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On Wed, 2006-10-04 at 14:51 +0000, Rafe Donahue wrote:
> In lugnet.robotics.edu, Merredith Portsmore wrote: • <snip>
>
> Meredith,
>
> Thanks for posting this. It is wonderful first shot at some of these • building
> topics.
>
> I am concerned, however, about the Pythagorean triangles on the • Stability link.
> The figures show two Pythagorean triangles, namely the 3-4-5 and • 6-8-10
> triangles. The figures, unfortunately and arguably incorrectly, show • the
> lengths as 4m, 5m, and 6m and 7m, 9m, and 11m. The first course on • beams
> defines one 'm' to be the distance between the centers of adjacent • holes. As
> such, the figure labels of 4m, 5m, and 6m (and the 7-9-11) are • misleading.
> Agreed, there is discussion in the text of there being six holes but • the
> distnace is really 5m, but this has all the ingredients to send your • typical
> 12-year-old packing. They can learn to count starting at zero or • compute the
> distance by subtracting one from the number of holes; we should work • hard to
> make sure that the explanations aren't internally inconsistent. The • 3-4-5 works
> with the Pythagorean theorem; 4-5-6 does not. Telling them that the • distances
> are 4-5-6 in the figure and then doing Pythagoras with 3-4-5 creates, • methinks,
> more problems than it solves.
This I would be concerned with too, as it would confuse my group also.
<snip>
>
> (It might be helpful to show that 5-12-13 and 7-24-25 are Pythagorean • triangles,
> too!)
>
> There are actually two further issues; although more minor, they • nonetheless
> should be addressed. First, the 'm' used in the figures is a • lower-case 'm',
> while in the text it is upper-case 'M'. Some standardization should • be used.
> Secondly, if one chooses to use lower-case 'm', one might want to • address issues
> in conflict with the SI base unit m, which is meters.
>
> Since we are working with Lego, I might suggest using 'stud' as a • unit,
> eventhough it is not part of the SI lexicon, as far as I know! My • understanding
> of 'stud' as a unit of measure in the Lego context is that it is • equivalent to
> the 'module' defined on your pages.
My own take on this is maybe Lego should borrow the "LDU" from the
community and use it. It is a measurement suited to Lego, and is already
in use. It means LDraw Unit I believe, and was specifically created for
representing Lego measurements in Lego CAD tools.
Cheers,
Danny
--
Danny Staple MBCS
OrionRobots
http://orionrobots.co.uk/blogs/dannystaple
(Full contact details available through website)
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In lugnet.robotics.edu, Danny Staple wrote:
> Rafe Donahue wrote:
>
> > The figures, unfortunately and arguably incorrectly,
> > show the [wrong lengths]
Dang. Yes, they do... and I'm ashamed to say I've known about those for some
time, and neither myself nor several other folks never picked up on that. Drat.
> > They can learn to count starting at zero
Since that's the way numbers work, that's how I'd teach (more to the point
that's how I *have* taught this - 3-4-5 (& other) triangles like this entered
the piture long before studless parts. I've also used the 1.5-2-2.5 version of
this.
> > I might suggest using 'stud' as a unit...
> ...maybe Lego should borrow the "LDU"...
I don't have a big problem with using "m" or "modulus" (confusion with meters is
possible... but, sadly, perhaps only for kids in Europe, where they would also
realize immediately how silly that was). As to "stud" or "LDU", well... there
are no studs (even if we adults know they are the same thing, distance-wise),
and LDU is longer. Personally, I'll still call them studs (or even just a
unitless number... "hey can you hand me that 12 long axle?").
--
Brian Davis
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On Sat, 2006-10-07 at 12:26 +0000, Brian Davis wrote:
> I don't have a big problem with using "m" or "modulus" (confusion with meters is
> possible... but, sadly, perhaps only for kids in Europe, where they would also
> realize immediately how silly that was). As to "stud" or "LDU", well... there
> are no studs (even if we adults know they are the same thing, distance-wise),
> and LDU is longer. Personally, I'll still call them studs (or even just a
> unitless number... "hey can you hand me that 12 long axle?").
Hmm I generally use a unitless number when working with Lego here.. But
I do remember having it drilled into me at school how bad that is, we
had a math teacher who used to bounce up and down red in the face when
people failed to mention the units.
I forgot they still use old imperial units over the pond.. Do they
actually still teach using those in schools? Isn't SI on the curriculum
over there?
Danny
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