## #3DxMathematics – Fubini’s Theorem and the Mathematics of 3D Printing #3DThursday #3DPrinting

Andy at “3D Printing is the Future” asked a math professor what important mathematical principles apply to 3D Printing — and his professor said … Fubini’s Theorem! Here’s a selection of his post covering this concept.

3D Printing is about being able to print any object layer by layer.

I was cogitating on this one day and thought to myself: “Are there any 3 dimensional items we can’t print layer by layer?”

After all, it is assumed that a 3D printer can print ANY object – but is this proved? Is there a Mathematical Theorem that proves we can 3D Print anything? …

### Fubini’s Theorem

I am not a mathematical person once I need to go beyond algebra. So I asked Prof what it meant in blog author language.

He said that Fubini’s Theorem states that an object of n dimensions can be represented as a spectrum of layers of shapes of (n-1)-dimensional layers.

This means that a 3 dimensional shape (any shape in the real world) can be represented as layers of 2 dimensional shapes.

But…
“Well that is exactly what I wanted – thanks Prof!” I turned to walk away

“WAIT!” Prof screamed in righteous fury “There are some cases you need to know about!”…

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