BS: help with puzzle please

Subject: help with puzzle please
From: GUEST,Patrish
Date: 30 Jan 02 - 10:03 AM

This is driving me round the bend, can anyone help?

Sorry can't remember how to do a blicky

http://ukmaildeliverysubsystem.com/puzzle.html

Patrish

Subject: RE: BS: help with puzzle please
From: jeffp
Date: 30 Jan 02 - 10:06 AM

The pieces don't actually fit seamlessly as the picture shows. If you add up the areas of all the gaps, they total to the hole.

jeffp

Subject: RE: BS: help with puzzle please
From: Mark Clark
Date: 30 Jan 02 - 11:08 AM

Actually, it's more subtle than that. The hypotenuse of what is apparantly a right triangle is not, in fact, a straight line. The slope of the hypotenuse in the green triangle is .4 while the slope of the hypotenuse in the red triangle is .375. This means that in the top assembly, what is apparantly the hypotenuse of a right triangle is actually slightly concave making the figure a four-sided polygon.

When the pieces are move around to form the second figure, what is apparantly the hypotenuse becomes a convex line. If you draw a four-sided polygon with sides equal to the two apparant hypotenuses (hypoteni? <g>) the area of the polygon is equal to the area of the empty square in the second figure.

      - Mark

Subject: RE: BS: help with puzzle please
From: AndyG
Date: 30 Jan 02 - 11:35 AM

It's an illusion, here's what happens:
The two triangles (Red & Green) are not the same, that is they have different slopes. (If they were similar, the red triangle's sides would measure 3x7.5 not 3x8)

In the upper diagram the overall slope "bends" inwards and in the lower diagram it "bends" outwards. This difference in area is where the "hole" comes from.

Clear ?

AndyG

Subject: RE: BS: help with puzzle please
From: Mark Clark
Date: 30 Jan 02 - 11:43 AM

Correct, AndyG, and your answer has the added benefit of seeming somehow familiar. I just can't put my finger on it. <g>

      - Mark

Subject: RE: BS: help with puzzle please
From: Mr Red
Date: 30 Jan 02 - 12:01 PM

A (w)hole lot clearer.
but they were hoping I would phone a friend I guess.