Puzzle

[Eddy Matthews]

Okay, all you mathematical geniuses out there.... Explain this one, it's driving me nuts!

[Roderick Smith]

The master shape isn't a triangle.
The dark green has a slope of 2/5 = 0.4
The red shape has a slope of 3/8 = 0.375.
In the top arrangement, the shapes are concave compared to a pure 5x 13 triangle.
In the lower arrangement, the shapes are convex compared to a pure 5x13 triangle.
The difference adds up to 1 unit.

A 5x13 has an area of (5x13)/2 = 32.5
The four areas are:
Red: (3x8)/2 =12
dark green (2x5)/2 = 5
orange = 7
light green = 8
total: 32

In the top, they are arranged 0.5 short of the illusion; in the bottom they are arranged 0.5 above the illusion.

Regards,
Roderick B Smith
Rail News Victoria Editor

[Eddy Matthews]

So basically it's an optical illusion, and the answer was staring me in the face all the time - Literally!

Thanks Roderick, I knew there had to be a solution!

[derekwarner_decoy]

OK.... it had me stumped with

red= 5X2 divided by 2=....... :rant ....& the sum  of....=  :shock:  :?:  :idea:  :arrow: = 32 again & again  

thank goodness it was an OZ  :respect2 member who resolved the question.....on ya Roderick..... .....Derek... I will now go back to bending bits of 5/32" brass tube    

[Roderick Smith]

A vaguely marine joke heard on Darwin radio news:
For our friends in the airforce, the time is 15.00
For our friends in the navy, the time is 3 pm
For our friends in the army, the big hand is on the 12 and the little hand...

Regards,
Roderick B Smith
Rail News Victoria Editor

[derekwarner_decoy]

Hi PD's - outside of our WEBsite, my CA [Computer Associates] Internet Security Suite 2007 canned   the posting>>>>> possibly as being  .... ....not sure how these computer people  :computer  understand word structures & the like  :?:  :arrow: or am I missing something?................Derek