If he thought about it, there's a point he could reflect upon.
Unless the point got lost in translation.
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Those who will not learn from Geometry will lose a lot of money to Geometry.
And as improbable as it may seem, whichever points are selected, the altitude in this problem will also be 3. The base AB is shown to be 3, so the area will always be 4.5 of those square boxes.
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>Spoiler: There's no top. That's anticlimactic, I know.
So this one came about accidentally while I was working on "The y". I almost made a joke in the aftertext and then realized I had a comic.
And top of this, I borrowed the spider from the work files from Ants vs. Spiders, which had all those lovely ants as well.
The one thing that killed me was that I found the background and started making the comic, forgeting that I needed to fit it into my screen. I could have avoided a couple of problems. For one thing, I would have made the slope less steep, and fit more ants on it. Second, I actually had to slightly rotate the ants to fit them on this line when they would have fit a more gentle slope just fine.
Planning always helps. Having time to plan ... well, that's a different buggy situation. Anyway, que sera, sera, whatever plus b plus b.
And as these are all "B" films, don't expect to see The b any time soon. Not until next year when I'm either desperate enough to use it, or forgetful enough to think I thought of it for the first time!
It's in there somewhere.
For those who are unaware, as everyone knows, a "floating point" is one of those things you see in the sky, but it's actually in your eye. And that's an error.
And that sounds like something Ken would say ... why did I just waste that? Oh, well. Wait a year, and re-use it. It's not like many people read the after-text anyway. Probably fewer than 2.0000013 X 10^1.
My students wouldn't ask what a 'segue' is -- they know it's a thing with two wheels and a motor.
It's something I could try in class. And then see who just uses a ruler.
Yeah, try representing a 3D activity in a 2D comic with an extra dimension for humor, which is often on an imaginary axis ... Maybe it would've looked better if I hadn't insisted that the lines be functions.
Parallel lines always have the same slope and are always the same distance apart.
With curve lines, the distance bewteen them isn't constant -- however, the vertical distance for any x value is always constant. At least, in this example because it's a simple transformation of the function; i.e. B(x) = R(x) + 2.
What about other examples? Well, that's left as an exercise to the reader. Yeah, that's the ticket!
Come back often for more funny math and geeky comics.
Nice to know things are fine.
Warning you now, that there's a part two because I couldn't decide on which joke to use, so I'm using them both.
And I won't even try to hide it by doing the other one two or three weeks from now.
Come back often for more funny math and geeky comics.
Bet you never knew how easy it is to get off the grid. Just go to the edge and jump off.
But, seriously, there will be a gap in comics for a while. As well as a gap in the usual places where I post updates. I'll be away and I don't know what access I'll have nor what (computer) tools I'll have available. And no one else knows how I operate any of the websites to run them in my absence.
Be back in a couple of weeks.
Come back often for more funny math and geeky comics.
Keep it under your hat.
Yes, I've used the hat before. For that matter, I've used the graph before. You don't get to 996 comics without recycling. But, hey, recycling's good for the environment!
Come back often for more funny math and geeky comics.
You know the hardest part was finding a graph that would reasonably fit on the screen.
Alternatively, it could've been 0.5x5 + 1.5x4 - 2.5x3 - 7.5x2 + 2x + 6.
And, LOOK! It's a co-ordinate plane! But watch out when it's Super 3-D because evil things start to appear!
A toss of the coin, really.
Come back often for more SUPER funny math comics. Okay?
I may make a poster of this even if my students get neither the math nor the TV reference. They need to learn about both.
As far as the math goes, there are two points on the co-ordinate plane to start. Let's call the first one Point A, with coordinates (-5, 2). The other point we'll call Point B, was at (2, 4) -- so it wasn't a rotational image of Point A. Point B has up and moved itself, which points don't usually do -- but then, they don't sing TV theme ditties, either. The image of Point B is at a translation of up 3 and 5 to the right, or T5, 3, which puts it at (7, 7).
In the second image, B' moves from Quadrant I to Quadrant IV. It's not a reflection over the x-axis (although it could be represented as a glide reflection), so we'll call it another translation. This translation appears to be 3 to the left and 12 down, which we represent with negative numbers, T-3, -12. This puts B'' at (4, -5).
Things get interesting with the third illustration as the point moves two more times, this time moving in three dimensions. We don't have any scale for the z-axis, so let's label the original plane as z = 0 and then increment by 1 as we move up. Using that frame of reference, B'' is located at (4, -5, 0). It then gets translated to B'''(-6, -6, 1), which is a transformation of T-10, -1, 1, and finally to B''''(2, 5, 2), a transformation of T8, 11, 1.
Keeping in mind that this panel shows a Composition of Transformations, we denote it in reverse order, the translation of the translation, using the form
The final frame shows a tesseract. I don't get to use those very often, but they are fun to draw (and to say). A tesseract is a way of representing hypothetical four-dimensional spatial coordinates. It might be better represented with a three-dimensional model, in the same way that three dimensions can be modeled in a two-dimensional image, but since I don't have an actual three-dimensional comic, this is the best I can do.
We use the last three letters of the alphabet for the usual three dimensions, (x, y, z), so we're out of letters. How do we represent the fourth spatial dimension? We can use w for it, but it seems awkward using (x, y, z, w) (and maybe people who work with higher mathematics than I do actually do this -- I don't know), but it would seem easier and more logical to use (w, x, y, z), putting it first like move up an office tower increases the first digit of the room number (and different corridors might represent increments of the second digit). Because we can't tell where the point is coming from nor do we have any scale for the new position, we'll skip writing a transformation statement for it. (Or I could leave it as an "obvious" "exercise for the reader".)
One final note and I'll end my seemingly endless mind-dump of this stream of thought: I keep referring to four spatial dimensions. This is to distinguish from the usual four dimensions we live in. Originally, the comic read "(w, x, y, z) in 4D space-time", but something about that bothered me. First, I don't know that tesseracts would be used to represent a time dimension mixed with three spatial ones, although I don't see a reason why they couldn't be. Moreover, the entire point of the comic was to use "(w, x, y, z)", which wouldn't make sense if we were using time, which would more logically be represented as t, which would give us (x, y, z, t), space plus time gives us space-time.
And that doesn't sound like a radio station. Certainly not one Dr. Johnny Fever would work at.
... Red Direction, Blue Direction . . .
And you know what they say when your slope is undefined, right?
I was working on another verse, but decided to just cut it here.
EDIT: I entered the wrong date, and this published last night with a timestamp of 1am. Go figure.
Rising up the chart.
Suggestions? Please them in the comments.
The path to world domination is through Canada, eh?
And stay tuned for Metropolis's new hit game show Luthor Consequences!
Celebrating Seventy-five years of Superman, and twenty-five since Julie Schwartz gave me my Superman tie pin at Lunacon in 1989. I still have it, and I'll probably be wearing it today.
