Titanium Orbiform & Orbiform Mini: A solid of constant width

Rolls smoothly like a ball, without the smooth edges. Machined from Titanium, Steel & Copper. Used by Leonardo da Vinci & Euler.

Story

Welcome to our 16th Kickstarter campaign! We have a track record on Kickstarter for providing unparalleled customer service and delivering quality products. We have been privileged to share our products with over 7,000+ backers around the world!

Introducing the Orbiform Titanium & Mini!

An Orbiform is a shape whereby its closed curves result in a constant width. A 2D Orbiform and circle can both be rotated between two parallel, fixed-distance lines and remain tangent to both lines at every orientation, as shown in the diagram below. Interestingly, the perimeter length of a circle and Orbiform can both be calculated with the equation pi*D=circumference.

No matter how the Orbiforms roll, the flat board always stays the same height. It’s as if there were three spheres underneath the board instead of these 3-dimensional shapes.

We are currently exploring how to add flamed titanium as an option.

Math Talk ◯

An Orbiform is a shape whereby its closed curves result in a constant width. A 2D Orbiform and circle can both be rotated between two parallel, fixed distance lines and remain tangent to both lines at every orientation, as shown in the diagram below. Interestingly, the perimeter length of a circle and Orbiform can both be calculated with the equation pi*D=circumference.

A 3D Orbiform is an analog to the 2D case. It is rotated on its axis of symmetry to create a convex body of revolution. A 3D Orbiform can be placed inside of a cube in any orientation and simultaneously, tangentially touch all six faces just like a sphere of the same width.

It is commonly thought that only a circle or sphere has constant width, but that is not the case. Leonardo da Vinci was unaware of the Orbiform’s constant width property, even while he used the shape in his own work. It would take another 257 years until the constant width property of Orbiforms was realized and mathematically proven by Leonhard Euler.

The Orbiform can roll like a sphere, even while having a point, an edge and not being a smooth curve. The main difference, is the center of mass of an Orbiform is not central like a sphere, so it won’t continue rolling unless a force remains on it.

Design & Precision Machining

AltDynamic Quality

Each Orbiform is machined from a solid bar of Titanium, Stainless Steel or Copper. We will NOT be casting them. Below you can see how our mini Orbiform compares to some of our other shapes.

Metals: Titanium, Copper, Stainless Steel

Weights

  • Copper: Classic Weight: 6.31 oz, 178 g, Mini Weight: 1.66 oz, 47 g
  • Stainless Steel: Classic Weight: 5.6 oz, 158 g, Mini Weight: 1.45 oz, 41 g
  • Titanium: Classic Weight: 3.2 oz, 90 g, Mini Weight: .85 oz, 24 g

Titanium is roughly half as dense as Copper. A US nickel is .18 oz (5 g), for reference.

Material Notes:

  • Copper will oxidize due to exposure to oxygen in the air, and will naturally patina and darken (just like a penny). Our Copper is solid Copper, not plated. The Copper can easily be cleaned in seconds with a patina removing solution. Copper is a very soft metal and scratches easier than Titanium or Steel. If you are concerned about scratching or color changing, we do not recommend Copper.
  • Stainless Steel and Titanium are similar. Both are hard, scratch resistant and will not patina like Copper will. Titanium is a slightly darker metal than Steel. The biggest difference is that Titanium is half as dense as Steel is.

Finishes – Machine, Mirror Polish, Satin

Machine Finish: This finish is straight off of the lathe. There is a fine radial texture from top to bottom. The Machine Finish will show all machining marks and textures, including light scratches inherent in the process. The underside of the Orbiform may have a small section with a lightly brushed finish to remove any burr which might be left from machining and to ensure roundness. The raw Machine Finish is rarely found on consumer goods.

Mirror Polish: This finish is highly polished to achieve a mirror finish. It is so reflective you can see yourself or see what is happening behind you. It is extremely lustrous.

Satin Finish: This finish has a flat sheen and hides fingerprints well. The surface is dotted with microscopic craters which diffuse light. This finish is similar to that found on the Apple MacBook Pro (and numerous other Apple products).

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