How to draft angles without protractors
Kaleidoscope patterns are based on equal angles making up a complete circle. A circle always contains 360 degrees. This geometric tidbit is the key ingredient in the recipe for piecing any wellbehaved eightpointed stars and hexagonal designs, including kaleidoscopes.
One difficulty quilters frequently run into is extending the angles generated by a protractor into long wedges. Now, through the magic of computers and the skills of mathematically savvy quilters, Sue Heltzer of College Park, MD and Susan Feldman of Kirkwood, MO, I present a painless, protractorless and faultless method for drafting a wedge up to 25" long, using 8totheinch graph paper. The following charts include the figures for 45, 60, and 36degree angles which result in eightsided, sixsided, and tensided kaleidoscopes, respectively.
To use the chart, plot point A (the apex of the wedge) at the junction of a bold horizontal and vertical inch line on 8totheinch graph paper. The following example refers to the 45degree chart. The idea is to:
1. Measure the first vertical length (1 1/2") from the apex down the axis. Use the graph paper's grid as a ruler to measure this distance quickly yet accurately. Resist the urge to mark a pencil dot. Instead, position a ruler horizontally on the grid line. Read across the chart to find the corresponding number (5/8") in the Horizontal Length column.
2. From this position, count and mark the corresponding measurement left and right along the horizontal length.
3. When three or more right and left dot positions have been marked in this way, connect the dots and you will have an accurate 45degree wedge.
Number of Pie Slices = 8 Degrees in Pie Slice = 45 



1 1/2"

..........................................  5/8"  
3 5/8"

..........................................  1 1/2"  
5 1/8"

..........................................  2 1/8"  
7 1/4"

..........................................  3"  
8 3/4"

..........................................  3 5/8"  
12 3/8"

..........................................  5 1/8"  
16"

..........................................  6 5/8"  
17 1/2"

..........................................  7 1/4"  
21 1/8"

..........................................  8 3/4"  
24 3/4"

..........................................  10 1/4" 
Number of Pie Slices = 6 Degrees in Pie Slice = 60 



2 3/8"

..........................................  1 3/8"  
3 1/4"

..........................................  1 7/8"  
5 5/8"

..........................................  3 1/4"  
6 1/2"

..........................................  3 3/4"  
8 7/8"

..........................................  5 1/8"  
12 1/8"

..........................................  7"  
14 1/2"

..........................................  8 3/8"  
15 3/8"

..........................................  8 7/8"  
17 3/4"

..........................................  10 1/4"  
21"

..........................................  12 1/8"  
24 1/4"

..........................................  14" 
Number of Pie Slices = 10 Degrees in Pie Slice = 36 



4 3/4"

..........................................  1 1/2"  
9 5/8"

..........................................  3 1/8"  
10"

..........................................  3 1/4"  
14 5/8"

..........................................  4 3/4"  
15"

..........................................  4 7/8"  
20"

..........................................  6 1/2"  
24 5/8"

..........................................  8"  
25"

..........................................  8 1/8" 