Integraph
Encyclopedia
An Integraph is an instrument used in mathematics for plotting the integral
of a graphically defined function
.
It was invented independently about 1880 by the British physicist Sir Charles Vernon Boys and by Bruno Abakanowicz
, a Polish-Lithuanian mathematician from the Russian Empire
.
An integraph consists of a rectangular carriage which moves left to right on rollers, two sides of which run parallel to the x axis on the Cartesian plane
. The other two sides are parallel to the y axis. Along the trailing vertical (y axis) rail, slides a smaller carriage holding a tracing point. Along the leading vertical rail slides a second smaller carriage to which is affixed a small, sharp disc, which rests and rolls (but does not slide) on the graphing paper. This disc can rotate about its point of contact with the paper. The trailing carriage is connected both with a point in the center of the carriage and the disc on the leading rail by a system of sliding crossheads and wires, such that the tracing point must follow the disc's tangential path.
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
of a graphically defined function
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
.
It was invented independently about 1880 by the British physicist Sir Charles Vernon Boys and by Bruno Abakanowicz
Bruno Abakanowicz
Bruno Abdank-Abakanowicz was a mathematician, inventor and electrical engineer.- Life and Nationality :Abakanowicz was born in 1852 in Vilkmergė, Lithuania, then part of the Russian Empire. After graduating from the Riga Technical University, Abakanowicz passed his habilitation and began an...
, a Polish-Lithuanian mathematician from the Russian Empire
Russian Empire
The Russian Empire was a state that existed from 1721 until the Russian Revolution of 1917. It was the successor to the Tsardom of Russia and the predecessor of the Soviet Union...
.
An integraph consists of a rectangular carriage which moves left to right on rollers, two sides of which run parallel to the x axis on the Cartesian plane
Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...
. The other two sides are parallel to the y axis. Along the trailing vertical (y axis) rail, slides a smaller carriage holding a tracing point. Along the leading vertical rail slides a second smaller carriage to which is affixed a small, sharp disc, which rests and rolls (but does not slide) on the graphing paper. This disc can rotate about its point of contact with the paper. The trailing carriage is connected both with a point in the center of the carriage and the disc on the leading rail by a system of sliding crossheads and wires, such that the tracing point must follow the disc's tangential path.
Reference
- Granville, William. Elements of Differential and Integral Calculus, New Edition. Ginn and Company. NY, NY, 1934