Tam Pattern v 1.0

My first thoughts on 
how to construct the tam pattern
(using high school geometry)

  1. First, calculate the radius of the circle that marks the edge of the seam allowance for the headband.  (See HERE on how to figure this out).
  2. Next, inscribe a circle of that radius on a piece of paper (marking center). Draw a line through the center of the circle & then bisect the angles with a compass until you have eight equal angles (8 spokes):

    figure 6
  3. Bisect one of those eight angles with a line that we will call z, which intersects the original circle at Y:

    figure 7
  4. Using compass and ruler, find a point X along z that is equidistant from point Y and from each of the adjacent bisecting lines at a right angle from z.  (X will be the center of a circle passing through W, Y, and V; think of it as the largest circle abutting Y that will fit between the two spokes on either side of z).  (This is the hardest part, but not impossible):

    figure 8
  5. Once you have marked points W & V, you have the radius of the circle in which the octagon will be inscribed.  Use a compass, with point in center of original circle, draw the circle that passes through W and V.  The points where this new circle crosses the eight spokes are the corners of the octagon.  Using a ruler, draw the sides of the octagon:

    figure 9
  6. Then mark point U on z, whose distance from X = X’s distance from Y.  (This will be the point of the triangle that gets folded under when you make the cap.   It is also the point where the circle centered on X and passing through W and V crosses z (see #4).  Isn't geometry amazing?
  7. Now construct another circle on the original center point, this time passing through U (the outermost circle in figure 10).  This will be the line that, when pleated, folds down to the original seam line (the innermost circle in figure 10):

    figure 10
  8. Finally, figure out how much bigger your fabric circle needs to be than the circle through U.  From my paper model, I’d suggest extending the radius by a little more than half of the distance from X to U.

    final pattern (in miniature)!
Of course, you won't be able to fit the real pattern onto a sheet of graph paper, unless you are making a tam for a doll.    

 Here's a better pattern

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