Crocheted Model of the Hyperbolic Plane
date: label: date made
content: 2002
name: label: maker
content: Taimina, Daina
notes: label: Description
content: 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.
label: Description
content: 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.
label: Description
content: On page 27 of her book, <I>Crocheting Adventures with Hyperbolic Planes</I>, (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.
label: Location
content: Currently not on view
topic: label: web subject
content: Mathematics
label: Subject
content: Women's History
setName: label: See more items in
content: Medicine and Science: Mathematics
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content: Women Teaching Math
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content: Women Mathematicians
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content: Science & Mathematics
creditLine: label: Credit Line
content: Gift of Daina Taimina
dataSource: label: Data Source
content: National Museum of American History
identifier: label: ID Number
content: 2002.0394.01
label: catalog number
content: 2002.0394.01
label: accession number
content: 2002.0394
objectType: label: Object Name
content: geometric model
physicalDescription: label: Physical Description
content: fabric (overall material)
label: Physical Description
content: yarn (overall material)
label: Measurements
content: overall: 16 cm x 40 cm x 29 cm; 6 5/16 in x 15 3/4 in x 11 13/32 in