Nets and Wire Frames
Geometry & Trigonometry
3D wireframe structures — geodesic domes, lampshades, sculptural frames — are built from struts meeting at nodes. Calculate every edge length and every angle between members using 3D coordinates and vectors.
Introduction
Wireframe and net structures, such as geodesic domes, lampshades or sculptural frames, are built from straight struts meeting at nodes in 3D space. Given the coordinates of each node, the distance formula gives every strut's length, and the vectors along two struts at a node give the angle between them. This exploration develops a general function that takes a structure's dimensions and returns the total length of material needed, and rebuilds the structure in 3D (for example in GeoGebra) using vector equations of lines.
Guiding Questions
- Choose a 3D frame or net structure. Which lengths can you calculate rather than measure?
- Use 3D coordinates and the distance formula to find every edge length in the structure.
- What total length of wire or strut does the structure need? Where could a designer save material?
- Find the angles between members using vectors. Why do certain angles repeat in real structures?