Binom 3D

Binom 3D

This model demonstrates the binomial theorem for the third power as a puzzle of the different terms:

(a+b)³ = a³ + 3a²b + 3ab² + b³

When constructing a cube with a side length of a+b (where a and b represent the side lengths of the two smaller cubes), in addition to the cubes with volumes a³ and b³, you also need three rectangular prisms each with side lengths a, a, and b or a, b, and b. This creates the mixed terms 3a²b and 3ab².

In this puzzle, all terms of the binomial theorem are visible, showing how they combine to form a larger cube with the volume (a+b)³.

The puzzle features an elegant stand, allowing for a stylish display of the binomial theorem to the third power ;-)

Printing and Assembly

• Printing Plate 1: Parts
  Ideally print in 4 colors using AMS (print order “by object”).
  If you do not have AMS, you can also print the four different sets of parts individually in different colors
  I used a smooth printing bed (“Smooth PEI Plate”) and ironed the surfaces. This makes all sides of the cubes look uniform.
  I set the infill to 5% (Gyroid), as the cubes do not require high stability.
• Printing Plate 2: Stand
  The stand consists of three side parts and a base. I chose a subtle color (gray).
  The three side parts are first glued together with super glue.
  Then the resulting corner is also glued into the triangular recess of the base.

Have fun with the binomial theorem in 3D!