This reminds me of something I meant to mention earlier. In my early teens, I returned often to the Science Museum in South Kensington (London), where tucked away in an obscure gallery on an upper floor were a collection of decrepit plaster models of Archimedean polyhedra, their edges almost completely eroded by age and moisture. I eventually began painstakingly to design and build my own collection from cartridge paper, which with hindsight was a major step towards becoming a mathematician. The point of this is that there is --- in sufficiently geeky individuals at any rate --- a powerful intrinsic emotional response engendered by solid manifestations of symmetry --- and similar mechanisms --- which greatly exceeds that of flat representations, particularly where children are involved. Fred Lunnon [PS --- Henry, your reply address is malfunctioning again: when I hit "reply" this time (tho' not last time), my post was about to return only to you, rather than to math-fun!] On 8/19/11, Henry Baker <hbaker1@pipeline.com> wrote:
Some ideas for high school math (these are pretty obvious & lame):
* 3D plots, so students can actually feel the shapes. Yes, you can produce 3D color plots & manipulate them with 3D glasses using current high-end PC's, but sometimes kids like to see physical objects.
* experiment with reflective properties of different shapes -- e.g., lenses, reflective mirrors (need to be polished), etc.
* experiment with center of gravity, etc., of different shapes
* experiment with brachistochrone-type curves
* experiment with curves of constant width
* experiment with interlocking gears of different shapes
* experiment with boat/submarine hulls of different shapes being pulled through the water
etc.
Perhaps Mike's point also needing a laser scanner is quite important. But the XGP appeared before any decent digital cameras!
If I were a kid who had to get a CAT scan, I'd love to "print out" a copy of one of my own bones. That would be very cool!
--- I haven't studied CAD/CAM languages recently, but the ones from 10+ years ago were pretty uninspiring. Perhaps an artist/mathematician _without any "computer language" skills_ will show us how to do it better. We need some "direct manipulation" ideas for how to describe objects which are very different from the traditional computer language ideas.
At 03:57 PM 8/18/2011, Fred lunnon wrote:
The phrase "3-D printer" is catchy, but misleading: printing in the sense of reproduction of text is essentially two-dimensional.
Even in 2-D, pictorial reproduction and creation is technically more complex, involving skills lying completely outside the domain of DTP; its 3-D equivalent --- sculpture --- captures better what these devices do.
One obvious area of application (for which they are apparently already regularly used) is simply rapid prototyping of CAD/CAM designs, for which appropriate solid-modelling languages are already highly developed, having been utilised for many years to build virtual models for viewing on-screen, or (imposing crucial limitations) solid milling.
Looking beyond old-hat industrial plotting, there seems to be no obvious reason why --- for example --- PostScript cannot be immediately generalised to 3-D, and used to drive a laser sintering prototyper.
The technology is anyway still in its infancy: just around the corner are surely devices which will mix materials (cf. colour printing vs. black-and-white) and apply surface finishes, as well as improving resolution.
It will have arrived when some bright postgrad programs one of these engines to reproduce itself. Now there's a prospect providing food for thought ... [Though if Mike's 3-D photocopier hits the streets first, maybe even the postgrad will be redundant.]
Fred Lunnon
On 8/18/11, Henry Baker <hbaker1@pipeline.com> wrote:
I don't recall the exact date that the XGP showed up at MIT's Project Mac, but I think it was the very early 1970's. The XGP was the first bitmapped XeroGraphic Printer, and it changed the course of printing history, including leading inevitably to the Apple Macintosh/desktop publishing industry and the now ubiquitous "multifunction printer/scanner/fax" that probably all of you have in your homes.
The coolest thing about the XGP is that it was available to (nearly) anyone at 545 Tech Square, and it immediately became a huge hit. Once the appropriate page layout languages and fonts became available, people twiddled with them incessantly, until their theses looked like ransom notes!
One of the important steps along the way was the development of Knuth's TeX, which subsequently became the standard for mathematical publishing -- where it remains today.
---
Fast forward to 2011. 3D printers exist, but don't appear to have generated the same excitement as the original XGP. I'm not sure quite why, because a 3D printer is sooo much cooler than the XGP ever was. Maybe these printers are too expensive; maybe they're too slow; maybe they're too hard to access.
What is missing that would make the 3D printer today as exciting as the XGP was in the early 1970's ?
Does Knuth (or a Knuth-wannabe) have to come up with 3D TeX ?
What do mathematicians want from a 3D printer, anyway ?
What would be the effect of putting a free 3D printer into 100 universities ? 1,000 universities ? 5,000 high schools ? 10,000 grade schools ? 50,000 libraries ?
(I have no connection with any 3D printer company, but think that it is a major revolution.)