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The Steinhaus longimeter, patented by the professor
Length, shape and area
''Colloquium Mathematicum'' 3(1), 1–13, 1954. * Hugo Steinhaus:
Mathematical Snapshots
', 3rd ed. New York: Dover, pp. 105–110, 1999.
From
Information about patent
(DRGM 1241513)
Mathematical tools Cartography {{math-stub
The Steinhaus longimeter, patented by the professor Hugo Steinhaus
Hugo Dyonizy Steinhaus ( ; ; January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz Unive ...
, is an instrument used to measure the lengths of curves on maps.
Description
It is a transparent sheet of three grids, turned against each other by 30 degrees, each consisting ofparallel
Parallel is a geometric term of location which may refer to:
Computing
* Parallel algorithm
* Parallel computing
* Parallel metaheuristic
* Parallel (software), a UNIX utility for running programs in parallel
* Parallel Sysplex, a cluster of ...
lines spaced at equal distances 3.82 mm. The measurement is done by counting crossings of the curve with grid lines. The number of crossings is the approximate length of the curve in millimetres.
The design of the Steinhaus longimeter can be seen as an application of the Crofton formula In mathematics, the Crofton formula, named after Morgan Crofton (1826–1915), is a classic result of integral geometry relating the length of a curve to the expected number of times a "random" line intersects it.
Statement
Suppose \gamma is a ...
, according to which the length of a curve equals the expected number of times it is crossed by a random line.
See also
*Opisometer
An opisometer, also called a curvimeter, meilograph, or map measurer, is an instrument for measuring the lengths of arbitrary curved lines.
Description
A simple opisometer consists of a toothed wheel of known circumference on a handle. The whe ...
, a mechanical device for measuring curve length by rolling a small wheel along the curve
* Dot planimeter
A dot planimeter is a device used in planimetrics for estimating the area of a shape, consisting of a transparent sheet containing a square grid of dots. To estimate the area of a shape, the sheet is overlaid on the shape and the dots within the ...
, a similar transparency-based device for estimating area, based on Pick's theorem
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by Georg Alexander Pick in 1 ...
References
Bibliography
* Hugo Steinhaus: Zur Praxis der Rectification und zum Längenbegriff, ''Berichte der Sächsischen Akademie der Wissenschaften'' 82, 120–130, 1930. * Hugo Steinhaus: ''Przeglad Geogr.'' 21, 1947. * Hugo Steinhaus: ''Comptes Rendus Soc. des Sciences et des Lettres de Wrocław'', Sér. B, 1949. * Hugo SteinhausLength, shape and area
''Colloquium Mathematicum'' 3(1), 1–13, 1954. * Hugo Steinhaus:
Mathematical Snapshots
', 3rd ed. New York: Dover, pp. 105–110, 1999.
External links
From
MathWorld
''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science Dig ...
— A Wolfram Web Resource.
Information about patent
(DRGM 1241513)
Mathematical tools Cartography {{math-stub