parallel to a given line through a given point not on the given line. In this model lines are shown in yellow. The given line is the one closest to the top of the photograph and the given point is where the four other lines meet. None of those four lines will ever meet the given line, so they are all parallel to it.
- On page 27 of her book, Crocheting Adventures with Hyperbolic Planes, (Wellesley, MA: A. K. Peters, 2009), Taimina has a photograph of a similar model, with only three yellow lines through the given point. On page 28 she has another photograph of that model with the caption: “The red line is a common perpendicular to only two of these yellow lines.” That photograph illustrates that on a hyperbolic plane, just as on a Euclidean plane, there is only one line through a given point not on a given line that is perpendicular to the given line.
- Location
- Currently not on view
- date made
- 2002
- maker
- Taimina, Daina
- ID Number
- 2002.0394.01
- catalog number
- 2002.0394.01
- accession number
- 2002.0394
- Data Source
- National Museum of American History, Kenneth E. Behring Center
Adjustable String Model
- Description
- From the early nineteenth century, mathematicians and engineers have studied surfaces generated by motion. The gold threads of this model form a cylinder, the red ones a double cone. Rotating the top circle of the frame twists the gold threads and untwists the red ones, forming surfaces called hyperboloids. The blue threads, which initially lie in a plane, become a hyperbolic paraboloid. This model was made in Germany and exhibited at the Columbian Exposition, the world's fair held in Chicago in 1893. It came to the Smithsonian from the mathematics department of Wesleyan University in Connecticut.
- Location
- Currently not on view
- Currently not on view
- Date made
- 1893
- maker
- Brill, L.
- ID Number
- 1985.0112.009
- accession number
- 1985.0112
- catalog number
- 1985.0112.009
- Data Source
- National Museum of American History, Kenneth E. Behring Center
Model of a Riemann Surface by Richard P. Baker
- Description
- The mathematician R. P. Baker believed that models were essential for the teaching of mathematics. This model, which he constructed in about 1930, represents a Riemann surface defined by the equation w3=z, where the variables w and z represent complex numbers, i.e., numbers of the form a + bi where i is the square root of -1. Riemann surfaces are named after the 19th-century German mathematician, Bernhard Riemann. They are different from surfaces in three dimensions, such as spheres, that are defined by equations in three variables, all of which represent real numbers.
- Real and complex numbers behave differently. For example, any non-zero complex number has three distinct cube roots. For 1 the three cube roots are 1, (-1 + √3) / 2, and (-1 + √3 i) / 2 while for i the three cube roots are -i, (√3 + i) / 2, and (-√3 + i) / 2 .
- In this model, the bottom level represents the w plane, a plane of complex numbers that is not part of the Riemann surface. That surface is represented by the other three levels and rectangles connecting them. There are three levels because there are three different values of w that produce the same value of w cubed. The coloring of the surfaces indicates the connections between the values of w on the bottom level and the points that satisfy the equation w3=z on the surface.
- Location
- Currently not on view
- maker
- Baker, Richard P.
- ID Number
- MA*211257.074
- accession number
- 211257
- catalog number
- 211257.074
- Data Source
- National Museum of American History, Kenneth E. Behring Center
Model of a Hyperbolic Paraboloid
- Description
- In the late nineteenth century, a few Americans began to make geometric models like those previously imported from Europe. This string model, made by the firm of Eberbach in Ann Arbor, Michigan, is very similar to one made in Germany at about the same time. The model is adjustable. When the metal triangles lie flat, the surface formed by the strings is a rhombus. If the tips of the triangles are raised, the threads form a surface called a hyperbolic paraboloid. The model came to the Smithsonian from the Department of Mathematics at the University of Michigan.
- Location
- Currently not on view
- maker
- Eberbach
- ID Number
- 1982.0795.31
- accession number
- 1982.0795
- catalog number
- 1982.0795.31
- Data Source
- National Museum of American History, Kenneth E. Behring Center
Ship Model, Lighthouse Tender Joseph Henry
- Description
- This model represents the U.S. Lighthouse Tender Joseph Henry, a side-wheeled steamer built by Howard & Company in Jeffersonville, Indiana, in 1880. This 180-foot-long vessel was built for service along the nation’s inland waterways. Lighthouse tenders served both coastal and inland areas by delivering supplies, fuel, news, and relief and maintenance crew to lighthouses and lightships. They also maintained aids to navigation, including markers identifying channels, shoals, and obstructions. Based out of Memphis, the Joseph Henry worked along the Mississippi and Missouri Rivers until 1904.
- The vessel’s namesake, Joseph Henry, was America’s foremost scientist in the 19th century. His expertise was in the field of electromagnetism. Henry was a professor at the College of New Jersey (Princeton) when he was named the first Secretary of the Smithsonian Institution, a position he held from 1846 until his death in 1878. He also served on the U.S. Lighthouse Board (1852-78), and implemented various improvements in lighting and signaling during his tenure. This lighthouse tender was named in his honor at its launching two years after his death.
- Date made
- 1880
- 1962
- used
- late 19th century
- ID Number
- TR*321486
- catalog number
- 321486
- accession number
- 245714
- Data Source
- National Museum of American History, Kenneth E. Behring Center