Description
This drawing illustrates different geometric techniques to construct a parabola. Mode 1: Use the slider to go through the parabola construction using tangents: 1-2) the lines tangent to the parabola at the supports intersect on the vertical centreline of the parabola at twice the height of the parabola above the closing string (rise h); 3) subdivide the tangents into the same number of segments; 4-8) connecting the corresponding points results in the discrete enclosing curve of the parabola. Mode 2: Use the slider to go through the parabola construction using secants: 1-2) the lines tangent to the parabola at the supports intersect on the vertical centreline of the parabola at twice the height of the parabola above the closing string (rise h); 3) connecting the supports with the apex of the parabola results in the secants of the parabola; 4) a parallel line to the closing string is tangent to the apex of the parabola. A vertical line at quarter span l intersects with the secant and the tangent of the parabola. The midpoint of these intersection points is the quarter point of the parabola. 5-8) the procedure is repeated to construct the eighth points of the parabola.