A catenary is a shape resembling a parabola; it looks like “a hanging flexible chain or cable when supported at its ends and acted upon by a uniform gravitational force (its own weight),” as stated by Wikipedia. Originally Leonardo da Vinci concluded it was a parabola. However, later in the century, a group of mathematicians and physicists proved that this was incorrect and eventually named this new curve a hyperbolic cosine. Another interesting property about a catenary is that “a polygon, such as a square… can ‘roll’ smoothly on a track made of segments of catenaries,” according to the UBC Mathematics Department.

An image was added, coordinated, and tabulated in Geometer’s Sketchpad. When all the coordinates were provided, two points were chosen and were plugged into the hyperbolic cosine equation. When the equation was used to find some y-values when x-values were inserted, they were very close to the actual original image curve.

Furthermore, when three points were selected and the equation a parabola that passed through all three points was calculated. When this parabola was sketched on top of our original catenary, they were very similar but they did not match directly over each other. When the parabola was graphed, the slope of the catenary was steeper than the one of the parabola.

Our model is best described as a catenary because our points labeled in Geometer’s Sketchpad fit best under an equation of a catenary. When a parabola or any other curve is applied, all points do not match up directly on top of the curve; the points near the vertex or the slope or steepness of the curve move away or towards the selected points. Thus, the given equation will not be of greater accuracy compared to the equation of the catenary.