[HN Gopher] An artist's perplexing tribute to the Pythagorean Th...
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An artist's perplexing tribute to the Pythagorean Theorem (2009)
Author : nyc111
Score : 23 points
Date : 2024-04-12 08:44 UTC (14 hours ago)
(HTM) web link (mathtourist.blogspot.com)
(TXT) w3m dump (mathtourist.blogspot.com)
| caturopath wrote:
| The 2-3-4 right triangle. What's the problem?
| scoot wrote:
| 13 != 16
| dudeinjapan wrote:
| The triangle is not right, its wrong.
| ploxiln wrote:
| (possible sarcasm detected ;)
|
| (A 2-3-4 triangle is _not_ a right triangle, no angle is 90o)
| Izkata wrote:
| 3-4-5 is a right triangle, not 2-3-4.
|
| The intent was apparently to use nuts to represent edges, but
| he put them on points instead.
|
| The artist's realization isn't even correct.
| baruz wrote:
| I believe you are responding to a joke.
| Izkata wrote:
| I figured they remembered it was three consecutive numbers,
| but misremembered which three.
| jb1991 wrote:
| I still don't get it. The image is a 3-4-5 right triangle,
| which is mathematically fine. What do you mean by "nuts" and
| "points"?
| Izkata wrote:
| The image in the article is of hazelnuts (I originally
| wrote "stones" then quickly edited it), and it's not a
| 3-4-5 triangle.
|
| 3-4-5 describes the length of each side - if you count the
| lengths of the triangle drawn in the image (the lines of
| chalk visible between the nuts on each side), it's only
| 2-3-4. To get 3-4-5 you're counting the number of nuts on
| each side, but those aren't lengths - those are the number
| of points marking the start/end of each unit length.
| jb1991 wrote:
| I see, I think you are referring to the unequal spacing
| of the nuts on each side, i.e. the side with 5 nuts has
| them closer together than the other sides.
|
| I thought there was some point being made about the use
| of nuts vs. some other arbitrary item. Why does it matter
| they are hazelnuts and not something else?
| Izkata wrote:
| It doesn't. The entirety of my comment is that they're
| representing the wrong thing.
| partdavid wrote:
| No! X--X--X 0 1 2
|
| That diagram represents a length of 2, not a length of 3,
| see? Here's three: X--X--X--X 0
| 1 2 3
|
| It's not that the hazelnuts are somehow imperfectly laid
| out or are an imperfect representation. It's wrong in
| principle, not practice (I mean it's wrong in practice
| too but every representation is).
| topherclay wrote:
| Nice example of a fencepost error.
| baerrie wrote:
| The rub is the thinking a length of 4 maps to four points when in
| reality, the points are 4,3,2,1,0, totaling 5. I feel like this
| could all be helped if in casual counting we started at zero,
| then our entire concept of where the measurements start would be
| more in line with math. I think often about these fundamental
| conflicts in how we casually think about numbers and how they are
| actually modeled in math
| scoot wrote:
| _But when he created his pattern, he found that he had three
| stones left over. Finally, it dawned upon him that the surplus
| came from counting the corners of the triangle twice.
|
| [...]
|
| Bochner welcomed the rediscovery of this "discrepancy" so many
| years after he had created the artwork. Yet he also wondered
| "about the unwillingness to assume that I already knew what they
| had just discovered (do mathematicians still think all artists
| are dumb?)._
|
| Apparently so, because he failed to understand that what was
| being commented on was not the absence of three stones (or
| wallnuts), but rather of significantly more.
| ElevenLathe wrote:
| "counting the corners of the triangle twice" is just another
| way of saying he got the math wrong. It's just a fencepost
| error. Or am I missing something?
| spacecadet wrote:
| As an artist who explores mathematics through multi-dimensional
| art and works with mathematicians, can confirm, they find us all
| dumb. But! I have genuinely intrigued a few too.
| crubier wrote:
| There are only two hard problems in computer science: Cache
| invalidation, naming things, and off-by-one errors.
| karmakaze wrote:
| This is taking _artistic license_ too far. It 's different than
| an explosion making a sound in space in a movie. It's missing the
| core point of the thing, which could easily been illustrated. Bad
| math _and_ bad art.
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