How maple inspires me - Kid's Rule
212)
I mentioned in another blog entry that I was considering doing something with slide rules.
I mentioned in yet another entry how I hope to pass on some of newly acquired mathematical knowledge to my grandkids.
I'm working on a slide-rule for kids project. Although I didn't use maple in any phase of this project, it was definitely a stepping stone on the path that lead up to it. Below is a picture of one of the prototypes - a very rough prototype.
read more about it by clicking the "read more" link below ---
At the bottom of this message are a couple of links of pdfs that you can print-out to make your own. Be sure to follow the instructions or the scales won't be accurate. The one has the name of one of my grankids on it, so I also water-marked it. Anyone who wins the "prestiges" maple recognition award here as Jacques and Robert Israel have, are entitled to a copy of the watermarked version, non-watermarked, with the name of a kid replacing the name of my grandson. You guys let me know if you want one.
This may be a pipe-dream, but I hope to try and get these things into the school system for kids just starting to learn their multiplication. Those multiplication tables full of numbers are no way to learn anything "well", and looking at static numbers on a calculator is even worse.
The pdfs:
KidRuleBasic.pdf
KidRuleBetter.pdf
For those who might be interested, this project is a culmination of my understanding of the C and postscript languages, a little understanding of working with CAD and interpretation of g-code (used for cnc cutting), a little math, a little work with image editing, some wood working experience, and of course a love of the grandkids.
For those who think something like this can be done with image editing, I should let you know that I couldn't figure out how to do it that way. I started by trying to do it in just imaging software and found out pretty quickly that wasn't going to work. I then tried using C to create the bitmap file and was then confronted with how to send a file that was about the same size as an amish barn to the printer. Finally I figured out the only way to do it was with postscript. I'm pretty good with C and not so good with postscript, so I essentially, used C to create the postscript for the pdf, which seems to work pretty well.
My future plans are to do some screen printed on aluminum ones like the old Pickett rules, and some similar to the old celluloid-on-wood ones. The fancier one shown in "KidRuleBetter.pdf" will be embedded in some fine wood, the lesser one will be made similar to what is shown in the pdf and image above, and I will also make a simple set of sliding scales (non-logarithmic) that just do addtion and subtraction to get the kids started in sliding rules. Also, unless I burn-out somewhere along the way, I may make one with a LCD display that plots as well. Kinda like the same principle as a digital vernier caliper. In my opinion something that gives a lot of visual with the least amount of work such as a slider does compared with keypad entry is just so much easier to deal with.
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Comments
Creating postscript
Very cool.
Note that you have just taken your first steps towards the land that I am currently enjoying so much: programs-that-write-programs. Postscript is a full-fledged programming languages (which is a fact not enough people know); it just happens that it was mostly designed as a domain specific language (DSL) for ``printing'', even though it can be used for general purposes too. So writing a C program to generate Postscript really is writing a program-that-writes-programs. And you also stumbled upon another important point: some programs are hard to write by hand, but relatively easy to generate.
And to tie it in with Maple: mathematical programs are particularly easy to generate with Maple. Some time next week, I hope to have a blog post on just that.
Hi Jacques
I see what you mean - sometimes it just makes more sense.
I "could" make the multi-colored "Kid's Rule" using something like CorelDraw since it allows a separation between line art and graphic images. A program such as Corel's PhotoPaint or Adobe Illustrator does not - although PhotoShop does as far as I know. The separation is required in order to have the sharp black lines for the scales, while also having antialiasing for the fonts so the edges look nice and smooth. CorelDraw also makes it somewhat simple (comparitively speaking) to place the tick marks along the ruler since a line can be drawn and then it's x/y location along the datum line can be fixed manual according to it's logarithmic location but it's still so much simpler and quicker to just do it programmatically. I can create a scale from scratch programmatically in about 10 minutes, while it could take several hours using something like the CorelDraw. For example an entire scale can be drawn with a single loop within the C code generating the postscript and it's page offsets. Since it's vector type drawing, I can also easily scale and place anything anywhere on the page outside of the main scale drawing code.
I was also confonted with the dilemna of how to write the required g-code for my cnc router if I decide to cut one in aluminum or wood - such a task would require a lot of lines of code, but I can reuse some of the same code used to generate the postscript to create the g-code for the router. I was thinking about using postscript to print film that I could then use to screenprint all the colored text and backgrounds on aluminum (including the eye-saver yellow below the scale) and then using the router to cut the scales which I could then fill with ink to make them black. I've never done any screenprinting, but I learn pretty quickly so I should be pretty good at it by the time I'm ready to do it.
To embed the slide rule made with paper-on-wood ("http://2timv.com/math/SlideRule/primes/KidRuleBetter.pdf") into the fancy wood as I mentioned, I do need to use the cnc router in order to get an exact match between the cutting of the finished ruler and the cut-out in the wood - something the cnc is really exceptionally good at. If you're interested, here is a link showing my router, "http://2timv.com/math/SlideRule/router.gif" mine has a very good quality Kress spindle rather than the Porter Cable (a decent quality spindle), as ultimate precision where the bit meets the machine is of upmost importance. Anyhow, to do that, I just take a screenshot of the ruler, take that into CorelDraw and use it's bezier tool to make a spaced outline around it. Since CorelDraw will export CAD style DXF files in various formats, I can create a DXF from the outline which can then be translated into the g-code required by my CNC router by router software. If I need to edit the g-code directly for some final tweaking, I can do that either within the software or within a typical ascii text editor.
This is all probably a whole lot more than you're even interested in, but someone might be so there it is - for whatever it's worth.
CorelDraw does not scale either
I like the point about CorelDraw -- it agrees with what I just said in another thread about pointy-clicky solutions being sub-optimal because they do not scale up nicely.
circular sliderule begun
Yesterday, I began writing some of the code for a circular version of my "Kid's Rule" slide rule. I'm going to make it pretty colorful as I have the linear version. The full length lines will be shrunk into "tick-marks". I'll have some colored backgrounds and text as I have with the linear version shown in one of the pdfs listed above (not the image shown above). I'll be making it out of wood and it will have 3 rotating disks. This is really just a rough draft of the very beginning. For those familar with rulers, I'll have C,D,CF,DF on one side and A,B along with addition/subtraction on the other.
Here is a link to a pdf that contains it:
SRuleCirc1.pdf
If you decide to print the pdf to have a better look, make sure you choose an option to "fit page" rather than resize of the lines can become distorted.
here's a screenshot (too small to show the numbers at the green line ends):
about the learning of slide rules
I had someone ask me the other day how difficult it is to learn a slide rule so I should perhaps mention here that it's very easy.
Prior to back in august when I saw (and purchased) my first slide rule in an antique shop in abilene kansas, I had never held one in my hands or had even a clue as to how the things worked. I was quickly surprised to find out that even though they have only about 10" worth of tick-marks defining the scales they are capable of dealing with very large numbers with very good precision. For example, a sequence of numbers to multiply and divide usually require only a few placements of the slide to come up with the correct answer. Large numbers are easily broken down and again require only a few moves of the slide. They are great for electronics as well where they excel at determing things like phase angle, impedance, capacitive and inductive reactance, back and forth between rectangular to polar transformation, and of course things like parallel resistance, ohm's and watt's law, and a lot of other calculations are a cakewalk for the humble slide rule!
Did you know that some of the first astronauts in space took a 6" slide rule along with them on their trip to use as their calculating device. In fact that very rule was up for auction for over $6,000 on ebay about a month ago. Copies of that rule can be purchased for less than $40 occasionally on ebay.
Believe me when I say that if I can figure out how to use one, just about anyone is most ikely able to as well.
So, what does any of this have to do with Maple? Well, as with anything else the more you learn about any subject, the easier it is to apply those very same principles to other subjects. As I mentioned earlier in this thread, some of what I learned in Maple helped me in understanding and develop the "Kid's Rule" slide rule that I'm beginning to make.
Kid's Virtual Rule
I made a "virtual" Kid's rule:
virtual Kid's Rule
because a couple people asked me if I would. I really threw the thing together so it's kinda squished, the numbers are too big, and all the lines don't line up precisely due to pixelation. I'll make a couple of really nice ones a little later.
more circular slide rule
here's where the circular slide rule I'm making for the kids now stands:
if you want a pdf of it to print and try yourself, it's at the link below.
SRuleCirc3.pdf
Printing of the .jpg above is not recommended due to problems associated with pixellation of the image. Since the code used to create the rule is postscript for the pdf, printing the pdf will present the scales as intended.
This is a project still under construction. I'll have three rings for two scales on front for C/D and CF/DF. On the back, I'll have A/B and something else - not sure at this time what.