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Rolls smoothly like a ball without the smooth edges. Used by Leonardo da Vinci and discovered by Euler.
Rolls smoothly like a ball without the smooth edges. Used by Leonardo da Vinci and discovered by Euler.
Rolls smoothly like a ball without the smooth edges. Used by Leonardo da Vinci and discovered by Euler.
1,629 backers pledged $126,296 to help bring this project to life.

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Orbiform: A mathematically perfect solid of constant width

$126,296

1,629

Thank you Backers for the successful campaign!!!!

If you missed out on our Kickstarter, jump on over to AltDynamic.com to get your Orbiforms!

Click to Visit. We will be posting Orbiform updates there too.
Click to Visit. We will be posting Orbiform updates there too.

An Orbiform is a little-known, unintuitive geometric shape, with fascinating mathematical properties. Orbiforms were unwittingly used by polymath Leonardo da Vinci in 1514, mathematically discovered by mathematician Leonhard Euler in 1771 and placed in application by engineer Franz Reuleaux in 1876.

We are Kickstarting a 3D Orbiform derived from a triangle to spread our enjoyment of mathematics and design with math lovers, designers, creators, educators and students.

Some of the many prototypes made in Copper, Brass and Stainless Steel.
Some of the many prototypes made in Copper, Brass and Stainless Steel.

An Orbiform is an amazingly aesthetic and elegant desktop sculpture to add to any workspace. It is a great conversation piece, yet also meditative to roll around. Made from high quality materials and precision machined, the stylish Orbiform is a representation of where art and math meet.

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Math Talk

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

This 2D diagram shows how an Orbiform keeps the exact same width, in all orientations.
This 2D diagram shows how an Orbiform keeps the exact same width, in all orientations.

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

This diagram shows how a 3D Orbiform can simultaneously touch all six faces of a cube regardless of how it is positioned.
This diagram shows how a 3D Orbiform can simultaneously touch all six faces of a cube regardless of how it is positioned.

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 Euler.

Leonardo da Vinci and  Leonhard Euler
Leonardo da Vinci and 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. 

The the flat board above the Orbiforms always stays at the same height, regardless of how it is rolled, just as if three spheres were under it.
The the flat board above the Orbiforms always stays at the same height, regardless of how it is rolled, just as if three spheres were under it.

The Orbiform also holds a unique property, as it is the smallest rotated shape by volume to have constant width, meanwhile a sphere is the largest. Below is the derivation of an Orbiform with width of unit 1.

Integral Solid of Revolution Method Used
Integral Solid of Revolution Method Used

The above total volume (purple plus green) is .449. A Sphere, of diameter 1, would be .52, 15.8% larger than an Orbiform.

Precision Machined

Orbiforms are available in stainless steel, copper and brass. Each metal is precision CNC (computer numerical control) machined and then hand finished in one of three surface finishes. You can choose a satin, mirror polish or machine finish. The pictures below show the nine different options. These are not renders. 

Each Orbiform is 1.4 in. (3.55 cm) in width. Stainless Steel weighs 161 g (5.67 oz.), Brass 159 g (5.96 oz.), and Copper 180 g (6.35 oz.).

Stainless Steel with Surface Finishes: Satin, Mirror Polish, Machine
Stainless Steel with Surface Finishes: Satin, Mirror Polish, Machine
Copper with Surface Finishes: Satin, Mirror Polish, Machine
Copper with Surface Finishes: Satin, Mirror Polish, Machine
Brass with Surface Finishes: Satin, Mirror Polish, Machine
Brass with Surface Finishes: Satin, Mirror Polish, Machine

Notes on Finishes: The satin finish is just like the metal finish on an Apple computer, it is not reflective and hides finger prints extremely well. The mirror polish is literally as reflective as a mirror. You can shave in it or see what is happening behind you. We didn't call it mirror polished for nothing. The machine finish looks brushed, but it is actually a precision machined surface. The machine finish is so precise and fine, that it creates a diffraction grating, which will reflect poly-chromatic light into its constituent colors, showing a rainbow.  

A macro shot of the Machine Finish where you can really see the even and precise texture.
A macro shot of the Machine Finish where you can really see the even and precise texture.
Mirror Polished at every angle.
Mirror Polished at every angle.
Satin Finish absorbs light and has a texture similar to an Apple computer.
Satin Finish absorbs light and has a texture similar to an Apple computer.

Production Milestone Timeline

Each dot represents a milestone. We will send project updates about these milestones as they happen to keep you updated just as we have done in our past campaigns. We will not be like other Kickstarter campaigns that leave their backers in the dark and guessing as to what is happening. Every order will also have tracking. 

Pledge Rewards

When the campaign ends, you will receive a Kickstarter Backer Survey. In every Backer Survey you can choose your material options and finish options. We have listed May as to when pledges will be shipped. Message us if you have a question on how to pledge.

Notes on Pledges: We are trying to make as many combinations of materials and finishes available as possible. Here is an example. If you choose the "3 Orbiforms" reward category, you can choose any combination of metals. You can also choose any combination of finishes for those metals. For example, you can choose a brass mirror polished, a copper in satin, and a stainless steel machine finish.

The Brass Machine Finish Orbiform with some of our other favorite gear.
The Brass Machine Finish Orbiform with some of our other favorite gear.

Risks and challenges

All of the pictures in our campaign are of prototypes we have made to ensure quality and we will be following the same machining methods for large scale production. We have manufacturing nailed down! Additionally, we will ship all packages with tracking!

We have a track record of successfully fulfilling our campaigns and we are confident we can successfully bring Orbiforms to life for all of our backers! Thank you for visiting our campaign! :)

We will give regular updates post-campaign to make sure all backers are in the loop!

Please contact us at AltDynamic.com or send us a message through Kickstarter's messaging system if you have a question!

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    1 Orbiform - Early Bird Special!

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    1 Orbiform - Steel Early Bird Limited!

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    1 Orbiform - Early Bird

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    1 Orbiform - Early Bird Limited!

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    2 Orbiforms Early Bird

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    Metals: Copper, Brass & Stainless Steel.

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    2 Orbiforms Early Bird Limited

    Mix and match. Any combination of metals and finishes. Choose your favorites!

    Metals: Copper, Brass & Stainless Steel.

    Finishes: Mirror Polish, Satin, Machine Finish.

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    2 Orbiforms

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    Metals: Copper, Brass & Stainless Steel.

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    3 Orbiforms Early Bird

    Mix and match. Any combination of metals and finishes. Choose your favorites!

    Metals: Copper, Brass & Stainless Steel.

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    3 Orbiforms Early Bird Limited

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    Metals: Copper, Brass & Stainless Steel.

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    Metals: Copper, Brass & Stainless Steel.

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    4 Orbiforms Early Bird

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    Metals: Copper, Brass & Stainless Steel.

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    4 Orbiforms

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    6 Orbiforms Early Bird

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    Metals: Copper, Brass & Stainless Steel.

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    6 Orbiforms

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    8 Orbiforms Early Bird

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    9 Orbiforms Early Bird

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    Metals: Copper, Brass & Stainless Steel.

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Funding period

- (49 days)