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HOW CAN THIS BE TRUE ?
Explanation by Julian H. Stacey
The Puzzle
Search on the net for your own copy of one of these two
graphics files (which look the same):
- Name: 1-44.gif
-
- Size in bytes: 19476
- Md5: 66c33b53f897a56497ef19c38795f1ed
- Name: triangle.gif
-
- Size in bytes: 22241
- Md5: 59761ba4d4e33675f5dac9ce909838f1
They are not online here in case they are copyright &
not public domain, though I received mine as semi infinitely
forwarded public joke type mails, & "strings 1-44.gif |
grep -i copyright" & strings 1-44.gif | grep -i copyright
"strings triangle.gif | grep -i copyright" shows nothing.
The Explanation
Best enjoy solving it yourself I suggest.
But if you want the answer, scroll
down.
Down
Down
Down
Down
Down
Down
Down
It's an an optical
illusion.
The Illusion
- One feels the diagonal looks the same on both the red
& green triangle.
- One assumes a straight line joining red & green
diagonals.
- One assumes same straight diagonal line on both
diagrams.
- One knows 2 straight lines at same angle must cover
same area & number of squares underneath.
The Reality
- There is not one diagonal on each diagram, but
two.
-
The diagonals are different but optically similar
gradients:
- Red:......: 3 vertical in 8 horizontal = 0.375 =
Shallower slope
- Dark Green: 2 vertical in 5 horizontal = 0.400 =
Steeper slope
- The top diagram is thus somewhat concave, or hollow (
think of a very large white / invisible squashy ball on top
left, pushing right, into the dent left by the 2 coloured
slopes.
- The lower diagram is opposite: somewhat convex, it
bulges upwards in the middle
- The lower diagram, as it has bulged outward, has used
all its material up doing so, & has left a space
underneath.
Prior email answer to a friend (quoting dc (a Unix tool)).
Did you know the attached puzzle?
No, & I must admit it took me a few minutes to spot
the answer. Mainly 'cos I knew it must be damn simple & I
should be spotting it pretty much instantly. I was on the
right lines when I guessed diagonals probably weren't
parallel, but instead of peering closer, or just sitting back
& thinking, I took to counting squares on X & Y,
which I guess most do. Damn I must be getting slow. :-)
Anyway the Unix based proof of the differential gradient
& visual trickery is below:
dc 200000 5 / p 40000
dc 300000 8 / p 37500
Advert
Notes
dc
A little integer arithmetic tool I think has been in every
Unix since or before 1977. It works in
"Reverse Polish" notation ( if you stack numbers &
operators (ie + - / * ) in right order, you don't need any
brackets on equations, & that cut calculator
electronics cost, or bought you a better calculator for the
same money, or an affordable calculator instead of no
calculator, back when calculators were expensive (even now
it saves space for calculator brackets keys).
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