2D to 3D Spaces Using Straight Lines

2D to 3D Curves using Straight Lines Authors: Juliette Hancock, Jeanine Hancock, Valentina Sandoval and Caleb Sandoval Hyperbolic Paraboloid Our project explores how to create curves using straight lines in two-dimensional and three-dimensional spaces. Two-dimensional Parabolic Curve In two dimensions, we are going to use pencil and paper to create parabolic curves using straight lines. A parabolic curve is a U-shaped curve that is formed by intersecting lines to equally spaced points. Then, we are going to sew colored string on the parabolic curves to create string art. Three-dimensional Hyperbolic Paraboloid We plan to expand our two-dimensional projects into three dimensions by creating two different types of hyperbolic paraboloids. A hyperbolic paraboloid is a saddleshaped structure that has both convex and concave curves. In the first project, we are going to use long coffee stirrers to create a hyperbolic paraboloid sculpture that is embedded in a tetrahedron, or triangular pyramid. In the other, we are going to use sliceforms to create hyperbolic paraboloids. Applications Hyperbolic paraboloids are used in everyday life. We see examples of it in food, bridges, roofs, and apparel. •Pringles potato chips use the hyperbolic paraboloid shape to perfectly stack their chips in a cylinder, which protects their chips from breaking and uses less shelf space. It also gives the consumers more chips per container. •In architecture, many structures use hyperbolic paraboloids. A church in Jackson NJ (our hometown), St. Aloysius, as cited in Architect Magazine, has a hyperbolic paraboloid roof. This is often used as an inexpensive solution to long-span roof requirements, such as in sports arenas. The roof at the church has elegant and fluid lines like those you might see in a fabric tent. The “tent” of St. Aloysius church is made from standing seam metal panels. It is a beautiful structure to view from inside and outside (convex and concave). •In apparel, we also see hyperbolic paraboloids on two sides of a tricorn hat (pirate hat), and a nun's Wimple (hat). What We Learned We learned what hyperbolic paraboloids are, how to create them in various ways, and practical applications of them. We discovered the difference between a two-dimensional parabolic curve and a three-dimensional hyperbolic paraboloid. We found out the definitions of convex and concave in relation to hyperbolic paraboloids.