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A N N A R B O R P I O N E E R H I G H S C H O O L
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This page is my response to a question that came up when a fellow
planetarium director asked for suggestions on how to find the center of
his dome.
To find the center of a dome, you can use a geometry technique of circumscribing a circle around two isosceles triangles, only reverse the process and start with the circle: Cut a piece of string to a length that is roughly 1.7 diameters of the dome (if it is a 30 foot dome, cut it to about 50 feet. Tie a knot close to each end of the string, and then tie a knot exactly half way between the two other knots. Attach the center knot to any convenient point on the dome’s edge. Stretch out the two sides of the string and attach each of the end knots to a point where they also touch the edge of the dome. You now have an isosceles triangle (two equal sides). Temporarily attach a second piece of string between the two end knots in the first string. Tie knots in ends of the second string so they fall exactly on the endpoints of the first string. Remove the second string, fold it exactly in half, and tie a knot in the center. Reattach the second string to complete the triangle. The center of the dome lies along a line that connects the center of the second string and the knot in the middle of the first string. Tie a third string along that line. Even if the second string pulls toward center knot of the first, it will still mark the correct line. Repeat the process at a different position around the dome. Where the two third strings cross, there is the center of the dome.
This technique can be very accurate. The longer the
string, the better the accuracy. In college I worked for a contractor
who laid out a huge pole barn using only string and knots. Working on
the hilly, rutted terrain, it produced a barn that was square and level.
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