Print and assemble the lampshade scale model as an aid to this discussion.
First, the top and bottom widths, s and t, of the panel are calculated. To visualize this calculation, the lamp shape is viewed from above. Each edge is inscribed in a circle with a diameter equal to the specified top and bottom width, d and e. These edge lengths can be approximated by dividing each circle's circumference by the number of panels. These dimensions, although not exact, will be close enough for stained glass work. Using, , 3.1416, the constant ratio of a circle's circumference to its diameter / radius, and knowing the circumference of a circle equals times its diameter, , the following calculations are made: , , where n = number of sides or panels. Last, the length of each panel, g, is determined by viewing the lamp shade shape from its side and observing that it can be divided into 2 right triangles and a rectangle. Each triangle contains the desired dimension, g, as its hypotenuse. Further, it can be observed that yielding . The Pythagorean Theorem is then applied to calculate g, in this case, . Substituting the value derived for f above, the final formula, , is developed. For example, for an 8sided lamp shade with desired dimensions of 12 inch height, 6 inch top width, and 12 inch bottom width, each panel is calculated to have a top width, s, of 3.1416 x 6 / 8 = 2.36 or 2 3/8 inches, a bottom width, t, of 3.1416 x 12 / 8 = 4.71 or 4 11/16 inches, and a length, g, of sq.rt.(144 + {(126)/2 x (126)/2}) = sq.rt.(144 + 3 x 3) = sq.rt.(144 + 9) = sq.rt.(153) = 12.37 or 12 3/8 inches. All dimensions are not exact but close enough for stained glass work. Some stained glass lampshade selfinstruction manuals and reference books express lamp patterns in terms of slope or angle of the sides to a horizontal plane. These patterns allow for resizing the finished piece while maintaining the desired shape and slope. In this case, the trigonometric SIN function is used to determine the length, g, of each panel. Given the slope angle, A, the formula is known, and with rearrangement, . For example a 12inch tall, h, lampshade with a slope of 76°, the height of each panel, g, will be 12/Sin 76° = 12/.97 = 12.37 or 12 3/8 inches. 

