I enjoyed the pun in this cartoon but noticed one math item it got right and three things that it got wrong. Maybe others will find more. That’s the problem with math nerds. We tend to look for flaws.
Mano Singham
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I enjoyed the pun in this cartoon but noticed one math item it got right and three things that it got wrong. Maybe others will find more. That’s the problem with math nerds. We tend to look for flaws.
I found these two errors:
1. The sine of an angle is not 60 degrees. It’s a ratio not an angle, so it has no units, and stays between -1 and 1.
2. The triangle does not seem to be a right triangle, so the sine of its angles doesn’t really make sense.
Kinda weird since you have to be pretty math literate to get the joke, but if you’re math literate than you’d probably see the mistakes. Maybe the author vaguely remembered something about sine being “adjacent over hypotenuse” of a triangle but forgot the rest.
@1 “Chased A Horse” (look again at the paper)
He could be a right triangle, if the drawing is showing him in perspective (much like the desk, chairs, walls, and picture frames).
But … is he cosigning for only 1/2? How would that work? I mean, I don’t want to sound prejudiced or whatever, but maybe they shouldn’t be giving loans to triangles which can’t do the full value.
OverlappingMagisteria:
Cosine (a pun on “cosign”) is adjacent/hypotenuse, while sine is opposite/hypotenuse. I learned it as “SOH-CAH-TOA,” pronounced like a word, which makes it easy to remember.
For non-right triangles, the law of cosines is your friend. But really, it’s always your friend. It is there for you, looking out for you and ready to help you, whenever you may need it. You probably don’t deserve a friend like that.
Ahh I mistook the joke as “signing” for the loan. “Co-signing” makes much more sense. And true… it might be a right angle with some perspective.
I figured it would be a bad joke. All the warning opp/hyps were there.
consciousness razor: I learned it as
“Oliver And Ollie
Had Hot Apples.”
But, as Google isn’t really turning up useful results, maybe that was a regional thing. The order of equations, then, was sine, cosine, and tangent. That part is lacking from mine.
The third error is that it looks almost like an isosceles triangle but not an equilateral one. Hence the base angle cannot be 60o.
@4, I also learned it as sohcahtoa. I always had to reconstruct formulas on tests, mnemonics like that helped me a lot. Although once you thoroughly understand the unit circle, it’s all over for trigonometry. At least at the high school level.
Of course we’re also talking geometry here. Unit circle is all rights.
@8, that seems more difficult because you need the s, c, t in assumed order. Or am I missing something?
@8, that’s why you don’t write a comment after just reading the mnemonic…. My bad.
@9 Mano,
“His hypotenuse” implies it is a right triangle. It could be a 30-60-90 triangle, assuming some perspective in the drawing that doesn’t look too far off. As noted above the big problem is that cosine has no units and furthermore is between 0 and 1 for an acute angle, so it can’t be 60 regardless units. I was unhappy with the implication that the triangle had a cosine, since cosine is a property of an angle. I guess you could make a case that the orientation implies the angle in question is the base angle opposite the right angle but, well, ugh.
I definitely agree with your main point: If you are going to publish a cartoon with a math joke you really should get the math right since they only people who are going to appreciate it are going to notice if you get it wrong.
I assumed to see a right triangle. Otherwise “60 degrees” wouldn’t work as a name, because it wouldn’t identify the triangle uniquely. The image doesn’t show a right triangle.
I understand that a right angle triangle can be made to look otherwise by shifting the perspective. But when drawing a cartoon that depends on it being a right triangle for its humor (already pretty obscure for most readers), why would a cartoonist make it even more obscure by making it seem otherwise? It would it have been as easy to make it clearly a right triangle.
While one could argue that the 2nd triangle (the one who’s writing) *could* be a right-angled triangle due to the perspective, the only way the 1st (left) triangle could have a 90-degree angle would be if it was leaning heavily to either the right or left, but the face doesn’t line up with that.
It’s a straight up error; these are not right triangles.
So the trangles don’t look right. Is that a meta-pun?
Mano:
Because it’s a drawing, and use of perspective is extremely common in drawings. (Especially with faces, which are not really portrayed straight-on as often as other things are.)
Also, as I brought up in #3, except for the ones on the back wall, all of the right angles that we all can very comfortably believe are in the picture are not actually seen (from the “camera’s” POV) as being 90 degrees. If you get out your protractor and measure them, it will not tell you they are right angles. But you know perfectly well that’s what they’re supposed to be, and you know why your protractor is not cooperating.
So I don’t think you would’ve complained if the joke were somehow about the desk having a rectangular surface (not a parallelogram) on the top…. I mean, there just wouldn’t be any need to show it “as a rectangle” by framing the shot so that the “camera” is hung from the ceiling and pointed straight down toward the desk. It would be a kind of weird stylistic choice that you could make, if you thought that was a good way to portray the scene/characters/etc., but you definitely wouldn’t have to do anything like that.
It’s also worth pointing out that the bottom left corner of the one holding the pen looks like it’s pretty close to a right angle anyway. If I had to convince you that what seems like a 15 degree angle (e.g.) is actually 90 degrees, then that may be another story. But even then, if perhaps there were some highlighting/shading (due a light source), multiple frames showing different perspectives of the same object, or something along those lines, then it might seem like a pretty normal way to interpret the image in the first place, so maybe we wouldn’t even be talking about it…. It really does happen all of the time in drawings, animations, etc., and usually nobody cares or notices. They would be really bothered if it weren’t happening.
In any case, we’re not talking about a straightforward mathematical error anymore. You can decide that you think the image should be looked at in a certain way rather than in another way, but that decision is up to you and isn’t a question that is answered by mathematics.
consciousness razor @#17,
You are right that I wouldn’t have complained “if the joke were somehow about the desk having a rectangular surface (not a parallelogram) on the top…. I mean, there just wouldn’t be any need to show it “as a rectangle” by framing the shot so that the “camera” is hung from the ceiling and pointed straight down toward the desk”, but that is because everyone would assume that a desk surface was rectangular. When do we encounter any other shape? But that is not the case for triangles. They are not assumed to be right triangles.
There are no math errors, just minor abuse of English. The first filled in line is the sign of Jim. The second filled in line is the cosign of 60 degrees.
As for the triangle with glasses (the cosigner), the angle their base makes with the front of the chair seat demands that the angle below their mouth is slightly larger than the apparent angle, so easily could be 90 degrees.
My high school geometry teacher had a couple clauses to remember the “trig using right triangles” identities. sine, cosine, tangent were “Over hill and hump Ollie ambles,” and “Oscar had a hunk of apples.” There were also several members of the moderately good (for Las Vegas high school) soccer team in the class. It was the early 80s and they had a reputation of having no problem with partaking in illicit substances. Not as much as Jeff Spicoli from “Fast Times at Ridgemont High,” but probably adjacent. Anyway, the last name of one of the team members was Orci, and one of the other team members blurted out a couple seconds after the second clause above, “Orci had a hit of acid.” The teacher was not amused, although she was one of the few in the room who weren’t.
I have been amused by the number of mnemonics that people say they used in order to remember the definitions of these trigonometric terms. I don’t recall ever being taught mnemonics for them in Sri Lanka. They did not seem that hard to remember.
Mano @21: The only pre-university mnemonic I remember is Richard Of York Gave Battle In Vain.
Rob @22,
We just remembered it as VIBGYOR.