Abstract: A visual aid in which a background sheet, FIG. 1, features a diagram. It is desired to demonstrate that one part of the diagram, in this case the angle ACD can fit exactly on another part, in this case the angle ABC. The two parts are jointly used as the basis of a geometrical construction to locate the position of the center of rotation P. A transparent sheet (FIG. 2) is laid over the background sheet. The point Q is marked corresponding to P and the two sheets are pivotally assembled through P and Q. The relevant part of the background diagram, in this case the angle ACD is now copied onto the overlay sheet, in this case angle G. Pivotal movement of the overlay sheet will allow angle G to be alternately superimposed on angles ACD or ABC. The tongue T, fits in the slot S to limit the pivotal movement.

Abstract: FIG. 5 shows a background sheet A featuring the axes X and Y. A transparent strip E is pivotally assembled to A at the pivot point O. A transparent flat tube F is slidable on E. A straight line D is drawn on E and F through O. An operating button G is attached to F. A transparent cover sheet H is placed over the assembly. A small gap K is left between A and H by means of the distance pieces L. A slot J in the cover sheet H provides access to G. The axes may be calibrated to represent any entities involved in linear relationships, such as percentages, elements of multiplication, division etc. The gradient of the line D may be varied manually, thereby illustrating varying rate of proportionality.

Abstract: A planar member 21, is pivotally assembled to a transparent planar member 22, at pivot point 23. On the planar member 21, are the calibrated circle 24, the cosine/secant scale 25, and the sine/cosecant scale 26.On the transparent member 22, are the sine/cosine cursor circle 27, the tangent/cotangent scale 28, and the arrow head 29.For any relative position of the two members, the arrow head 29, points to an angle. Each of the six trigonometric functions of that angle is read where the appropriate scale is intersected by another line.FIG. 2, shows the device set at 150 degrees as an example. The sine and the cosine of 150 degrees are read at intersections 33 and 34 respectively. The secant and the tangent at intersection 31. The cosecant and cotangent at 32. The sign of any cotangent reading needs to be reversed.