Science Mom here with Math Dad. We're back for challenge problem number 24.
Yes we are. This one is a triangle counting problem
again. In this figure the challenge is to count all the triangles that are there.
I'm giving you only two minutes to accomplish this feat. Okay. If you're
watching the video at home please pause now. Try the problem out of yourself. See
if you can come up with the right number of triangles. Science Mom begin. All
right. So I'm going to try and come up with a more systematic way because last time I'm
missed a lot, so I'm gonna start with this line right here and say:
what triangles can I make using this line? So there's 1, 2, 3. Are there anymore? I want to
make sure that I got them all. Oh there are. There are smaller ones, so let me
use a slightly different... There's that one. 1, 2, 3, 4, 5, 6, and I don't think
there's a way I'm gonna get another one so there's 6 for this line right here.
And then I would bet there's gonna be six for this line as well, but I'm double
counting this one. Mm-hmm. So I'm gonna say 5 cuz I don't want to
double count, and then I'm gonna guess that there are also... oh no things are
getting different down here. It's all symmetric. It's all symmetric? I
think that counts as a hint. You're not supposed to give me hints... but thank you.
So 5 all the way around, but when I get around to here it's gonna be
4 because... Good. 12 seconds. Yep okay five, ten, fifteen, twenty, twenty-five.
Are there some that don't touch the outer edge? Yes there are. There is this
one here in the middle. It doesn't share an outer edge. Is that the only
one? Look there's this one and.... There are five of that flavor. There's five of that flavor?
No way. I'm out of colors
There's 1, 2, 3, 4.... I don't see the fifth one.
Well, let me make it a little easier for you.
This angle... so I'm looking at this inner Pentagon. Yeah, yeah.
So that's inside one triangle. That's inside one triangle, one triangle, one
triangle, one triangle. Yeah, so you missed those five, but also what about
these five little ones here? Oh I totally missed those. Okay, so I missed that.
So there were thirty five. In this case because of all the symmetry of the shape
I think it's probably easiest just to count them in groups of five. Identify
a given triangle. Do all five possible rotations of it. Move on to another
triangle that you haven't yet counted. Do all five possible rotations of it.
So you've got seven different triangles that have a five-fold symmetry. Exactly
right. We've got seven triangles we can rotate each of those. Yeah. That's
impressive to me. I'm always way, way higher than you think. I would not guess
thirty-five triangles. Yeah it's surprising. In two minutes that's a
pretty tall challenge to meet. Yeah. But you didn't gloat about the previous
problem being too easy if I recall correctly. Serves me right.
Indeed.
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