#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!”…
Adafruit publishes a wide range of writing and video content, including interviews and reporting on the maker market and the wider technology world. Our standards page is intended as a guide to best practices that Adafruit uses, as well as an outline of the ethical standards Adafruit aspires to. While Adafruit is not an independent journalistic institution, Adafruit strives to be a fair, informative, and positive voice within the community – check it out here: adafruit.com/editorialstandards
Stop breadboarding and soldering – start making immediately! Adafruit’s Circuit Playground is jam-packed with LEDs, sensors, buttons, alligator clip pads and more. Build projects with Circuit Playground in a few minutes with the drag-and-drop MakeCode programming site, learn computer science using the CS Discoveries class on code.org, jump into CircuitPython to learn Python and hardware together, TinyGO, or even use the Arduino IDE. Circuit Playground Express is the newest and best Circuit Playground board, with support for CircuitPython, MakeCode, and Arduino. It has a powerful processor, 10 NeoPixels, mini speaker, InfraRed receive and transmit, two buttons, a switch, 14 alligator clip pads, and lots of sensors: capacitive touch, IR proximity, temperature, light, motion and sound. A whole wide world of electronics and coding is waiting for you, and it fits in the palm of your hand.
Have an amazing project to share? The Electronics Show and Tell is every Wednesday at 7pm ET! To join, head over to YouTube and check out the show’s live chat – we’ll post the link there.
