Laying Out a Circle

squareOld time carpenters were able to use framing squares to do amazing design work.  They were able to draw perfect circles with a framing square without using the center point of a circle.

Challenge:  Draw a 6 inch diameter circle on a piece of OSB using a framing square without using the center point of the circle.

Materials:  scrap OSB board, 2 nails, 1 framing square per pair

Procedure:  Students are given the materials to draw a 6 inch diameter circle using a framing square.  Remind students they need to use both nails.  Remind students they cannot use the center point of the circle.  Allow time for students to play and experiment.

Once students find the “method” of drawing a circle, they need to provide geometric reasoning for why this works.

Solution:  Tack two nails to set the diameter you want, then rotate a framing square against the nails while you hold a pencil in the corner of the square (see photo below).  A right angle is inscribed in a semi circle.

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