Hexagons Width Computation

Hexa-Flexagons Made Simply from A Strip of Paper

Just A Strip of Paper

Any piece of paper may be used to create a flexagon. Thin paper often works better for flexing purposes than thick paper. Unprinted flexagons, the kind made from a blank piece of paper are better suited to decoration than printed flexagons.

Accurately making the first 60º angle and the side it creates,
Accurately folding each new equilateral triangle,
Determining the width of the strip so that equilateral triangles may be formed and the full length of the paper may be utilized.

Determining the Width of A Hexa-flexagon Strip

Problem: Determine the width of a strip of 10 adjacent equilateral triangles so that the strip extends the full length of piece of paper and wastes no part of the length of the paper. Determine the width for:: a.) an 8 1/2" by 11" sheet of paper.; b.) a "W by L" sheet of paper.; c.) and 1 1 " by 17" sheet of paper.
Recall that an equilateral triangle may my be divided into two 30º - 60º - 90º triangles whose sides are 1 - - 2 in ratio. The width of the strip is units. The length is 5 1/2 triangles long or (5.5)(2) long or 11 units long.

a.)	For an 8 1/2" by 1 1 " sheet of paper, solve for W, the width:
	length ------ width	11 ------	=	11 inches ------ W inches
	W = or about 1.732 inches
b.)	For a W by L sheet of paper, solve for W, the width:
	length ------ width	11 ------	=	L inches ------ W inches
	W = L/11, about .1575L inches. For a "W by L" sheet of paper, the desired width is .1575 of the length of the paper.
c.)	For an 11 " by 17" sheet of paper, the desired width is 2.6768 or a small bit more than 2 2/3".

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