How to Wrap a Sphere

Overview

Objectives/Goals My goal is to find shapes that wrap a unit sphere with small area and perimeter in order to economize material usage in wrapping spherical objects. Methods/Materials I defined wrapping to be a noncrossing contractive mapping of a piece of paper into Euclidean 3-space, specifically sphere here. I computed and compared four different methods of wrapping a sphere -- two circles wrapping, two circles and a strip wrapping, strip wrapping, and petal wrapping. Results Two circles wrapping generates a 23.35% area waste but small perimeter. Two circles and strip wrapping generates a 7.08% area waste but big perimeter. In both petal wrapping and strip wrapping, as the number of petals increases and the width of strip decreases, the area of wrapping paper decreases and will approach infinitely close to the surface area of the sphere. However, the perimeters of strip increase much more rapidly than those of petals. Conclusions/Discussion From my project it is concluded that petal wrapping is the most optimal method in order to minimize material usage in wrapping spherical objects. The result is also useful to problems involving unfolding spheres from 3-dimension to 2-dimension, such as map projection and disassembly and reconstruction of spherical objects.

Competition history

• CSEF 2016 Mathematics & Computer Science · Entry S1403

Resources

• CSEF project summary ↗

Related projects

Closest projects by meaning, across every fair and year in the corpus.

Browse more like this

• All Computational Sciences projects
• CSEF Computational Sciences projects
• Every CSEF 2016 project