The Multi Space Dimension of Autodesk Inventor

Relativity says we live in four dimensions. String theory says it is 10. What are ‘dimensions’ and how do they affect reality?

With three axes, we can describe forms in three-dimensional space. And Every point is uniquely identified by three coordinates. A Sphere can be described as:  x² + y² + z² = 1.

So, a sphere that sit in four-dimensional space can be legitimately described as:

x² + y² + z² + p² = 1

Our human brain can only receive and interpret a 3D world. When it comes to a 4, 5 or more dimension, our Engineering drafting become completely useless. Here are some examples I did with Inventor using its solid bodies Sweep feature:

1. Colliding 3 dimensions to a common point, Inventor created an object that can be both sphere/cube. Is it a sphere or a cube?

2.  Inventor can also be used to create a Hypercube frame in which our Engineering Standard CAN NOT present it on a drafting paper.

These are 6 views of the same object, but why the 3 isometric views are completely different? Inventor showed that the shadow of 4D cube frame is the 3D cube.

3.  Turn 3D cube frame into a 4D spiral ramp, we can see how De Vinci created a staircase that have the same entrance, but King, Queen, servants, and chauffeurs can never run into each other 😊

4. My Klein Flower Vase is a 4D object of a 3D möbius loop.

The log was inspired after watching this fantastic video:  Things to See and Hear in the Fourth Dimension. A great and simple mathematic lecture where it shows how four-dimensional shapes appear in a 3D world in a hands-on talk. Another great reading is this Radical dimensions