Round Square Combinations are Surprising

November 30, 2023 · Posted in 1st Principles, science · Comment 

All four of these solids are Round Squares. I thought I had a general rule for calculating the combinations when I found the first two but then I found another and another. Is there a general formula for all the possible combinations. What are the parameters? Numerically there could be 6 but I do not think geometrically 6 are possible. This gets more confusing for Round Triangles or Square Triangles.

Cylinder is the obvious round square.


Cones are round triangle. Two triangles for a square. Two cones form a round square.

Union of two cones

Combinations of 3D shapes are either unions or intersections. The intersection of a cylinder and a wedge makes a Round Square Triangle. The union of two half height Round Square Triangles form a Round Square.

Intersection of a cylinder and a diamond extrusion.

Intersection of two cylinders rotates 90 degrees from each other leaves a square and two rounded sides for the Fourth Round Square.

Intersection of cylinders rotated 90 degrees from each other,

I found the first two using pencil and paper. The third with FreeCAD thinking in a subtractive then additive fashion. The fourth I found using OpenSCAD. The different approaches enabled finding the alternatives. I would not have found the fourth type using pencil and paper, the CAD software showed me what I described.

How would you go about finding a proof for a general formula?

Day 34 in Bangkok – Measuring Fat, Products, & Desires

March 20, 2019 · Posted in innovation · Comment 

Day 34 of First Principles in Bangkok is a product review of a Xiaomi Mi Fit Smart scale as an example of measuring fat to explain my startup app QuickMatch that measures “fuzzy” desires. I cover the entire process of choosing the product, receiving it, setup, & using it. There are many meta lessons in this video.

Easily Solving Your Biggest Future Challenges Keynote @ BTOES

July 22, 2017 · Posted in innovation · Comment

The world is changing faster and faster. Automation, globalization, and the Internet changed the rules that worked in the past. The future challenges will not be like the past.

Today, rules change almost as quickly as you can learn them. Process will not help you in this increasingly more rapid paced, higher stakes environment. To succeed, you need a new way of thinking.

You need to think predictively.

In this keynote I explain the discovery of a new way of thinking that anyone can use to:

  • Solve seemingly unsolvable problems on demand
  • Map future innovations for products & services, processes, & business strategy
  • See 5X, 10x, even 20X improvements hiding in plain view

The crucial piece needed for success that is missing from Agile, Lean, 6 Sigma and all process focused systems.