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Here's a typical matchstick, or toothpick, puzzle. And I had somebody ask me how they
could use The Geometer's Sketchpad to create some matchsticks or toothpicks in order to
be able to manipulate them and work on these puzzles on a computer.
So I'm going to show how to create a Custom Tool that will allow us to make several matchsticks
or toothpicks easily.
So the first thing I'm going to do is go and—Document Options—I want to create a new blank page
in order to give us a workspace.
First thing I'm going to do is just create any old segment that's going to define the
length of the matchstick. And for reasons that I'll explain to you later, I want to
label the points… this is going to be the head of my matchstick. And I will label this
one the tail of the matchstick. Alright.
So, I want—oh, I didn't tell you about this part. The—when this person asked me "how
do I make these matchsticks or toothpicks, um, in Sketchpad," my first statement was
"well you could just of course use segments and explore the problem that way, right?"
But the problem with using just segments is that they don't always stay the same length,
and this might cause some problems with certain types of prob—um, certain types of puzzles
that require things to be the same length. So this person really wanted to be able to
create matchsticks that are the same length.
So, let me delete these. Now I can go back and and talk about the next step. In order
to create a bunch of segments that are the same length, or even one segment that's the
same length, in geometry the way that we duplicate lengths is with a compass. So I might in geometry,
uh, I would measure this length with a compass. I would put the pointy part of the compass
here and the pencil part of it here in order to measure that length. And then I would come
over here and say, okay, I use that length in order to create a circle. And then I can—or
even just an arc of a circle—and then I can create a segment that has that same length.
So this is just how I would do it with and actual compass on paper. But that doesn't
work in Sketchpad, because this circle is defined by this point and this point, and
it has nothing to do with the length of that segment. So I'm going to get rid of these
and show how to do this in Sketchpad, to use this segment to define the radius of the circle.
So, circles need a center and they need a radius, so what I'm going to do is put here
a point that's going to be the center of the circle. And I'm going to use this as the radius.
So with those two things selected and only those two things selected, I go to Construct
| Circle by Center + Radius. And then I have this circle, and I can see that if I change
the length of the segment, it changes the radius of the circle. Okay, great. So now
I can put a segment in there. And I don't need this circle anymore. I need it to be
there, but I don't need it to be shown, so I will go to the Display menu and say Hide
Circle. And here I have this segment, um, remember this is the center of my circle.
So if I drag my point around, then it's, uh, it moves the whole segment. But if I drag
this point, then that's the point that's on the circle, so this will allow me to change
the orientation. And of course you can see that if I change the length of the original
defining segment, then it also changes the length of the new segment. Alright, so this
is wonderful. And now I'm going to go and use all of this—these are all of the pieces
of information that I need in order to create a Custom Tool. So I select those, and I go
down here and say Create New Tool. And I'm going to call this tool a Match Stick. And
I want to go and Show Script View. And I'm going to—okay, I'm in the arrow—I have
the Arrow tool selected. And the Script View you can see this gives me basically the script
of how that segment was constructed. I started with a head and tail, those are the defining
segments for the length, and then I need a point A, which is the center of the circle.
And it shows, you know, I need a segment between head and tail, I made a circle, I constructed
another point on that circle, and I put a segment between the center of the circle and
that point on the circle.
And now I can use this Custom Tool. With this Custom Tool selected. And it says I need to
select a point head and a point tail and that other point. So I select the point head. Select
tail, and another point, and that gives me another matchstick.
Head, tail, and another point, head, tail, and another point. And so I can very quickly
create a bunch of matchsticks. But, um, one thing that becomes annoying is that every
time I create a new matchstick I need to select that point head and that point tail, and I'm
—it's always the same two points that I'm selecting there. The point A here, that one's
always a different point. But the point head and the point tail are always the same point
head and the same point tail. So it would be nice to be able to tell Sketchpad I want
the same points always selected for these two pieces of the Given information. And this
is the way you do that. I'm going to double-click on that, and click this box that says Automatically
match sketch object. And what this does is that, Sketchpad, when I'm running my Custom
Tool, looks in my sketch and asks "Is there a point anywhere in the sketch that's labeled
head?" If so, I'm going to use that as my given information here. And this is actually
why I chose to name this point head and this point tail, is because it's helpful to have
meaningful names—meaningful labels—when you're working through this—when you do
the Automattically match sketch object. Select OK. Now you can see that the point head has
moved from the Given information into Assuming information. So Sketchpad says, well we already
have a point head in the Sketch, I'm assuming there's a point head in the sketch. And now,
um, I can also move the point—oh, I need the Arrow tool, I'm going to change that.
Um, so I can also drag the point tail into that Assuming area. And all I have to give
Sketchpad, then, is the point A, which is the center of the circle. So now let's look
at using that Custom tool. And all it takes is one click to create a new matchstick. And
I can easily create a whole bunch. Okay. So now, I want to go over here and look at all
of these segments that I've created. Notice that I have, if I change my original length,
then that changes the length of all of them, which is convenient. And each of these has
I can move it by dragging the segment or, um, one of the points changes the orientation
and one of the points changes the movement. So that's a little annoying that, uh, it would
be helpful to get some visual cues on which point on the segment does the rotation and
which point does the moving. So that's actually why I chose to make matchsticks instead of
toothpicks. Because matchsticks have different ends, you know there's something different
on each end.
So what I'm going to do now is actually create a visual change. So the head of a matchstick
is red typically. The tail of a matchstick is nonexistent, so I'm going to right-click
this and say I want this to be Dot instead of the Medium size I want it to be Dot. And
then that point doesn't show up anymore. And while I'm at it, I might as well just change
the color. Select the tail point and the segment and go to Display | Color and I have a tan
color. But that's also because I edited my color menu, so if you don't have a tan color,
you can go to the Other menu. And let me bring my color palette over here. And I can then
go through and just, you know, choose a color, create my own color, or go into some other
menu, here's a brown. Of course I don't like that brown, I like to change it a little bit.
Make it a little lighter. Okay. And then I have a matchstick that looks like this color.
However, I just changed this particular segment. But the Custom Tool actually has all of the
information already built into it, so when I go ahead and construct new matchsticks,
well, just because I changed the appearance of a point and Sketchpad by default is set
up to automatically change the styles of newly constructed points. So these points are tan
and tiny, but all of the rest of the matchstick is the same as it was before, blue matchstick
and red head. So let me go in here and Show Script View again. And I can show you how
to change that in here. So point B was the point on the circle, this is the head of the
matchstick. And that's fine as it is, a medium sized red point. So I want to change the segment.
This is the actual—the stick itself. So I can actually label—I can label this the
stick. And, um, I can label this too. But if I was to label that I would call it head,
and I don't want that to be confused, I'm just going to leave it alone. Okay, so I can
change the stick color by right-clicking on it in the script view. And I want this to
be—I'm just going to use this brown here. And I will also change the line style and
call it Thick. And now when I create a new matchstick, look at that. I can create all
these matchsticks all I want, with just a little click and no effort at all. And the
fact that I made the two ends different means that I know that this is the end that moves
the matchstick, which I can also do just by dragging the stick itself. And this is the
end that changes the orientation. And of course, just to remind you, I can change the lengths
of all of those matchsticks by changing the length of my original defining segment.
Okay. And since I started with a puzzle, let's go back to the other page. Um, for some reason
I hid my page tabs. Let's bring those back. And we have our puzzle. Move 3 matchsticks
to make 2 squares. And I have—I don't know if there are other solutions, but my solution
is to take these two matchsticks and move them up here, and then this matchstick I will
change it to be horizontal, and I'll put it there, and I have one small square and one
big square.