Workshops will be held concurrently between 1:15-3:15 p.m. and 3:30-5:30 p.m.
ProvWash 215, 1:15-3:15 p.m.
A hyperbolic plane is a mathematical surface that has constant negative curvature-the opposite of a sphere, that has constant positive curvature. In this workshop you will crochet your own hyperbolic plane, even if you’ve never crocheted before. Our research shows that these models are a wonderful antidote to math anxiety.
Artwork by Ruthie Ford
Chace Room 504, 1:15-3:15 p.m. & 3:30-5:30 p.m.
Although it would be unworkable for a single-frame dome, the ‘floppy hub’ seems very stable with a trussed structure. Although the trussed dome seems very complex, it may be more forgiving in terms of tolerances than a single-frame dome. A tetrahedron is very strong even if the vertices are somewhat floppy. It may allow the construction of fairly large structures with little if any staging.
The floppy hub also accommodates a range of strut diameters, rather than requiring standard dimensions, and therefore can utilize bamboo. Any component of the trussed floppy hub bamboo dome can be replaced.
The purpose of this model is to investigate the possibility of low-cost domes that can enclose traditional houses, and provide for modified temperature areas for recreation and food production.
As they say in the fracking ads: “Just think about it.”
Artwork by Zendome
Nature Lab Room 11, 3:30-5:30 p.m.
Everyone is invited to participate in the construction of a cool geometric sculpture from laser-cut wooden components, which connect in an intricate manner. The spherical geometry of the form relates to icosahedral ideals that Fuller promoted, but unlike most of Fuller’s designs, the structure is chiral and based on interpenetrating planes. The best way to understand it’s geometry is to build it and learn by doing.
All materials will be provided and Hart will explain the mathematical ideas along the way. Thematically, the design is inspired by the harbor seals, which visit the area, so at the end of the workshop, expect to see a three-foot diameter assemblage of sixty seals.
Artwork by George Hart
Nature Lab Room 11, 1:15-3:15 p.m.
Professor Pavlides will show how to fold and weave paper into rigid crystals and shape-shifting elastegrities, which comprise a network of rigid and elastic parts. First order elastegrities have an unusual property: when squeezed, they compress from an expanded icosahedron rotating three dimensionally contracting into a rigid octahedron, but when released, they spring back into the original icosahedron. The internal elastic forces maintain the shape’s integrity, thus the name ‘elastegrity.’
Artwork by Leftheris Pavlides
ProvWash Room 205, 1:15-3:15 p.m. and 3:30-5:30 p.m.
The workshop will focus on the polygon chaining methodology and how it is applied to standard geodesic topologies, and allows for an entire new set of geodesic patterns to be explored and built. Presentation will detail the mathematics behind the methodology as well as the development and short history with respect to the standard approaches to geodesics based on IASS papers from 2011 and 2013. This workshop will focus on a small subset of paper models (3) to be assembled that will illustrate the approach and results.
Nature Lab Room 12, 1:15-3:15 p.m. & 3:30-5:30 p.m.
The Amazing Geometry Machine is an invention of tubes and strings to form a dynamic model exhibiting symmetries in polyhedral assemblies. Polyhedra are built with tubes passing through a polyhedral core and colored loops of string through those tubes. The color loops of string define the edges of a resulting polyhedron. The polyhedra change shape and/or interpenetrate as a result of sliding the tubes inline (inline translation) depending on the pattern.
Dynamic Polystring Transformahedra Modeling extends the realm of tensegrity into dynamic models. Materials provided for both three and four tube models.
Artwork by Dick Esterle
ProvWash Room 215, 1:15-3:15 p.m. & 3:30-5:30 p.m
On a flat surface, a circle and its radius can be used in a self-guided way to define an inscribed hexagon. This relationship is static, in that it’s constant for all circle sizes. A similar, but more complex and dynamic relationship exists between circles on a sphere’s surface. This is a dynamic relationship, in that it is a function of the circle’s size and the curvature of the sphere. From this dynamic relationship, will emerge geometric properties similar to that of the Platonic solids.
Participants will explore these geometric properties by drawing circles on a sphere’s surface. Using just a compass and following some simple rules, symmetric arrangement of circles will result define the vertices of the various Platonic solids. These circular patterns on the sphere will then be used as a blueprint to build cones structures. As a result, the cones will have inherited the geometric properties of Platonic solids which will become evident when these cones are used to create other 3D structures.
Chace Room 506, 1:15-3:15 p.m. & 3:30-5:30 p.m.
Joseph Clinton & Edward Popko
A short introductory description will be given on ‘Divided Spheres: Spherical Design in STEAM.’ The workshop will focus on building connections between multiple disciplines through hands-on modeling making. The art forms used will come from inspirations chosen from mathematician and monk Father Magnus Wenninger’s lifelong explorations of polyhedron.
Artwork by Magnus Wenninger