For smart people... can you explain this?

[Timber Loftis]

Andrewas: Both larger shapes have a "run" of 13 squares and a "rise" of 5. Yet, we all agree the difference is found in the hyptenuse. If that line (the hypotenuse) has equivalent end-points, the only way the slope can vary is if one or both of them is curved. At least one of the lines is simply not straight.

[edit] Oh, and my statement that equal triangles *are* similar was made to disprove the assertion made by you that "all components are the same" which I took to mean you thought the triangles were equal but not similar.

[ 11-07-2002, 06:04 PM: Message edited by: Timber Loftis ]

[Night Stalker]

Originally posted by andrewas: The triangles are the same size in each diagram. All the components are identical. The illusion is caused by the fact that the triangles are not mathematicaly similar. The rectagles just serve to show the effect.

Andrewas - thank you ....

Daveros - *bthththtlt* [img]tongue.gif[/img]

[Night Stalker]

Originally posted by Timber Loftis: Andrewas: Both larger shapes have a "run" of 13 squares and a "rise" of 5. Yet, we all agree the difference is found in the hyptenuse. If that line (the hypotenuse) has equivalent end-points, the only way the slope can vary is if one or both of them is curved. At least one of the lines is simply not straight.

Thats right. It's not a straight line. It is actually two straight lines with an angle of apx 0 but not exactly 0. As andewas pointed out there is a vertex.

[Timber Loftis]

Okay, now I see where we misunderstood each other. The "curvature" I mentioned was regarding the single long hypotenuse of each shape. Now that you point out that this line is actually two lines, each of which is straight, I see we are in agreement. Thanks. PS - I don't think *any* mention of the "hypotenuse" on my part *ever* referred to the smaller red and green triangles, and that's perhaps why I was confusing folks.

[Night Stalker]

Yeah, we all agree .... we were just nit picking on each others approach! And who started all of this by the way?!?! My head now hurts! Bubye! [img]tongue.gif[/img]

[Ace of Spades]

Originally posted by andrewas: Red = 3*8, giving a gradient of 2.33 Green = 2*5, giving a gradient of 2.5 They are *not* similar triangles, they are also not curved in any way. They will appear curved in your monitor, but this puzzle works with straight lines. I will do the maths if I get bored tonight.[/QB]

I agree with this statement 100%, as I've seen this geometrical puzzle before.

[Azred]

The leftmost angle in the green triangle has a measure of arctan .4 = 21.8 degrees.
The leftmost angle in the red triangle has a measure of arctan .375 = 20.56 degrees.

Take the first diagram, invert it, and slide it next to itself to create a rectangle. You would find that
there is a sliver whose area equals 1.

A wonderful problem to let your high school geometry students try to solve for a week. [img]graemlins/firedevil.gif[/img]