The Incredible Puzzle Thread

[Didero]

Yeah, she was just bragging
If you were to calculate it, I'm sure there would at least be a square root involved somewhere.

[GinnyN]

I just trying to not give away inmediatly the answer, because, the actual answer in "Mathese" is "It's the Radius" and the Radius is 20.

Originally Posted by Didero

Yeah, she was just bragging
If you were to calculate it, I'm sure there would at least be a square root involved somewhere.

Well, if they give us the length of AC and AB, you can use AD = sqrt(AC^2 + AB^2), which will me probably the first thing a math student will think off, except they will lack information. Also, you can use trigonometric stuff, if they give us the angle of DAC (let's say it alpha), because cos alpha = AB/AD, so AD = AB / cos alpha (you can use also sen alpha = AC/AD), but you are lacking information again.

In that moment a math student will saw the problem, figure out, and jump out of the window.

[Avistew]

That's not mathese at all. That's what I would have said too, if you hadn't used number and confused me. Something doesn't qualify as mathese if I can understand it

EDIT: by the way, my whole reasoning was "they only give us one number, and it's for something that doesn't even have a name. The thing kinda look like a circle. I'm gonna say it's one so the answer is 20".

So out of curiosity, how do you actually know that AB? and AC? are the same length? Is it because of the right angles?

[GinnyN]

Originally Posted by Avistew

So out of curiosity, how do you actually know that AB? and AC? are the same length? Is it because of the right angles?

It's a Rectangle, thanks to the right angles. If you separate them with AD, you get two Square Triangles. AB has the same lenght than CD, and AC has the same lenght than BD. Since you have an Square Triangle, you can use the Pythagorean Theorem to figure out AD, which is the hypotenuse, by using AB (or CD) and BD (Or AC). So, it's something like this:

=> (AD^2) = (AB^2) + (BD^2)
=> AD = sqrt(AB^2 + BD^2)

By the way, there's a way to figure out AC and AB if you suppose those are equal. Of course, by knowing AD = 20.

[Psy]

Originally Posted by GinnyN

It's (((40 / 2) - 5) / 3) * 4.

What's about, the only place in the world if you go 1 mile to the south, 1 mile to the east, and 1 mile to the north and come back to the exactly same point?

There are quite a few specific locations, but the answer you're looking for is the north pole

[GinnyN]

Originally Posted by Psy

There are quite a few specific locations, but the answer you're looking for is the north pole

Now I'm curious for the other few specific locations!

[Avistew]

Er, thanks, but that's not what I was asking. You can't calculate AD this way with knowing what AC and AB are.

When I said AB? and AC? I meant the ones that don't have names. Like, [AE] (the one with B on its way) and [AF] (the one with C on its way).
To know that [AD]=[AF], you need to know that [AE]=[AF], don't you?
My question was, how do you do that?

EDIT: Here, I changed the picture to show what I mean.
In my new picture, A isn't the center of the circle anymore.



In this case, it's obvious, since I wanted to show you what I meant. But how do you know that in the first picture, A is the center? What is the way to calculate it? Surely when you're just looking it's easy to get it wrong if it's just off the center, right?

[taumel]

Uhm, it's 20, as it's all about, and so the distance AD, the radius.

[GinnyN]

Originally Posted by Avistew

Er, thanks, but that's not what I was asking. You can't calculate AD this way with knowing what AC and AB are.

When I said AB? and AC? I meant the ones that don't have names. Like, [AE] (the one with B on its way) and [AF] (the one with C on its way).
To know that [AD]=[AF], you need to know that [AE]=[AF], don't you?
My question was, how do you do that?

In a equation, I can't think in a way to do it.

In fact, you can say there's no actual answer (For lack of information), because we're just assuming it's a quarter of a Circle. If it were the quarter of a Elipse, for example, AE =/= AF and we're screwed, unless they also give us AE.

So, in typical Math fashion, I assume it's a Quarter of a Circle. If it's a quarter of a circle, by definition all the lines from the middle to the perimeter of the circle has the same lenght (Because that's the definition of the circle). (I think). Since AF is a line from the middle to the perimeter, and AD is also a line from the middle to the perimeter, then AF = AD.

[taumel]

@Avistew
You then solve it geometrical.

[Avistew]

Okay, so you assume it's a quarter of a circle, without a real way to be sure of it. And due to the lack of information there probably isn't a way to be sure of it that doesn't involve getting out your compass. Did I get that right?

[GinnyN]

Originally Posted by Avistew

EDIT: Here, I changed the picture to show what I mean.
In my new picture, A isn't the center of the circle anymore.



In this case, it's obvious, since I wanted to show you what I meant. But how do you know that in the first picture, A is the center? What is the way to calculate it? Surely when you're just looking it's easy to get it wrong if it's just off the center, right?

That's a quarter of a Elipse! You screw me!

Originally Posted by taumel

@Avistew
You then solve it geometrical.

I totally forgot that, you right!

Grab a rule, measure the lenght of AF (Let's say it's 10 cm) and then measure the lenght of AD (Let's say it's 12 cm). Then you say:

10 cm -> 20 units
12 cm -> X units

Then x [units] = (12 [cm] * 20 [units]) / 10 [cm]

That's only works if the Drawing has the correct proportions. If it's not, we're screwed again.

Originally Posted by Avistew

Okay, so you assume it's a quarter of a circle, without a real way to be sure of it. And due to the lack of information there probably isn't a way to be sure of it that doesn't involve getting out your compass. Did I get that right?

Yes and no. If it's nobody telling you that's not a quarter of a circle, there's no reason I can't assume that, because it's nobody telling you either that drawing is correct at all. (That's always happen in a test the drawing are just demostrative, and normally you can't simple believe it's a circle because it's look like one.).

If we don't assume is a quarter of a circle, I cannot figure out a way to do it. And, if you want to know for sure it's a quarter of a circle, bad luck, because not always the drawings had the correct proportions. If you don't telling me that drawing had the correct proportions and it's not just demostrative of the example, I still can assume is a quarter of a circle, unless the problem itself tell me is not a quarter of a circle.

But, if the drawing has the correct proportions, you can use rule of three!

[Tor]

Easy! In GIMP, just use the measure tool (shift-M) to find the length of AD. I get 320 pixels

[Psy]

Originally Posted by GinnyN

Now I'm curious for the other few specific locations!

It has to do with the fact that terms like North, South, East, and West become undefined in specific locations. Consider if you were one mile north of the south pole; You'd go one mile south, there would be no east to travel (so you'd stand still) and then when you go one mile north, you could end up where you started- Or at an infinite number of other locations forming a circle 1 mile north of the pole.

Alternately, if you're willing to say that you *start out* heading N/S/E/W, then you can do some tricks with crossing the north pole and having the directions all change names.

[Avistew]

Originally Posted by GinnyN

That's a quarter of a Elipse! You screw me!

Okay, a quarter of an ellipse then. I'm so math-challenged that I just thought it was a bigger circle and off-center >.>

Originally Posted by GinnyN

I totally forgot that, you right!

Grab a rule[...]

Er, yeah, if I have a ruler I'll measure it directly and I'll know what size it is I was assuming you were supposed to calculate it.
I guess I'm just making things complicated. You just assume it's a quarter of a circle. Like I did.

I just was fairly sure math-people wouldn't just assume something like that without checking first in a more scientific way than their eyometre.

[taumel]

This is boring, a more interesting but still easy to answer question would be: How does a turtle (with some painting on her tail) has to move, in order to draw the picture (the lines and the circle) so that every distance is only walked once. Those interested in, also can offer a turtle code otherwise a picture showing the way is sufficient.

[Psy]

If you're referring to the semicircle image that is being discussed, it can't be done.

[Avistew]

Just want to point out that it doesn't have to be an ellipse, it CAN be a circle with A as not-the-center.

Here is an example, and I showed where the center is, too.

[taumel]

@Psy
Are you sure? :O)

[Psy]

Originally Posted by taumel

@Psy
Are you sure? :O)

Yes.