A harmonograph is a mechanical apparatus that employs pendulums to create a geometric image. The drawings created typically are Lissajous curves, or related drawings of greater complexity. The devices, which began to appear in the mid-19th century and peaked in popularity in the 1890's, cannot be conclusively attributed to a single person, although Hugh Blackburn, a professor of mathematics at the University of Glasgow, is commonly believed to be the official inventor.^[1] Simple gravity pendulum assumes no air resistance and no friction of/at the nail/screw. ... Lissajous figure on an Oscilloscope Lissajous figure in three dimensions In mathematics, a Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations which describes complex harmonic motion. ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ... The University of Glasgow, founded in 1451, is the largest of the three universities in Glasgow, Scotland. ...

A simple harmonograph uses two pendulums to control the movement of a pen relative to a drawing surface. One pendulum moves the pen back and forth along one axis and the other pendulum moves the drawing surface back and forth along a perpendicular axis. By varying the frequency of the pendulums relative to one another (and phase) different patterns are created. Even a simple harmonograph as described can create ellipses, spirals, figure eights and other Lissajous figures. An open surface with X-, Y-, and Z-contours shown. ... Perpendicular is a geometric term that may be used as a noun or adjective. ... Sine waves of various frequencies; the lower waves have higher frequencies than those above. ... The ellipse and some of its mathematical properties. ... In mathematics, a spiral is a curve which turns around some central point or axis, getting progressively closer to or farther from it, depending on which way you follow the curve. ... A figure 8 is an expression describing a geometric shape that resembles the number 8. ... Lissajous figure on an Oscilloscope Lissajous figure in three dimensions In mathematics, a Lissajous curve (Lissajous figure or Bowditch curve) is the graph of the system of parametric equations which describes complex harmonic motion. ...

More complex harmonographs incorporate three or more pendulums or linked pendulums together (for example hanging one pendulum off another)

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External links

• A complex harmonograph with a unique single pendulum design
• Free plans: how to make a Large Harmonograph
• Online interactive Harmonograph