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

Fubini's Theorem

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!”… 

Read more.

Associate Professor Alan Branford Director of Studies in Mathematics and Statistics 2


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