Kevin's Watch

Posted: **Fri Jan 04, 2008 1:06 pm**

www.123opticalillusions.com/opt38.htm

Posted: **Fri Jan 04, 2008 1:12 pm**

The green triangle has a steeper slope than the red one.

Posted: **Fri Jan 04, 2008 1:20 pm**

James wrote:The green triangle has a steeper slope than the red one.

That's not right - they share the same angle.

Edit: I think I've worked it out. It's a play on Pythagoras' Theorem.

Posted: **Fri Jan 04, 2008 1:29 pm**

Not quite, Lore. 3:8 and 2:5 aren't on the same scale. 22.6 degrees vs 21.8. Still, I'm not convinced that's the reason.

Posted: **Fri Jan 04, 2008 1:31 pm**

I think James has a point - the slopes are not the same. But what's your explanation Lore?

Posted: **Fri Jan 04, 2008 1:33 pm**

If you stare long enough into the hole in the triangle, the hole in the triangle also stares into you.

Posted: **Fri Jan 04, 2008 1:33 pm**

Murrin wrote:Not quite, Lore. 3:8 and 2:5 aren't on the same scale. 22.6 degrees vs 21.8.

Just curious, how did you come to that conclusion that the angles are different? I'm not saying that you are wrong, mind you.

Posted: **Fri Jan 04, 2008 1:34 pm**

Vain wrote:I think James has a point - the slopes are not the same. But what's your explanation Lore?

I'm not really certain.

Edit: The answer is that the triangles aren't the same.

Posted: **Fri Jan 04, 2008 1:35 pm**

Loremaster wrote:
James wrote:The green triangle has a steeper slope than the red one.
That's not right - they share the same angle.

...Green triangle has length 5 height 2, red triangle has length 8 height 3

so the green triangle's hypotinuse slopes up by 1 square every 2.5 squares in length.

red triangle slopes up by 1 square every 2.67 sqares in length.

Doesn't sound like the same angle to me...

As a whole, the first shape bows in, the second bows out.

Posted: **Fri Jan 04, 2008 1:37 pm**

Loremaster wrote:
Murrin wrote:Not quite, Lore. 3:8 and 2:5 aren't on the same scale. 22.6 degrees vs 21.8.
Just curious, how did you come to that conclusion that the angles are different? I'm not saying that you are wrong, mind you.

When I saw James mention it, I had a closer look, and saw that he was right--if they were the same the red would cross a grid point at 2:5. Counted the squares, then a quick bit of trig gave me the angles (a/b=tanA).

Posted: **Fri Jan 04, 2008 1:38 pm**

James wrote:
Loremaster wrote:
James wrote:The green triangle has a steeper slope than the red one.
That's not right - they share the same angle.
...Green triangle has length 5 height 2, red triangle has length 8 height 3

so the green triangle's hypotinuse slopes up by 1 square every 2.5 squares in length.

red triangle slopes up by 1 square every 2.67 sqares in length.

Doesn't sound like the same angle to me...

As a whole, the first shape bows in, the second bows out.

For the first one, you're wrong, but the second one - then the red and green triangles diverge slightly.

Posted: **Fri Jan 04, 2008 1:41 pm**

Loremaster wrote:
Vain wrote:I think James has a point - the slopes are not the same. But what's your explanation Lore?
Edit: The answer is that the triangles aren't the same.

I've seen this one before, and Lore's right. I forget the exact details, and maths bores me stiff, but there's a difference in size between the two triangles by about 3% or so (with the bottom one being slightly larger). Primarily, these things are always visual tricks.

Posted: **Fri Jan 04, 2008 1:41 pm**

Loremaster wrote: For the first one, you're wrong, but the second one - then the red and green triangles diverge slightly.

Each individual shape is identical from the first to the second.

Posted: **Fri Jan 04, 2008 1:43 pm**

James wrote:
Loremaster wrote: For the first one, you're wrong, but the second one - then the red and green triangles diverge slightly.
Each individual shape is identical from the first to the second.

The fact is that the second triangle's slope is slightly concave.

Posted: **Fri Jan 04, 2008 1:44 pm**

The first is concave, the second is convex. The sum of the two vectors forms the length of what would be the hypotenuse; reversing their order gives the same resultant, but a different path between the points.

Posted: **Fri Jan 04, 2008 1:46 pm**

Haha exactly, that's basically what I was getting at with my first post

Posted: **Fri Jan 04, 2008 2:17 pm**

James wrote:Haha exactly, that's basically what I was getting at with my first post

In a vague way.

Posted: **Fri Jan 04, 2008 3:03 pm**

It's quite obvious.

A wizard did it.

Posted: **Fri Jan 04, 2008 11:54 pm**

Hmm I printed the page, cut the pieces out (just to be sure) and damned they still match one on top the other, even with the extra space. It is a puzzler! I got a headache now.

Posted: **Fri Jan 04, 2008 11:55 pm**

just count the bottom squares on each piece. the difference is between 12 and 13. It's the math.

8 + 5

5 + 2 + 5

Kevin's Watch

You figure it out

You figure it out