Why does the triangle have extra uncovered area?

[RandallB]

But really, "paralellogram" isn't the answer to the question you asked, either.

Get a life for crying out loud it is a brainteaser (an old one at that with a fresh twist) not religion.

Are you saying you already understood it so well you knew that the small shape could increase in size by pushing the false concave ‘hypotenuse’ out to a convex one, with area bounded by those two false ‘hypotenuses’ exactly matching the empty square that appears inside the larger shape. And you already knew and understood that space well enough to describe it and you’d pick something other than "parallelogram" to name it.

I don’t think so. I’m sure not convinced.
And no, I don’t mind calling Sour Grapes for what they are.

What’s with you and others -- What are you going to do if someone comes up with something important like a truly new theory that legitimately displaces your favorite theory? Say thanks and congratulations for finding it, or complain that you didn’t come up with it first?

 

[davee123]

Get a life for crying out loud it is a brainteaser (an old one at that with a fresh twist) not religion.

Right back atcha :)

Are you saying you already understood it so well you knew that the small shape could increase in size by pushing the false concave ‘hypotenuse’ out to a convex one, with area bounded by those two false ‘hypotenuses’ exactly matching the empty square that appears inside the larger shape. And you already knew and understood that space well enough to describe it and you’d pick something other than "parallelogram" to name it.

I don’t think so. I’m sure not convinced.

I'm not sure I understand-- you're still maintaining that the necessarily unique solution in one word is "parallelogram"? I agree that it's what I would consider to be an acceptable answer, but I would also accept others. Perhaps you could elaborate on why "hypotenuse" is necessarily incorrect? Or perhaps "hypotenuses", which together would describe the parallelogram you were looking for?

As I elaborated in my previous post, "parallelogram" is an incomplete explanation, and I would argue that it's likely that ANY one word solution is similarly incomplete. Hence, I would maintain that in the absence of a complete solution, a either a partial solution must be acceptable, or none must be.

However, I think you're approaching the problem strangely emotionally, which is why I commented on the fact. You appear to be overly proud of your particular solution, and are a bit too eager to discount other people's interpretations and claim they lack understanding of the problem, when in fact, their interpretation may just be different than your own. And I think that was pretty insulting of you. Long story short, I would advise that if you're going to come up with a brain teaser, make sure that either:

1) You have a well-defined solution, allowing you to disprove incorrect answers.
2) You're open to other possible interpretations apart from your own.

DaveE

 

[RandallB]

Perhaps you could elaborate on why "hypotenuse" is necessarily incorrect?

In no way can the word discribe something that has an area.[/QUOTE]As I elaborated in my previous post, "parallelogram" is an incomplete explanation, [/QUOTE]You mean where you detailed the location of a polgon that can only be completely discribed as a parallelogram (defining an area or "space")?

All I was doing was correcting incorrect interpretations based on the brainteaser given. Emotional reactions like yours seem way to unproductive to waste time on – maybe I should just ignore them even if it does leave incorrect assumptions uncorrected and trust the more attentive to get the point on their own.

I’ll unsubscribe from my thread, do as you please.

 

[davee123]

In no way can the word discribe something that has an area.

Think of it as though it were an animation. Going from diagram 1 to diagram 2, the "hypotenuse" of the large triangle goes from being concave to convex. The area that is contained within the change of the hypotenuse is the same area that's described by the parallelogram. Hence, by viewing the hypotenuse as a discrete, flexible element that changes with 'time' over an area, "hypotenuse" describes the location and the area just as well as "parallelogram" does.

In fact, I might argue that human-understainding-wise, "hypotenuse" might be a better answer, because the hypotenuse of the large triangle is already clearly drawn on each diagram, hence it's already been established and can be examined as a potential answer. The "parallelogram" you reference, however, isn't clearly drawn on the diagram, and as such isn't as immediately clear of a concept.

Emotional reactions like yours seem way to unproductive to waste time on – maybe I should just ignore them

Why wouldn't you? For that matter, why did you bother making the assesment "Complaints to the contrary are just sour grapes over not figuring out the whole solution on their own"? You're quite intentionally pointing out other people's emotional reactions and branding them as negative, as well as implying their stupidity, more directly by declaring that they lack understanding of the problem. I think it was a waste of your time to point that out, and only served to hurt other people's feelings (probably making them feel defensive), and (as I'm trying to point out) could be entirely inaccurate.

The only reason I'm pointing it out here is to try and get you to realize that the comment (the attitude really) was unnecessary and divisive. I'm making the point in the hopes that you won't do such things in the future. It doesn't help to the understanding of the brain teaser in question, and only serves to make a more hostile environment in the forums.

If you think someone has an incorrect solution, try and either explain why it isn't correct or have them try to explain why it *is* correct. Please don't just assume that they're clueless and treat them as such.

DaveE

 

[NateTG]

I think that a better explanation would be:

Neither of the shapes are actually triangles, even if we fill in the 'missing square'. This puzzle is based on an opticall illusion that makes you assume that the 'hypotenuse' is a straight line when, in fact, the 'hypotenuse' is bowed in in one geometry, and bowed outward in the other, and, moreover, the difference in areas between that covered by the bowed and unbowed hypotenuse is exactly equal to the 'missing square'.

(As soon as people see that the shape/hull in question is not a triangle, but a quadrilateral, the rest is very easy to understand. Notably, this optical illusion is especially insidious because we're trained to use sloppy sketches as triangles in math.)

 

[hrishikesh]

ohh tell me the answer damnit :(